Fitting distributions with R - r
Good afternoon. I have a vector 'a' containing 16000 values. I get the descriptive statistics with the help of the following:
library(pastecs)
library(timeDate)
stat.desc(a)
skewness(a)
kurtosis(a)
Especially skewness=-0.5012, kurtosis=420.8073 (1)
Then I build a histogram of my empirical data:
hist(a, col="lightblue", breaks = 140, border="white", main="",
xlab="Value",xlim=c(-0.001,0.001))
After this I try to fit a theoretical distribution to my empirical data. I choose Variance-Gamma distribution and try to get its parameter estimates on my data:
library(VarianceGammma)
a_VG<-vgFit(a)
The parameter estimates are the following:
vgC=-11.7485, sigma=0.4446, theta=11.7193, nu=0.1186 (2)
Further, I create a sample from the Variance-Gamma distribution with the parameters from (2)
and build a histogram of created theoretical values:
VG<-rvg(length(a),vgC=-11.7485,sigma=0.4446,theta=11.7193,nu=0.1186)
hist(VG,breaks=140,col="orange",main="",xlab="Value")
Bu the second histogram differs absolutely from the first (empirical) histogram. Moreover, it is built on the basis of the parameters (2), which I got on the empirical data.
What's wrong with my code? How can I fix it?
P.S. When I type dput(a[abs(a) > 5e-4]) I get:
c(0.000801110480004752, 0.000588162271316861, 0.000555169128569233,
0.000502563410256229, 0.000854633994686438, 0.00593622112246628,
-0.000506168123513007, -0.000502909585836875, 0.000720924373137422,
0.00119141739181039, 0.000548159382141478, -0.000516511318695123,
-0.000744590777740584, 0.000595213912401249, 0.000514055190913965,
-0.000589061375421807, -0.00175392114572581, 0.000745548313668465,
-0.00075910234096277, -0.00059987613053103, 0.000583568488865538,
0.00426484136013094, 0.000610760059768012, 0.000575522836335551,
0.000823785810599276, 0.00181936036509178, -0.00073316272551871,
-0.00184238143420679, -0.000519146793923397, -0.00120324664043103,
-0.000882469414168696, -0.00148118339830283, 0.000929612782487155,
0.000565364610238817, 0.000578158613453894, 0.00060479145432879,
-0.00520576206828594, 0.000708404040882016, 0.00105224485893451,
0.000636486872540587, -0.00359655507585543, 0.000769164650506582,
0.000635701125126786, 0.000570489501935612, -0.000641260260277221,
0.000735092947873994, 0.000757195823062773, 0.000556002742616357,
-0.00207489740356159, -0.000553386431560554, 0.000511326871983186,
0.000504591469525195, -0.000749886905655472, -0.0013939718643865,
-0.000513742626250036, -0.00105021597423516, -0.00156667292147716,
0.000864563166150134, 0.00433724128055069, 0.00053855648931922,
-0.00150732363190365, 0.00052621785349416, 0.000987781100809215,
0.000560725818171903, 0.00176012436713435, -0.000594895431092368,
-0.000686229580335151, 0.00138682284509528, -0.000531964338888358,
-0.00179959148771403, 0.000574543871314503, -0.000686996216439084,
-0.000559043343629995, 0.00055881173674166, -0.000636332688477736,
-0.000623778186703561, -0.00173834148094443, -0.000567224129968125,
-0.00122578683434504, 0.00130960156515414, -0.000548203197176633,
-0.000522749285863711, -0.000820371086264871, 0.000756014225812507,
-0.000714081490558627, -0.000617600335221624, 0.000523639760748651,
-0.000578502663833191, 0.00107478825239227, 0.000612725356974764,
-0.00065509337422931, 0.000505887803587513, -0.000566716376848575,
0.000511727090058756, 0.000572807738912218, -0.000756026937699161,
0.000547948751494332, 0.000628323894238392, -0.000541350489317693,
-0.00133529454372372, -0.000590618859845904, -0.000700581963648972,
0.000735987224462775, 0.000528958898682319, 0.000838250041022448,
-0.000519084424130511, -0.00052258402856431, -0.000538130765869838,
-0.000631819887885854, 0.00054800880764283, 0.00266115500510899,
-0.000839092093771754, 0.000559253571783103, -0.000801028189803432,
-0.000608879021022801, -0.000538018076854385, -0.000689859734395171,
0.00329650346269972, 0.000765494493951024, -0.000689450477848297,
-0.000560199139975737, 0.00159082699266122, -0.00208548663121455,
-0.000598493596793759, 0.000563544422691464, 0.000626996183768824,
-0.000653166846808162, -0.000851350174739807, -0.00140687473245116,
-0.000887003220306326, -0.000765614651347946, -0.00100676206277761,
0.000724714394852555, 0.00108872127644233, -0.000678558537305918,
-0.000705087556212902, 0.000544828152248655, -0.000791700964308362,
0.000606125736727137, -0.00119335967326073, 0.00075413211796338,
0.000526038939010931, 0.00086543737231537, -0.000817788712950573,
-0.000584070926663571, 0.000619657281937691, 0.000680783312420274,
-0.000513831718574664, -0.00050972403875349, -0.00114542220685365,
-0.00070564389723593, -0.01057964950882, -0.000610357922434801,
0.000818264221596365, 0.000940825400308043, -0.000726555639413817,
-0.000591089505560305, 0.000564738888193972, -0.00068515060569041,
0.000668920238348747, -0.00110103375121717, -0.0015480433031172,
0.000663030855223568, 0.000500097431997304, -0.000600730311271391,
-0.000672397772962796, -0.000607852365856587, 0.000536711920570809,
0.000595055206488837, 0.000523123873687581, 0.000977280737528119,
0.000616410821629998, 0.000788593666889881, -0.000671642905915704,
0.000717328711735021, -0.000551853104219902, -0.000565153434708421,
-0.000802585212152707, 0.000536342062561701, 0.000682048510343591,
-0.000541902545439399, 0.000779676683974273, 0.000698841439971787,
0.000559313965908359, -0.00064986819016255, 0.000795421518319017,
0.00364973919549527, 0.000669658692276087, 0.00109045476974678,
0.000514411572742901, 0.000503832507211754, -0.000507376233564116,
0.001232871590787, 0.000561820312542594, -0.000501190337518054,
-0.000769036505996468, -0.000695537959007453, -0.000572065848166048,
-0.00167929926328192, 0.000597078186826749, 0.00710238430870014,
0.000745192112519888, -0.00116091022028009, -0.000791139281769659,
-0.00148898466632552, 0.000565144038962018, -0.000514019821833855,
-0.00148427996685285, -0.000822717245339888, -0.00062922111212238,
-0.000636011367371125, 0.00119640327632808, 0.000548455410294579,
0.000652678152560426, 0.000509244387833618, 0.000961872348987924,
0.000662064072514568, -0.00068116858054168, -0.000569930302445343,
0.00188358126928101, 0.00130560555273895, 0.000593470885775105,
0.00160093110088155, 0.000785262438315115, -0.000912313442922752,
0.000609996052359563, 0.000720137994393966, 0.000568163899000496,
0.00128685533068307, -0.000756787473447318, 0.000765932134255465,
0.00064884753100003, 0.000687571386270847, -0.000582094290400903,
-0.000693177295971736, -0.000601776208094762, 0.000503616387996786,
-0.000615095866544735, -0.000799593899689199, 0.000773750859128342,
-0.000522576090260074, 0.000503578107212022, -0.00104492224837571,
0.000547928732299141, 0.00310304337507183, 0.000893382870797765,
-0.000577792878910799, -0.000647710366578735, -0.00061992948706191,
0.000825702487162516, 0.000606579510524341, 0.000552792484727505,
0.000688600840895504, 0.000505093563534231, -0.000728420573667066,
-0.00157924525963438, -0.000603846616019865, -0.000521941317177976,
0.00150498158245682, -0.000584572670337735, 0.000713757870583365,
0.000524287801789924, 0.00107217649464886, 0.00213147531822244,
0.000566012832157625, -0.00069828890607937, 0.000641567963736378,
-0.000509531713644762, -0.000547564140049417, -0.00115275240244728,
0.000560465768010943, -0.000651807371497171, -0.00096487058986483,
0.000753687665266511, -0.000665599418910645, -0.000691278087025182,
-0.000578010050725553, -0.000685833148198256, 0.000698470819832764,
0.00102943368139208, -0.000725840586788706, 0.00125882415960632,
-0.000630791474954151, -0.000764813558678412, -0.000638539347184164,
0.000654486496518558, 0.000547453642294471, 0.000572020020495501,
-0.000605791001705214, 0.00660211658324172, 0.00114928683282756,
0.000985676480677711, -0.000694668292547718, -0.000528955637964401,
0.000647975568638159, 0.00116454536417443, 0.000506748841724303,
-0.000500925156604382, -0.000567015088082101, 0.00128711230206946,
0.000533633762033858, 0.00505991432758357, 0.000518058378462527,
-0.000592822519784875, 0.00177414999018666, 0.00059845426944527,
-0.000511614433724716, 0.0016614697907098, 0.000852196464322219,
0.00241689725305427, -0.000614317948913978, -0.000729717143318709,
-0.000612900648802039, -0.000727983564232204, -0.000694965869158182,
-0.000527752006066251, -0.000584233784708843, 0.000522097476268968,
0.000543092880677776, 0.000947121210698398, -0.00241810275096377,
0.00181893137435019, 0.000931873879297385, 0.000512116215015013,
0.000724985702444059, -0.000566713495050664, 0.000603953591362227
)
After fitting the data look like the following (empirical histogram-blue, theoretical histogram-orange):
The same when include freq=FALSE in hist
This will all be due to anomalous values in a not represented by the histogram you've shown. This could be the cause of both the very high kurtotsis, and the vgFit() algorithm failing to find a good fit.
Type dput(a[abs(a) > 5e-4]) in the console and copy the output into your question. People then may be able to recreate aomething like the vector a without having to get all 16000 values and debug the vgFit issue.
Thanks for the extra data. There are some extreme values in there, but I don;t think those are what is causing the problem in vgFit. Fitting 4 parameters which can be almost any value is difficult, but you can help it along by rescaling your data to something typical. Try this:
b <- (a-mean(a))/sd(a)
vgf <- vgFit(b)
vgf$param
VG <- rvg(16000, param = vgf$param)
VG_rescaled <- VG*sd(a)+mean(a)
hist(VG_rescaled, breaks=140, col="orange", main="", xlab="Value")
and see if the two histograms are close enough now.
Related
Spatial analysis with R package spatstat, sidebar does not show correct values
I'm trying to create a map with the spatstat package of R so that the sidebar shows the values of the third (preferably) or fourth column of my data frame and that the colors are also reflective of that third (or fourth column) chosen. My script: x=c(6.839887, 6.671494, 6.651083, 6.655289, 6.591903, 6.653641, 6.661709, 6.671664, 6.660044, 6.624659, 6.648162, 6.536877, 6.654134, 6.674678,6.618935, 6.677705, 6.643918, 6.644119, 6.670517, 6.583619, 6.649991, 6.647649, 6.656308, 6.645772, 6.648740, 6.643103, 6.652199, 6.666641,6.633400, 6.621282, 6.635427, 6.646127, 6.630862, 6.657919, 6.671616, 6.622935, 6.648225, 6.676911, 6.640234, 6.719334, 6.653202, 6.656747,6.724692, 6.639747, 6.630575, 6.657916, 6.618957, 6.640006, 6.645280, 6.614058, 6.576136, 6.631994, 6.617391, 6.782351, 6.620072, 6.661061,6.597216, 6.648755, 6.618436, 6.659507, 6.653993, 6.663255, 6.630893, 6.656322, 6.617265, 6.649022, 6.629346, 6.595224, 6.540263, 6.623435,6.652709, 6.608565, 6.618335, 6.645100, 6.790914, 6.643620, 6.462808, 6.680115, 6.716004, 6.668781, 6.765199, 6.674251, 6.647542, 6.724564,6.724556) y=c(17.16749, 17.16727, 17.16678, 17.16673, 17.16813, 17.16663, 17.16652, 17.16636, 17.16629, 17.16856, 17.16521, 17.16519, 17.17002, 17.16465,17.17015, 17.16407, 17.16356, 17.17122, 17.16334, 17.17152, 17.16282, 17.16278, 17.16272, 17.17257, 17.16198, 17.17279, 17.16169, 17.16161,17.16146, 17.17352, 17.17389, 17.16076, 17.17420, 17.16046, 17.15917, 17.17571, 17.15895, 17.15881, 17.15860, 17.15827, 17.15797, 17.15776,17.17761, 17.15664, 17.15622, 17.15610, 17.15571, 17.15561, 17.15527,17.15514, 17.15494, 17.15447, 17.15438, 17.18041, 17.18053, 17.15402,17.18090, 17.15384, 17.18121, 17.15355, 17.15352, 17.15349, 17.18213,17.15242, 17.15201, 17.14978, 17.18591, 17.18688, 17.18707, 17.18761,17.14712, 17.18788, 17.18794, 17.14619, 17.18868, 17.14588, 17.14511,17.14471, 17.14440, 17.14430, 17.19116, 17.19140, 17.14222, 17.14123,17.33627) z=c(32.23228,526.46061, -1300.03539, -376.04329, 139.67322,-913.24800, -526.46061, 354.55511, 483.48424, 161.16141, 182.64960, 419.0196, 75.20866, -225.62598, -1536.40546, -397.53148, -1106.64169, -440.50786, 118.18504,-290.09054, -1471.94089, 440.50786,-848.78343, -1385.98814, -676.87793, -1622.35821, -1450.45271,75.20866, -1557.89365, 161.16141, 376.04329, 354.55511, -32.23228,-1171.10626,-75.20866, 547.94880, -805.80706, 870.27162, -698.36612,-32.23228, -2331.46842, -182.64960, 75.20866, -719.85431,-1837.24009,913.24800, -1106.64169, 698.36612, 483.48424, -676.87793, -3019.09045, 891.75981, 1106.64169, 333.06692, -913.24800,333.06692, 934.73619, 354.55511, 75.20866, -891.75981, -247.11416, -1966.16922, 139.67322, -784.31887, -569.43699, -118.18504,-440.50786, 397.53148, -655.38974, 139.67322, 53.72047, -633.90155,-633.90155, 419.01967, -547.94880, 75.20866, 569.43699, 290.09054, -376.04329, 547.94880, 75.20866, -10.74409, 182.64960,-397.53148, -479.53833 ) w=c(96326.91, 96769.46, 95127.94, 95960.41, 96423.22, 95476.93, 95825.18,96615.67, 96731.03, 96442.47, 96461.73, 96673.36, 96365.44, 96095.53,94914.31, 95941.10, 95302.53, 95902.47, 96403.96, 96037.64, 94972.60,96692.58, 95535.03, 95050.29, 95689.84, 94836.56, 94992.03, 96365.44,94894.87, 96442.47, 96634.90, 96615.67, 96269.09, 95244.36, 96230.54,96788.68, 95573.74, 97076.62, 95670.50, 96269.09, 94193.69, 96134.12,96365.44, 95651.15, 94642.01, 97114.98, 95302.53, 96923.12, 96731.03,95689.84, 93567.91, 97095.80, 97287.46, 96596.43, 95476.93, 96596.43,97134.15, 96615.67, 96365.44, 95496.30, 96076.24, 94525.17, 96423.22,95593.10, 95786.52, 96191.98, 95902.47, 96654.13, 95709.18, 96423.22,96346.17, 95728.52, 95728.52, 96673.36, 95805.85, 96365.44, 96807.89,96557.96, 95960.41, 96788.68, 96365.44, 96288.37, 96461.73,95941.10, 99451.20) shap.lo=data.frame(x,y,z,w) library(spatstat) shap.lo.win <- owin(range(shap.lo[,1]), range(shap.lo[,2])) centroid.owin(shap.lo.win) ; area.owin(shap.lo.win) shap.lo.ppp <- as.ppp(shap.lo[,c(1,2,3)], shap.lo.win) # making a ppp object plot(density(shap.lo.ppp,0.02), col=topo.colors(25), main='', xlab='x', ylab='y') points(x, y) the result is shown below I would like to know why the sidebar shows different values than the ones shown in the third column of my data frame, that is, in addition to displaying no negative values, shows values much larger than those contained in the third column. Is it possible to do this, that is, make the colors and the sidebar represent the third or fourth column of the data frame? I thank the help of all you!
Let me quote directly from the help file for density.ppp: This function is often misunderstood. The result of density.ppp is not a spatial smoothing of the marks or weights attached to the point pattern. To perform spatial interpolation of values that were observed at the points of a point pattern, use Smooth.ppp. The result of density.ppp is not a probability density. It is an estimate of the intensity function of the point process that generated the point pattern data. Intensity is the expected number of random points per unit area. The units of intensity are “points per unit area”. Intensity is usually a function of spatial location, and it is this function which is estimated by density.ppp. The integral of the intensity function over a spatial region gives the expected number of points falling in this region. So try Smooth.ppp (note the upper case S), and see if you can make that produce the results you expected.
Bootstrap p value contradicts p value for likelihood ratio test
I have the same problem as the one posted by #soapsuds here. I did not want to ask a duplicate question but when I tried to edit the original question to provide the reproducible example that was missing in the original post my edits got rejected. Since the reproducible example has a lot of elements, I could not write it as a comment to the original question either, so I provide my code and my reproducible data here, as a separate question.
I am trying to compare two models using the likelihood ratio test. From bootstrapping I get a set of 1000 p-values. Here are the numbers I get:
chi2 <- c(41.83803376, 69.23970174, 42.5479637, 50.90208302, 39.18366824, 78.88589665, 28.88469406, 34.99980796, 85.80860848, 66.01750186, 29.06286, 46.43221576, 46.50523792, 59.87362884, 46.17274808, 77.97429928, 48.04404216, 12.88592623, 43.1883816, 33.24251471, 53.27310465, 56.92595147, 47.99838583, 46.0718587, 49.0760042, 29.70866297, 66.80696553, 66.61091741, 37.82375112, 50.19760846, 30.99961864, 27.17687828, 37.46944206, 66.36226432, 48.30737714, 43.64410333, 23.78480451, 42.52842793, 60.49309556, 46.29154, 26.96744296, 32.21561396, 48.20316788, 38.73153704, 67.80328765, 55.00664931, 36.74645735, 23.3647159, 56.35290442, 38.11055268, 58.3316501, 36.00500638, 41.36949956, 49.09067881, 64.42712507, 23.97787069, 54.5394799, 87.02114296, 26.01402166, 50.47426712, 38.58006084, 48.47626864, 22.28809699, 58.87590487, 17.59264288, 33.32650413, 67.77868338, 60.95427815, 37.19931376, 36.23280256, 53.54379697, 70.06479334, 41.3482703, 34.54099647, 55.99585144, 30.60500406, 32.02745276, 37.92670127, 44.23450124, 40.38607671, 44.02263294, 40.89874789, 62.74174279, 50.95137406, 47.12851204, 26.03848394, 36.6202765, 61.06296311, 50.17094183, 35.93242228, 41.8913277, 35.19089913, 38.88574534, 66.075866, 26.34296242, 49.99887059, 42.97123036, 34.89006324, 66.5460019, 67.61855859, 48.52166614, 41.41324193, 46.76294302, 14.87650733, 24.11661382, 62.28747719, 43.94865019, 44.20328393, 41.17756328, 43.74055584, 49.46236395, 38.59558107, 42.85073398, 49.81046036, 36.60331917, 39.85328124, 59.31376822, 61.36038822, 52.56707689, 29.19196892, 46.473958, 39.12904163, 38.75057931, 36.32493909, 49.61088785, 33.42904297, 34.73661836, 33.97736002, 37.44094284, 57.73605417, 43.14773064, 42.78707831, 26.84112684, 48.47832871, 45.94043053, 71.13563773, 46.28614795, 42.33386157, 59.31216832, 46.72946806, 47.76027545, 52.45174304, 49.99459367, 59.00971014, 24.03299408, 17.09453132, 37.44112252, 46.6352525, 60.42442286, 39.35194465, 46.57121135, 56.28622077, 59.20354176, 57.72511864, 41.97053375, 27.97077407, 29.70497125, 46.63976021, 40.24305901, 24.84335714, 36.08600444, 61.619572, 69.31377401, 86.91496878, 44.47955842, 44.1230351, 46.12514671, 43.97381958, 71.99269072, 47.01277643, 50.08167664, 27.01076954, 31.32586466, 40.96782215, 19.07024825, 53.00009679, 43.15397869, 42.49652848, 53.47325607, 43.45891027, 42.57719313, 39.40459925, 42.15077856, 52.23784844, 33.07947933, 45.02462309, 59.187763, 51.9198527, 48.3179841, 76.10501177, 34.95091433, 40.75545034, 31.27034043, 39.83209227, 47.87278051, 46.25057806, 62.84591205, 41.24656655, 68.14749236, 53.11576938, 39.20515676, 61.96116013, 35.64665684, 72.52689101, 54.64239536, 34.14169048, 34.32282338, 49.60786171, 50.32976034, 43.83560386, 57.49367366, 81.65759842, 61.59398941, 37.77960776, 30.74484476, 34.72859511, 32.46631033, 37.41725027, 34.04569722, 54.11932007, 34.62264522, 28.36753913, 30.95379445, 84.06354755, 29.32445434, 56.7720931, 33.23951864, 48.61860157, 39.3563214, 32.44713462, 61.25078174, 32.49661836, 40.38508488, 26.73565294, 58.16191656, 61.12461262, 23.701462, 22.14004554, 57.80213129, 57.15936762, 31.51238062, 44.60223083, 30.60135802, 46.96637333, 42.79517081, 56.85541543, 48.79421654, 29.72862307, 41.61735121, 43.37983393, 41.16802781, 61.69637392, 37.29991153, 39.0936012, 57.39158494, 57.55033901, 50.72878897, 34.82491685, 42.66486539, 34.54565803, 55.04161695, 44.56687339, 53.46745359, 57.22210412, 34.8578696, 28.81098073, 51.4033337, 51.9568532, 60.98717632, 62.98817996, 44.1335128, 33.38418814, 59.71059054, 45.82016411, 29.47178401, 30.64995791, 28.52106318, 53.98066153, 64.22209517, 58.29438562, 39.18280924, 38.1302144, 41.90062316, 28.68650929, 69.42769639, 33.79539164, 26.08549507, 55.29167497, 97.25975259, 63.07957724, 56.59002373, 51.40088678, 71.33491023, 46.24955174, 33.90101761, 38.0669817, 52.50993176, 51.84637529, 39.93642798, 61.9268346, 30.25561485, 49.57396856, 44.70170977, 57.00286149, 40.39009586, 63.23642634, 59.23643766, 55.80521902, 68.58421775, 24.04456631, 51.64338572, 61.14103174, 59.29371792, 46.51493959, 43.48297587, 39.99164284, 44.62589755, 58.89385062, 60.96824416, 54.02310453, 43.54420281, 44.24628098, 47.0991445, 58.9015349, 60.54157696, 34.86277089, 33.79969585, 34.57183642, 47.21383117, 55.3529805, 36.49813553, 44.94388291, 29.43134497, 43.41469037, 43.033338, 63.37329389, 38.22029171, 43.2894392, 23.42769168, 55.18117532, 19.39227876, 28.29656641, 28.56075122, 39.57260362, 65.48606054, 31.05339648, 24.87488959, 61.6027878, 59.56983406, 37.53918879, 28.67095839, 36.51499868, 44.43350204, 53.35842664, 48.30182354, 31.03494822, 45.68689659, 46.11113306, 53.89204524, 29.75548276, 35.60906482, 53.35195594, 56.28657675, 44.77245145, 60.20671942, 41.62253735, 40.34528594, 38.48551456, 27.39317425, 51.05414332, 38.41986986, 75.05074423, 34.16773046, 52.18497954, 49.63059496, 28.7365636, 10.59466471, 38.1033901, 52.20531405, 47.031987, 47.45955635, 44.64312012, 50.32229588, 62.40798968, 37.7455721, 31.97746406, 51.17250147, 45.91231295, 66.58450378, 32.68956686, 34.35845347, 70.34703042, 41.47493453, 53.67684859, 35.66735299, 19.76630329, 35.69026569, 76.57475236, 62.11269107, 37.06632602, 57.91686258, 33.95869501, 55.18034702, 66.09725866, 46.80608564, 46.75623531, 55.49605214, 45.7813294, 22.37612777, 62.40414132, 50.51745906, 46.86535062, 54.4172637, 35.44713601, 45.40918234, 43.83215257, 57.14754799, 24.20941074, 44.8145542, 50.79673435, 42.14561269, 32.73720673, 28.51047028, 32.14753623, 28.43006627, 39.50188334, 58.51806717, 37.96898151, 73.14656287, 48.23605238, 75.31273481, 29.57608972, 43.62952257, 30.47534709, 43.24927262, 43.61475563, 53.48883918, 53.85263136, 41.91477406, 56.16405384, 46.21202327, 55.52602904, 49.88481191, 46.31478116, 72.29722834, 40.48187205, 35.31368051, 40.57713079, 34.15725967, 65.85738596, 32.16093944, 32.07117679, 46.44579516, 53.3243447, 69.35531671, 21.70205174, 44.30678622, 40.13349937, 51.7431728, 43.03690121, 26.53566586, 18.74773427, 25.97768442, 66.68668827, 42.97352559, 31.61567696, 61.57362103, 55.07104736, 25.05950764, 53.04884067, 30.47176616, 43.33249885, 44.48360752, 40.59006165, 44.29759954, 69.71063388, 47.70186943, 51.12166943, 40.15048072, 44.96459746, 56.31842906, 57.79593771, 49.19795057, 33.58506451, 42.67650993, 47.96512915, 57.98722437, 42.08107371, 66.85903821, 45.30286487, 38.39187118, 48.02442004, 35.97047743, 56.71378254, 40.51082047, 43.78022461, 60.33208664, 35.78159098, 40.98937317, 36.20547787, 45.2382906, 47.81497885, 20.44519563, 16.68817267, 38.31035896, 38.60590267, 70.75756511, 31.73001452, 45.85476281, 47.11473565, 31.40248172, 42.94971714, 39.34376633, 21.09018956, 31.45915941, 53.82696054, 73.59824534, 31.5694168, 39.02189966, 46.91790827, 60.66603832, 59.81148782, 20.46813743, 54.95108785, 66.71844123, 49.48461319, 25.10459028, 60.26169536, 21.90344297, 63.56310687, 38.70295559, 58.19794152, 25.68981924, 61.4804908, 41.97067608, 22.77156359, 48.51789441, 50.31845297, 42.36456456, 43.35814281, 41.32891651, 35.17106573, 48.45296117, 30.55292595, 55.26758567, 71.25929921, 34.62580089, 43.89804598, 46.06384675, 30.74209253, 47.99143497, 34.02715801, 37.95367551, 45.14366438, 40.73655716, 45.32116105, 48.17651965, 63.54774876, 16.32237452, 54.22730144, 46.02331286, 45.44633826, 53.56976595, 53.96781286, 19.79116777, 42.05820938, 45.48852278, 37.34932167, 45.134461, 49.60637239, 29.99017683, 35.2785614, 71.54855053, 61.55744768, 55.7627296, 37.72455372, 62.51288842, 48.17063649, 65.26648616, 48.4831201, 33.49833137, 32.10986243, 15.42586026, 41.95660905, 30.07072484, 42.33604863, 53.20660203, 48.27036556, 32.92677161, 33.59521848, 44.04333058, 59.30038922, 48.84064622, 63.31815488, 36.01169023, 44.42967033, 23.14247159, 53.6314237, 42.43225997, 28.18151375, 44.0733306, 55.93530003, 30.86515779, 34.10702034, 59.38495522, 57.79906004, 64.86160093, 56.70670687, 43.24880707, 40.00049219, 44.08430336, 17.50391283, 72.81320114, 41.55481964, 63.461066, 50.81938548, 58.7427594, 35.27822458, 33.5188344, 46.13196979, 56.94022883, 66.96258461, 39.19601268, 21.95750575, 51.67252792, 46.51047909, 30.42289547, 46.47496475, 41.6440483, 42.36900563, 68.29398345, 30.14059255, 38.90124252, 40.87014585, 51.33635945, 51.72908337, 50.8177621, 31.65411733, 56.75197699, 47.76885318, 34.18305356, 52.52137441, 48.39806899, 18.34609209, 32.5461584, 60.15104883, 36.29250847, 39.02418361, 34.68801402, 48.02453889, 31.36738248, 42.44522981, 71.79176852, 34.25588794, 38.46866138, 45.01393624, 63.38509325, 32.44823195, 64.59346474, 53.80793998, 41.2889141, 28.86534461, 34.85039051, 37.04622686, 31.83207726, 36.65410743, 27.66293315, 23.11203257, 41.61059067, 19.97321534, 59.879676, 39.84187157, 47.324581, 38.24903991, 41.0234849, 62.30809429, 48.47191326, 23.26696808, 29.91547934, 78.39181209, 41.86240014, 33.53717515, 39.63756903, 74.86377649, 56.30173648, 40.29403413, 59.12602764, 47.23561802, 51.32370456, 45.44426051, 55.54666292, 58.85362888, 38.30516953, 46.11300177, 37.96931091, 41.01315149, 63.09345867, 26.74145771, 31.37447907, 39.26896396, 65.35880308, 60.0670218, 45.48057201, 29.76683425, 51.39638136, 46.12180705, 60.72093818, 45.01613513, 37.04611291, 31.32979098, 57.82548455, 29.89919764, 38.77980495, 55.71511912, 66.9872235, 48.74616069, 32.87503301, 56.10335632, 28.72445387, 41.00675821, 55.22238115, 38.56391412, 21.82487917, 51.87394855, 41.62740713, 72.32943223, 49.85456187, 41.76869194, 55.686196, 46.18471338, 52.57455653, 23.03383172, 51.460223, 45.88045256, 47.91709836, 53.09464847, 65.17159616, 48.0076358, 42.50038253, 50.57143193, 22.05776575, 25.5770314, 57.41889173, 37.07408252, 69.83286794, 53.31690771, 36.14562381, 35.3626014, 70.74448842, 30.01870438, 41.95755074, 64.41141845, 48.12704663, 29.33183678, 47.45391445, 35.76760392, 17.57864013, 42.66918162, 27.84884911, 37.83419437, 56.38203205, 32.93395446, 19.45549279, 48.49557175, 63.74692618, 48.36501421, 38.45370018, 63.77499738, 43.40984685, 61.28735474, 47.00513455, 31.82012086, 40.85624032, 32.79590137, 43.79441893, 47.93350586, 26.44410209, 22.71480768, 41.74097624, 29.7828174, 35.24077319, 37.1436077, 63.62150539, 35.27952907, 30.9258966, 35.22384343, 45.0069715, 47.38652625, 60.86474384, 53.19528479, 37.61239521, 64.78497877, 39.50008676, 43.11733875, 34.67761458, 55.21401193, 57.22836509, 30.10411603, 30.03903287, 53.62027996, 40.63516283, 50.229386, 39.59707517, 55.53993024, 62.31160356, 48.65142538, 59.51279601, 51.46268896, 36.70086545, 45.73324953, 39.82026282, 51.51657943, 39.9507342, 26.65847555, 18.11032673, 41.57393548, 37.24804734, 59.78878572, 42.18870686, 57.73556775, 29.83442692, 24.27687775, 44.54663257, 48.40426261, 34.13830576, 64.47843419, 53.82888778, 45.77073351, 41.95910655, 56.25654343, 42.44938602, 18.92651056, 62.89841562, 42.28210051, 60.01632343, 56.38799965, 53.56842386, 71.059581, 59.21196097, 72.29678294, 40.0820475, 74.53163756, 46.35508897, 48.65592196, 36.69711286, 54.84914739, 57.62299813, 63.0750109, 25.53592874, 19.43203054, 63.18532427, 54.79806194, 28.75123602, 47.68037559, 36.06887062, 48.53619627, 42.05208952, 14.47366507, 26.25183654, 57.37741978, 24.92962789, 47.85306044, 35.55674275, 43.62606531, 51.98445971, 57.10441923, 45.20539557, 43.22417529, 48.20941756, 37.12416781, 39.54238987, 45.31000358, 24.59001204, 32.61256929, 31.61553515, 55.76617515, 57.82479513, 34.12465645, 52.1634834, 50.140277, 34.5334757, 70.76112738, 47.22161503, 35.44101995, 54.50312705, 47.74706989, 21.04494842, 42.42698916, 57.8551517, 49.67127478, 67.6702045, 30.64335682, 31.87819093, 45.79096976, 42.72129981, 56.22043416, 22.12571532, 31.93377902, 31.9561172, 60.28281847, 37.49005649, 30.63141229, 22.82707918, 29.55804713, 55.79929136, 39.64043613, 31.79538118, 61.92391469, 19.30462724, 37.00041938, 61.26446455, 47.10048686, 34.70929308, 33.34157984, 49.28331646, 39.9565451, 48.80158593, 29.25279435, 49.96980394, 68.7766356, 49.61949286, 18.80600378, 52.93721773, 24.29791779, 67.69568275, 54.22725318, 35.67531845, 58.05037476, 70.54029077, 55.59508174, 42.07974012, 61.62117032, 44.47174079, 40.13197612, 61.19863058, 35.16748823, 54.79320966, 46.40640448, 41.99222891, 53.33216862, 19.04146695, 29.60278169, 38.43089591, 61.22497978, 32.04678119, 30.77915985, 38.02625789, 74.25140223, 30.44626923, 42.69951906, 28.99988779, 49.76041564, 30.86941271, 58.65788956, 62.64967161, 23.5689175, 42.21941421, 54.88455829, 38.10115824, 24.12341961, 32.84464782, 81.72102673, 42.42771851, 37.75191241, 32.05927543, 43.55812503, 64.79161154, 61.05179286, 53.24693267, 36.29056269, 61.49030629, 53.68500702, 65.93501988, 50.7243041, 51.72139759, 64.80610623, 58.2860023, 33.16444766, 42.7872046, 55.14190562, 39.14341079, 36.05577261, 30.03351742, 24.16526837, 47.94163599, 52.55045103, 56.60625705, 61.6878126, 23.13212844, 50.50369148, 47.79873905, 47.01238239, 35.9159739, 53.18067189, 48.42928497, 67.48879213, 37.37609292, 19.7749038, 47.87115046, 48.90378974)
p.values <- c(9.92E-11, 8.72E-17, 6.90E-11, 9.71E-13, 3.86E-10, 6.58E-19, 7.68E-08, 3.30E-09, 1.98E-20, 4.47E-16, 7.01E-08, 9.48E-12, 9.14E-12, 1.01E-14, 1.08E-11, 1.04E-18, 4.17E-12, 0.000331062, 4.97E-11, 8.14E-09, 2.90E-13, 4.53E-14, 4.27E-12, 1.14E-11, 2.46E-12, 5.02E-08, 2.99E-16, 3.31E-16, 7.74E-10, 1.39E-12, 2.58E-08, 1.86E-07, 9.29E-10, 3.75E-16, 3.64E-12, 3.94E-11, 1.08E-06, 6.97E-11, 7.38E-15, 1.02E-11, 2.07E-07, 1.38E-08, 3.84E-12, 4.86E-10, 1.81E-16, 1.20E-13, 1.35E-09, 1.34E-06, 6.06E-14, 6.68E-10, 2.21E-14, 1.97E-09, 1.26E-10, 2.44E-12, 1.00E-15, 9.74E-07, 1.52E-13, 1.07E-20, 3.39E-07, 1.21E-12, 5.26E-10, 3.34E-12, 2.35E-06, 1.68E-14, 2.74E-05, 7.79E-09, 1.83E-16, 5.84E-15, 1.07E-09, 1.75E-09, 2.53E-13, 5.74E-17, 1.27E-10, 4.17E-09, 7.26E-14, 3.16E-08, 1.52E-08, 7.35E-10, 2.91E-11, 2.08E-10, 3.25E-11, 1.60E-10, 2.36E-15, 9.47E-13, 6.65E-12, 3.35E-07, 1.44E-09, 5.53E-15, 1.41E-12, 2.04E-09, 9.65E-11, 2.99E-09, 4.49E-10, 4.34E-16, 2.86E-07, 1.54E-12, 5.56E-11, 3.49E-09, 3.42E-16, 1.98E-16, 3.27E-12, 1.23E-10, 8.01E-12, 0.000114784, 9.07E-07, 2.97E-15, 3.37E-11, 2.96E-11, 1.39E-10, 3.75E-11, 2.02E-12, 5.21E-10, 5.91E-11, 1.69E-12, 1.45E-09, 2.74E-10, 1.34E-14, 4.75E-15, 4.16E-13, 6.56E-08, 9.28E-12, 3.97E-10, 4.82E-10, 1.67E-09, 1.87E-12, 7.39E-09, 3.77E-09, 5.58E-09, 9.42E-10, 3.00E-14, 5.08E-11, 6.10E-11, 2.21E-07, 3.34E-12, 1.22E-11, 3.33E-17, 1.02E-11, 7.69E-11, 1.35E-14, 8.15E-12, 4.82E-12, 4.41E-13, 1.54E-12, 1.57E-14, 9.47E-07, 3.56E-05, 9.42E-10, 8.55E-12, 7.65E-15, 3.54E-10, 8.83E-12, 6.27E-14, 1.42E-14, 3.01E-14, 9.27E-11, 1.23E-07, 5.03E-08, 8.53E-12, 2.24E-10, 6.22E-07, 1.89E-09, 4.17E-15, 8.40E-17, 1.13E-20, 2.57E-11, 3.08E-11, 1.11E-11, 3.33E-11, 2.16E-17, 7.05E-12, 1.47E-12, 2.02E-07, 2.18E-08, 1.55E-10, 1.26E-05, 3.34E-13, 5.06E-11, 7.08E-11, 2.62E-13, 4.33E-11, 6.79E-11, 3.44E-10, 8.45E-11, 4.92E-13, 8.85E-09, 1.95E-11, 1.43E-14, 5.78E-13, 3.62E-12, 2.69E-18, 3.38E-09, 1.73E-10, 2.24E-08, 2.77E-10, 4.55E-12, 1.04E-11, 2.24E-15, 1.34E-10, 1.52E-16, 3.14E-13, 3.82E-10, 3.50E-15, 2.37E-09, 1.65E-17, 1.45E-13, 5.12E-09, 4.67E-09, 1.88E-12, 1.30E-12, 3.57E-11, 3.39E-14, 1.62E-19, 4.22E-15, 7.92E-10, 2.94E-08, 3.79E-09, 1.21E-08, 9.54E-10, 5.38E-09, 1.89E-13, 4.00E-09, 1.00E-07, 2.64E-08, 4.79E-20, 6.12E-08, 4.89E-14, 8.15E-09, 3.11E-12, 3.53E-10, 1.22E-08, 5.02E-15, 1.19E-08, 2.09E-10, 2.33E-07, 2.41E-14, 5.36E-15, 1.12E-06, 2.53E-06, 2.90E-14, 4.02E-14, 1.98E-08, 2.41E-11, 3.17E-08, 7.22E-12, 6.08E-11, 4.69E-14, 2.84E-12, 4.97E-08, 1.11E-10, 4.51E-11, 1.40E-10, 4.01E-15, 1.01E-09, 4.04E-10, 3.57E-14, 3.29E-14, 1.06E-12, 3.61E-09, 6.50E-11, 4.16E-09, 1.18E-13, 2.46E-11, 2.63E-13, 3.89E-14, 3.55E-09, 7.98E-08, 7.52E-13, 5.67E-13, 5.74E-15, 2.08E-15, 3.07E-11, 7.56E-09, 1.10E-14, 1.30E-11, 5.67E-08, 3.09E-08, 9.27E-08, 2.02E-13, 1.11E-15, 2.26E-14, 3.86E-10, 6.62E-10, 9.60E-11, 8.51E-08, 7.93E-17, 6.12E-09, 3.27E-07, 1.04E-13, 6.08E-23, 1.99E-15, 5.37E-14, 7.53E-13, 3.01E-17, 1.04E-11, 5.80E-09, 6.84E-10, 4.28E-13, 6.00E-13, 2.62E-10, 3.56E-15, 3.79E-08, 1.91E-12, 2.29E-11, 4.35E-14, 2.08E-10, 1.83E-15, 1.40E-14, 8.00E-14, 1.22E-16, 9.41E-07, 6.66E-13, 5.31E-15, 1.36E-14, 9.09E-12, 4.28E-11, 2.55E-10, 2.39E-11, 1.66E-14, 5.80E-15, 1.98E-13, 4.14E-11, 2.90E-11, 6.75E-12, 1.66E-14, 7.20E-15, 3.54E-09, 6.11E-09, 4.11E-09, 6.36E-12, 1.01E-13, 1.53E-09, 2.03E-11, 5.79E-08, 4.43E-11, 5.38E-11, 1.71E-15, 6.32E-10, 4.72E-11, 1.30E-06, 1.10E-13, 1.06E-05, 1.04E-07, 9.08E-08, 3.16E-10, 5.85E-16, 2.51E-08, 6.12E-07, 4.20E-15, 1.18E-14, 8.96E-10, 8.58E-08, 1.51E-09, 2.63E-11, 2.78E-13, 3.65E-12, 2.53E-08, 1.39E-11, 1.12E-11, 2.12E-13, 4.90E-08, 2.41E-09, 2.79E-13, 6.26E-14, 2.21E-11, 8.54E-15, 1.11E-10, 2.13E-10, 5.52E-10, 1.66E-07, 8.99E-13, 5.70E-10, 4.59E-18, 5.06E-09, 5.05E-13, 1.86E-12, 8.29E-08, 0.001134145, 6.71E-10, 5.00E-13, 6.98E-12, 5.62E-12, 2.36E-11, 1.30E-12, 2.79E-15, 8.06E-10, 1.56E-08, 8.46E-13, 1.24E-11, 3.35E-16, 1.08E-08, 4.58E-09, 4.97E-17, 1.19E-10, 2.36E-13, 2.34E-09, 8.75E-06, 2.31E-09, 2.12E-18, 3.24E-15, 1.14E-09, 2.73E-14, 5.63E-09, 1.10E-13, 4.29E-16, 7.84E-12, 8.04E-12, 9.36E-14, 1.32E-11, 2.24E-06, 2.80E-15, 1.18E-12, 7.60E-12, 1.62E-13, 2.62E-09, 1.60E-11, 3.58E-11, 4.04E-14, 8.64E-07, 2.17E-11, 1.02E-12, 8.47E-11, 1.05E-08, 9.32E-08, 1.43E-08, 9.71E-08, 3.28E-10, 2.01E-14, 7.19E-10, 1.20E-17, 3.78E-12, 4.02E-18, 5.38E-08, 3.97E-11, 3.38E-08, 4.82E-11, 4.00E-11, 2.60E-13, 2.16E-13, 9.53E-11, 6.67E-14, 1.06E-11, 9.22E-14, 1.63E-12, 1.01E-11, 1.85E-17, 1.98E-10, 2.81E-09, 1.89E-10, 5.08E-09, 4.85E-16, 1.42E-08, 1.49E-08, 9.42E-12, 2.83E-13, 8.22E-17, 3.18E-06, 2.81E-11, 2.37E-10, 6.33E-13, 5.37E-11, 2.59E-07, 1.49E-05, 3.45E-07, 3.18E-16, 5.55E-11, 1.88E-08, 4.26E-15, 1.16E-13, 5.56E-07, 3.25E-13, 3.39E-08, 4.62E-11, 2.56E-11, 1.88E-10, 2.82E-11, 6.87E-17, 4.96E-12, 8.68E-13, 2.35E-10, 2.01E-11, 6.16E-14, 2.91E-14, 2.31E-12, 6.82E-09, 6.46E-11, 4.34E-12, 2.64E-14, 8.76E-11, 2.92E-16, 1.69E-11, 5.79E-10, 4.21E-12, 2.00E-09, 5.04E-14, 1.96E-10, 3.67E-11, 8.01E-15, 2.21E-09, 1.53E-10, 1.78E-09, 1.74E-11, 4.68E-12, 6.14E-06, 4.41E-05, 6.03E-10, 5.19E-10, 4.04E-17, 1.77E-08, 1.27E-11, 6.70E-12, 2.10E-08, 5.62E-11, 3.55E-10, 4.38E-06, 2.04E-08, 2.19E-13, 9.57E-18, 1.92E-08, 4.19E-10, 7.40E-12, 6.76E-15, 1.04E-14, 6.06E-06, 1.24E-13, 3.13E-16, 2.00E-12, 5.43E-07, 8.30E-15, 2.87E-06, 1.55E-15, 4.93E-10, 2.37E-14, 4.01E-07, 4.47E-15, 9.27E-11, 1.82E-06, 3.27E-12, 1.31E-12, 7.58E-11, 4.56E-11, 1.29E-10, 3.02E-09, 3.38E-12, 3.25E-08, 1.05E-13, 3.13E-17, 4.00E-09, 3.46E-11, 1.14E-11, 2.95E-08, 4.28E-12, 5.43E-09, 7.24E-10, 1.83E-11, 1.74E-10, 1.67E-11, 3.90E-12, 1.57E-15, 5.34E-05, 1.79E-13, 1.17E-11, 1.57E-11, 2.50E-13, 2.04E-13, 8.64E-06, 8.86E-11, 1.54E-11, 9.88E-10, 1.84E-11, 1.88E-12, 4.34E-08, 2.86E-09, 2.71E-17, 4.30E-15, 8.18E-14, 8.15E-10, 2.65E-15, 3.91E-12, 6.54E-16, 3.33E-12, 7.13E-09, 1.46E-08, 8.58E-05, 9.33E-11, 4.17E-08, 7.69E-11, 3.00E-13, 3.71E-12, 9.57E-09, 6.79E-09, 3.21E-11, 1.35E-14, 2.78E-12, 1.76E-15, 1.96E-09, 2.64E-11, 1.50E-06, 2.42E-13, 7.32E-11, 1.10E-07, 3.16E-11, 7.49E-14, 2.77E-08, 5.22E-09, 1.30E-14, 2.90E-14, 8.03E-16, 5.06E-14, 4.82E-11, 2.54E-10, 3.15E-11, 2.87E-05, 1.43E-17, 1.15E-10, 1.64E-15, 1.01E-12, 1.80E-14, 2.86E-09, 7.06E-09, 1.11E-11, 4.49E-14, 2.77E-16, 3.83E-10, 2.79E-06, 6.56E-13, 9.11E-12, 3.47E-08, 9.28E-12, 1.09E-10, 7.56E-11, 1.41E-16, 4.02E-08, 4.46E-10, 1.63E-10, 7.78E-13, 6.37E-13, 1.01E-12, 1.84E-08, 4.94E-14, 4.80E-12, 5.02E-09, 4.26E-13, 3.48E-12, 1.84E-05, 1.16E-08, 8.79E-15, 1.70E-09, 4.19E-10, 3.87E-09, 4.21E-12, 2.14E-08, 7.27E-11, 2.39E-17, 4.83E-09, 5.56E-10, 1.96E-11, 1.70E-15, 1.22E-08, 9.21E-16, 2.21E-13, 1.31E-10, 7.76E-08, 3.56E-09, 1.15E-09, 1.68E-08, 1.41E-09, 1.44E-07, 1.53E-06, 1.11E-10, 7.85E-06, 1.01E-14, 2.75E-10, 6.02E-12, 6.23E-10, 1.50E-10, 2.94E-15, 3.35E-12, 1.41E-06, 4.51E-08, 8.45E-19, 9.79E-11, 6.99E-09, 3.06E-10, 5.04E-18, 6.22E-14, 2.18E-10, 1.48E-14, 6.29E-12, 7.83E-13, 1.57E-11, 9.13E-14, 1.70E-14, 6.05E-10, 1.12E-11, 7.19E-10, 1.51E-10, 1.97E-15, 2.33E-07, 2.13E-08, 3.69E-10, 6.24E-16, 9.17E-15, 1.54E-11, 4.87E-08, 7.55E-13, 1.11E-11, 6.58E-15, 1.95E-11, 1.15E-09, 2.18E-08, 2.86E-14, 4.55E-08, 4.74E-10, 8.38E-14, 2.73E-16, 2.91E-12, 9.83E-09, 6.88E-14, 8.34E-08, 1.52E-10, 1.08E-13, 5.30E-10, 2.99E-06, 5.92E-13, 1.10E-10, 1.82E-17, 1.66E-12, 1.03E-10, 8.50E-14, 1.08E-11, 4.14E-13, 1.59E-06, 7.31E-13, 1.26E-11, 4.45E-12, 3.18E-13, 6.87E-16, 4.25E-12, 7.07E-11, 1.15E-12, 2.65E-06, 4.25E-07, 3.52E-14, 1.14E-09, 6.45E-17, 2.84E-13, 1.83E-09, 2.74E-09, 4.07E-17, 4.28E-08, 9.33E-11, 1.01E-15, 3.99E-12, 6.10E-08, 5.63E-12, 2.22E-09, 2.76E-05, 6.48E-11, 1.31E-07, 7.70E-10, 5.97E-14, 9.53E-09, 1.03E-05, 3.31E-12, 1.41E-15, 3.54E-12, 5.61E-10, 1.39E-15, 4.44E-11, 4.93E-15, 7.08E-12, 1.69E-08, 1.64E-10, 1.02E-08, 3.65E-11, 4.41E-12, 2.71E-07, 1.88E-06, 1.04E-10, 4.83E-08, 2.91E-09, 1.10E-09, 1.51E-15, 2.86E-09, 2.68E-08, 2.94E-09, 1.96E-11, 5.83E-12, 6.11E-15, 3.02E-13, 8.63E-10, 8.35E-16, 3.28E-10, 5.16E-11, 3.89E-09, 1.08E-13, 3.88E-14, 4.09E-08, 4.23E-08, 2.43E-13, 1.83E-10, 1.37E-12, 3.12E-10, 9.16E-14, 2.93E-15, 3.06E-12, 1.22E-14, 7.30E-13, 1.38E-09, 1.36E-11, 2.78E-10, 7.10E-13, 2.60E-10, 2.43E-07, 2.08E-05, 1.13E-10, 1.04E-09, 1.06E-14, 8.29E-11, 3.00E-14, 4.71E-08, 8.34E-07, 2.48E-11, 3.47E-12, 5.13E-09, 9.76E-16, 2.19E-13, 1.33E-11, 9.32E-11, 6.36E-14, 7.25E-11, 1.36E-05, 2.18E-15, 7.90E-11, 9.41E-15, 5.95E-14, 2.50E-13, 3.47E-17, 1.42E-14, 1.85E-17, 2.44E-10, 5.97E-18, 9.87E-12, 3.05E-12, 1.38E-09, 1.30E-13, 3.17E-14, 1.99E-15, 4.34E-07, 1.04E-05, 1.88E-15, 1.34E-13, 8.23E-08, 5.02E-12, 1.90E-09, 3.24E-12, 8.89E-11, 0.000142133, 3.00E-07, 3.60E-14, 5.95E-07, 4.59E-12, 2.48E-09, 3.98E-11, 5.59E-13, 4.13E-14, 1.77E-11, 4.88E-11, 3.83E-12, 1.11E-09, 3.21E-10, 1.68E-11, 7.09E-07, 1.12E-08, 1.88E-08, 8.16E-14, 2.87E-14, 5.17E-09, 5.11E-13, 1.43E-12, 4.19E-09, 4.03E-17, 6.34E-12, 2.63E-09, 1.55E-13, 4.85E-12, 4.49E-06, 7.34E-11, 2.82E-14, 1.82E-12, 1.93E-16, 3.10E-08, 1.64E-08, 1.32E-11, 6.31E-11, 6.48E-14, 2.55E-06, 1.60E-08, 1.58E-08, 8.22E-15, 9.19E-10, 3.12E-08, 1.77E-06, 5.43E-08, 8.03E-14, 3.05E-10, 1.71E-08, 3.57E-15, 1.11E-05, 1.18E-09, 4.99E-15, 6.74E-12, 3.83E-09, 7.73E-09, 2.22E-12, 2.60E-10, 2.83E-12, 6.35E-08, 1.56E-12, 1.10E-16, 1.87E-12, 1.45E-05, 3.44E-13, 8.25E-07, 1.91E-16, 1.79E-13, 2.33E-09, 2.55E-14, 4.51E-17, 8.90E-14, 8.76E-11, 4.16E-15, 2.58E-11, 2.37E-10, 5.16E-15, 3.03E-09, 1.34E-13, 9.61E-12, 9.16E-11, 2.82E-13, 1.28E-05, 5.30E-08, 5.67E-10, 5.09E-15, 1.51E-08, 2.89E-08, 6.98E-10, 6.88E-18, 3.43E-08, 6.38E-11, 7.24E-08, 1.74E-12, 2.76E-08, 1.88E-14, 2.47E-15, 1.21E-06, 8.16E-11, 1.28E-13, 6.72E-10, 9.04E-07, 9.98E-09, 1.57E-19, 7.33E-11, 8.03E-10, 1.50E-08, 4.12E-11, 8.33E-16, 5.56E-15, 2.94E-13, 1.70E-09, 4.45E-15, 2.35E-13, 4.66E-16, 1.06E-12, 6.40E-13, 8.26E-16, 2.27E-14, 8.47E-09, 6.10E-11, 1.12E-13, 3.94E-10, 1.92E-09, 4.25E-08, 8.84E-07, 4.39E-12, 4.19E-13, 5.32E-14, 4.02E-15, 1.51E-06, 1.19E-12, 4.72E-12, 7.05E-12, 2.06E-09, 3.04E-13, 3.42E-12, 2.12E-16, 9.74E-10, 8.71E-06, 4.55E-12, 2.69E-12)
While p-values range from 6.08038E-23 to 0.001134145, the bootstrapped p-value I get is 0.4995005 and I don't understand why. I am using the following function to find the bootstrapped p-value:
(1+sum(logit.boot$t[,2] > logit.boot$t0[2]))/(1+logit.boot$R)
where logit.boot$t[,2] takes on values from the p.values vector, logit.boot$t0[2] equals 2.664684e-11 and logit.boot$R = 1000.
EDIT
Here is the code I used for bootstrapping:
logit.bootstrap <- function(data, indices){
d <- data[indices, ]
Mf1 <- glm(Y ~ A + B + C, data = d, family = "binomial")
data.setM1 <- na.omit(d[, all.vars(formula(Mf1))])
M1.io <- glm(Y ~ A + B, data = data.setM1, family = "binomial")
my.test <- lrtest(Mf1, M1.io)
return(c(my.test$"Chisq"[2], my.test$"Pr(>Chisq)"[2]))
}
logit.boot <- boot(data=my.data, statistic=logit.bootstrap, R=1000) # 10'000 samples
In the result of the boot function, t0 should the p value on the original data, and t is some p values which are generated from random resampling/permutation on the original data. And in your case, you shouldn't use (1+sum(logit.boot$t[,2] > logit.boot$t0[2]))/(1+logit.boot$R) to get information from your bootstrapped p values, you may use quantile(logit.boot$t[,2], c(0.025,0.975)) or something like this to obtain a bootstrapped 95% confidence interval on your p value. This is not very meaningful, since the meaning of p value is already a probability (confidence level), why do you bother to obtain a confidence interval for p value? And the validness of the bootstrap method relies on the correctness of your parametric model. So if you want to use non-parametric approach toward this problem, I think you need to find some other approaches instead of this one.
How to fit a loess curve over this decomposed time series data in R?
We have time series data with some seasonality from the past 4 years. We want to predict the general rise in trend next year. For this, we decomposed the time series and observed the trend line:
However, this trend line is placed in the middle of the values rather than the values themselves. We are not satisfied with simply extrapolating this trend line since it falls very short of expected traffic.
Since we are interested in only the general rise in trend and not the seasonality, we remove the seasonality from the components:
mydata <- read.csv("values.csv")
mydataseries <- ts(mydata, start=c(2012,1,1),frequency = 365.25
mydataseriescomponents <- decompose(mydataseries)
mydataseriesminusseasons <- mydataseries - mydataseriescomponents$seasonal
We are now trying to fit a loess() curve in R around this time series data minus the seasonal component, that is mydataseriesminusseasons:
855154881.9
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However, we are not familiar with the form of the loess() function and it seems to expect a formula which we do not know. We tried the following:
y <- c(mydata)
x <- 1:1614
lo <- loess(y~x)
We get the error: Error in model.frame.default(formula = y ~ x) :
invalid type (list) for variable 'y'
How do we fit a loess curve around the values to get the general trend line? Also, after removing the seasonal component we have some negative values for some reason. Would this affect the loess() curve?
Resampling multivariate time series in R
I have a set of bivariate time series and want to resample them to the same length. I thought that it might be a good idea to use the mean length of all time series, since I wanted to avoid that some series will be shortened or extended too much. My first naive idea was using the resample method of the signal package, and resample each dimension of a series separately. I don't like this idea very much, since I have the fear that the alignment between the dimensions might suffer from the independent resampling, but I hoped this effect might be negligible. My current problem is that the resampling of the data creates artifacts at the end and beginning of a series. It seems that the resample method assumes that the series starts from zero. Now I'm wondering if there is a more suitable resampling method which in the best case is readily available (in R) and maybe also supports bivariate time series. Plot: http://i.stack.imgur.com/3OwAt.png Code example: example <- c(-2014.1, -2014.1, -2014.1, -2014, -2014, -2013.9, -2013.9, -2013.7, -2013.5, -2013.4, -2013.1, -2012.9, -2012.6, -2012.4, -2012, -2011.7, -2011.4, -2011, -2010.5, -2010.1, -2009.5, -2009.1, -2008.6, -2008, -2007.5, -2006.9, -2006.4, -2005.7, -2005.1, -2004.4, -2003.7, -2003, -2002.4, -2001.5, -2000.7, -1999.9, -1999.1, -1998.2, -1997.4, -1996.5, -1995.6, -1994.6, -1993.6, -1992.6, -1991.7, -1990.7, -1989.7, -1988.9, -1987.9, -1986.9, -1985.9, -1984.9, -1984, -1983, -1982.1, -1981.1, -1980.1, -1979.2, -1978.2, -1977.2, -1976.4, -1975.4, -1974.4, -1973.4, -1972.4, -1971.5, -1970.5, -1969.6, -1968.6, -1967.6, -1966.6, -1965.7, -1964.7, -1963.9, -1962.9, -1961.9, -1960.9, -1959.9, -1958.9, -1957.9, -1956.9, -1955.9, -1955, -1954, -1953, -1952.1, -1951.5, -1951.1, -1950.6, -1950.1, -1949.6, -1949.2, -1948.7, -1948.2, -1947.9, -1947.4, -1946.9, -1946.4, -1945.9, -1945.4, -1944.9, -1944.4, -1943.9, -1943.4, -1943, -1942.5, -1942, -1941.5, -1941, -1940.6, -1940.1, -1939.6, -1939.1, -1938.7, -1938.2, -1937.7, -1937.2, -1936.7, -1936.2, -1935.7, -1935.4, -1934.9, -1934.4, -1933.9, -1933.4, -1932.9, -1932.4, -1931.9, -1931.4, -1931, -1930.5, -1930, -1929.5, -1929, -1928.6, -1928.1, -1927.6, -1927.1, -1926.6, -1926.2, -1925.7, -1925.2, -1924.7, -1924.4, -1923.9, -1923.4, -1922.9, -1922.4, -1921.9, -1921.4, -1920.9, -1920.4, -1919.9, -1919.4, -1919, -1918.5, -1918, -1917.5, -1917, -1916.6, -1916.1, -1915.6, -1915.1, -1914.6, -1914.2, -1913.7, -1913.2, -1912.7, -1912.2, -1911.7, -1911.4, -1910.9, -1910.4, -1909.9, -1909.4, -1908.9, -1908.4, -1907.9, -1907.5, -1906.9, -1906.5, -1906, -1905.5, -1905, -1904.6, -1904, -1903.6, -1903.1, -1902.7, -1902.2, -1901.7, -1901.2, -1900.7, -1900.4, -1899.9, -1899.4, -1898.9, -1898.4, -1897.9, -1897.4, -1896.9, -1896.4, -1895.9, -1895.2, -1895, -1894.5, -1894, -1893.6, -1893.1, -1892.6, -1892.1, -1891.6, -1891.2, -1890.7, -1890.2, -1889.7, -1889.2, -1888.9, -1888.4, -1887.9, -1887.4, -1886.9, -1886.4, -1885.6, -1885.4, -1884.9, -1884.5, -1884, -1883.5, -1883, -1882.5, -1882.1, -1881.6, -1881.1, -1880.6, -1880.2, -1879.7, -1879.2, -1878.7, -1878.4, -1877.9, -1877.4, -1876.9, -1876.1, -1875.6, -1875.1, -1874.6, -1874.1, -1873.6, -1873.2, -1872.7, -1872.2, -1871.7, -1871.4, -1870.7, -1870.4, -1869.9, -1869.4, -1868.9, -1868.4, -1867.9, -1867.4, -1867.2, -1866.4, -1866, -1865.5, -1865, -1864.5, -1864.1, -1863.6, -1863.1, -1862.6, -1862.1, -1861.7, -1861.2, -1860.7, -1860.2, -1859.7, -1859.4, -1858.9, -1858.4, -1857.9, -1857.4, -1856.9, -1856.4, -1855.9, -1855.4, -1854.9, -1854.5, -1854, -1853.5, -1853.1, -1852.6, -1852.1, -1851.6, -1851.1, -1850.7, -1850.2, -1849.7, -1849.2) plot(example, t="l", main="Original") plot(resample(example,250,length(example)), t="l", main="Resampled")
geometric standard deviation for a log normal distribution
I am trying to calculate geometric standard deviation of each log normal distribution. In the below,for example, I have x data in first row, wich is bin size (from 10 to 1000), and corresponding five y data in the next rows.
10 10.9854 12.0679 13.2571 14.5635 15.9986 17.5751 19.307 21.2095 23.2995 25.5955 28.1177 30.8884 33.9322 37.2759 40.9492 44.9843 49.4171 54.2868 59.6362 65.5129 71.9686 79.0604 86.8511 95.4095 104.811 115.14 126.486 138.95 152.642 167.683 184.207 202.359 222.3 244.205 268.27 294.705 323.746 355.648 390.694 429.193 471.487 517.947 568.987 625.055 686.649 754.312 828.643 910.298 1000
0.0170496 0.0239502 0.0332355 0.0455609 0.0616994 0.0825406 0.109082 0.142408 0.18366 0.233988 0.294489 0.366137 0.449692 0.545614 0.653963 0.774317 0.905696 1.04651 1.19455 1.34698 1.50043 1.65109 1.79482 1.92739 2.04464 2.1427 2.21822 2.26854 2.29184 2.28729 2.25505 2.19628 2.11309 2.00838 1.8857 1.74903 1.60258 1.45057 1.29705 1.1457 0.999738 0.861783 0.733851 0.617327 0.513004 0.421137 0.341527 0.273605 0.216532 0.169284
0.564795 0.577687 0.5902 0.602296 0.61394 0.625095 0.635728 0.645804 0.655292 0.664162 0.672384 0.679932 0.686781 0.692908 0.698293 0.702918 0.706767 0.709826 0.712086 0.713539 0.71418 0.714007 0.71302 0.711223 0.708621 0.705224 0.701043 0.696093 0.69039 0.683953 0.676803 0.668965 0.660464 0.651327 0.641585 0.631268 0.620408 0.609041 0.5972 0.584922 0.572243 0.559201 0.545833 0.532178 0.518272 0.504155 0.489863 0.475433 0.460903 0.446307
1.88874 1.99575 2.1007 2.20265 2.30064 2.39374 2.48101 2.56155 2.63452 2.69913 2.75466 2.80051 2.83615 2.86117 2.87529 2.87836 2.87032 2.85127 2.82144 2.78116 2.7309 2.67121 2.60276 2.52629 2.44262 2.35262 2.2572 2.15731 2.0539 1.94791 1.84027 1.73188 1.62359 1.51621 1.41048 1.30706 1.20656 1.1095 1.01631 0.927365 0.842942 0.763252 0.688433 0.618555 0.553629 0.493609 0.4384 0.387865 0.341834 0.300104
0.190679 0.206669 0.223365 0.240726 0.258699 0.277225 0.296235 0.315651 0.335385 0.355342 0.375418 0.395503 0.41548 0.435228 0.454622 0.473532 0.491829 0.509384 0.526069 0.541758 0.556333 0.569679 0.58169 0.592269 0.60133 0.608797 0.614608 0.618714 0.62108 0.621687 0.620529 0.617615 0.612971 0.606636 0.598663 0.589119 0.578082 0.565642 0.5519 0.536964 0.52095 0.503979 0.486178 0.467675 0.4486 0.429082 0.409249 0.389225 0.36913 0.34908
1.63196 1.69464 1.75432 1.81053 1.8628 1.9107 1.95381 1.99177 2.02423 2.0509 2.07155 2.08598 2.09406 2.09572 2.09094 2.07977 2.06231 2.03872 2.00922 1.97406 1.93356 1.88808 1.83801 1.78377 1.72583 1.66463 1.60068 1.53447 1.46647 1.39719 1.32709 1.25664 1.18628 1.11642 1.04745 0.979718 0.913557 0.849249 0.787045 0.727157 0.669765 0.615008 0.562995 0.513798 0.467461 0.423997 0.383394 0.345615 0.310603 0.27828
So, I have five log normal distributions. (Actually, I have hundreds log normal distributions to be calculated.) Then, I want to calculate each geometric standard deviation, which does not seem to be implemented in r packages. R package ("psych") provides a tool to calculate geometric standard deviation, but not for such data I have..
Instead, it can be calculated following the equation below,
http://www.eng.utoledo.edu/~akumar/IAP1/lung/calculateDiameter.htm
But, I have no idea how to calculate using such equation in r. Hope someone help me to calculate a geometric standard deviation of each log normal distribution either using r package or calculating the equation. Thanks a lot for your help, in advance.
S
The easiest way is probably using: exp(sd(log(x)))