using Plots
using Distributions
gr()
plot(Uniform(0,1))
xlabel!("velocity")
ylabel!("probability density")
xlims!(-0.5, 1.5)
ylims!(0, 1.5)
I am trying to plot a uniform distribution with area under the curve = 1. I would like the edges of the curve to drop to zero so the curve looks more like a box and less like a straight line. Any suggestions?
Probably the easiest way to do this is to explicitly plot the actual pdf of the distribution over some relevant range of x values. For example:
using Plots, Distributions
x = -0.5:0.001:1.5
plot(x, pdf.(Uniform(0,1), x), label="distribution")
xlabel!("velocity")
ylabel!("probability density")
xlims!(-0.5, 1.5)
ylims!(0, 1.5)
yields
Related
I'm really new to R and I'm looking to create a graph similar to the one attached. I have tried to create a density plot using both ggplot and the base program.
I have used code ggplot(data, aes(x = Freq)) + geom_density() but the output is incorrect. I'm getting a spike at each number point rather than an overall curve. Every row is one data point of between 1 to 7 and the frequency distributions for one trait is as follows:
1: 500, 2: 550 3:700 4:1000 5:900 6:835: 7:550
As such I have 5035 rows as one row equates to one score.
Any help is much appreciated.
Here is what I wish the plot would look like. (Note I'll add other traits at a later stage, I just wish to add one line at the moment).
there are a few things going on here, first is generating summary statistics of the data. you just need to call mean and sd in the appropriate way to get mean and standard deviation from your data. you've not shown your data so it would be difficult to suggest much here.
as far as plotting these summary statistics, you can replicate the plot from the original paper easily, but it's pretty bad and I'd suggest you not do that. stronger lines imply more importance, the need to double label everything, mislabelling the y-axis, all of that on top of drawing nice smooth parametric curves gives a false impression of confidence. I've only scanned the paper, but that sort of data is crying out for a multi-level model of some sort
I prefer "base" graphics, ggplot is great for exploratory graphics but if you have hard constraints on what a plot should look like it tends to get in the way. We start with the summary statistics:
df <- read.csv(text="
title, mu, sigma,label, label_x,label_pos
Extraversion, 4.0, 1.08,Extra, 3.85,3
Agreeableness, 5.0, 0.77,Agree, 5.0, 3
Conscientiousness, 4.7, 0.97,Cons, 3.4, 2
Emotional stability,5.3, 0.84,Emot stab,5.9, 4
Intellect, 3.7, 0.86,Intellect,3.7, 3
")
I've just pulled numbers out of the paper here, you'd have to calcular them. the mu column is the mean of the variable, and sigma is the standard deviation. label_x and label_pos are used to draw labels so need to be manually chosen (or the plot can be annotated afterwards in something like Inkscape). label_x is the x-axis position, and label_pos stands for where it is in relation to the x-y point (see text for info about the pos parameter)
next we calculate a couple of things:
lwds <- 1 + seq(3, 1, len=5) ^ 2
label_y <- dnorm(df$label_x, df$mu, df$sigma)
i.e. line widths and label y positions, and we can start to make the plot:
# start by setting up plot nicely and setting plot limits
par(bty='l', mar=c(3, 3, 0.5, 0.5), mgp=c(1.8, 0.4, 0), tck=-0.02)
plot.new(); plot.window(c(1, 7), c(0, 0.56), yaxs='i')
# loop over data drawing curves
for (i in 1:nrow(df)) {
curve(dnorm(x, df$mu[[i]], df$sigma[[i]]), add=T, n=151, lwd=lwds[[i]])
}
# draw labels
text(df$label_x, label_y, df$label, pos=df$label_pos)
# draw axes
axis(1, lwd=0, lwd.ticks=1)
axis(2, lwd=0, lwd.ticks=1)
box(lwd=1)
# finally, title and legend
title(xlab='Level of state', ylab='Probability density')
legend('topleft', legend=df$title, lwd=lwds, bty='n', cex=0.85)
this gives us something like:
I've also gone with more modern capitalisation, and started the y-axis at zero as these are probabilities so can't be negative
My preferences would be for something closer to this:
the thin lines cover 2 standard deviations (i.e. 95% intervals) around the mean, thick lines 1 SDs (68%), and the point is the mean. it's much easier to discriminate each measure and compare across them, and it doesn't artificially make "extraversion" more prominent. the code for this is similar:
par(bty='l', mar=c(3, 8, 0.5, 0.5), mgp=c(1.8, 0.4, 0), tck=-0.02)
plot.new(); plot.window(c(1, 7), c(5.3, 0.7))
# draw quantiles
for (i in 1:nrow(df)) {
lines(df$mu[[i]] + df$sigma[[i]] * c(-1, 1), rep(i,2), lwd=3)
lines(df$mu[[i]] + df$sigma[[i]] * c(-2, 2), rep(i,2), lwd=1)
}
# and means
points(df$mu, 1:5, pch=20)
axis(1, lwd=0, lwd.ticks=1)
axis(2, at=1:5, labels=df$title, lwd=0, lwd.ticks=1, las=1)
box()
title(xlab='Level of state')
I am trying to do the following:
plot a time series in R using a polygonal line
plot one or more horizontal lines superimposed
find the intersections of said line with the orizontal ones
I got this far:
set.seed(34398)
c1 <- as.ts(rbeta(25, 33, 12))
p <- plot(c1, type = 'l')
# set thresholds
thresholds <- c(0.7, 0.77)
I can find no way to access the segment line object plotted by R. I really really really would like to do this with base graphics, while realizing that probably there's a ggplot2 concoction out there that would work. Any idea?
abline(h=thresholds, lwd=1, lty=3, col="dark grey")
I will just do one threshold. You can loop through the list to get all of them.
First find the points, x, so that the curve crosses the threshold between x and x+1
shift = (c1 - 0.7)
Lower = which(shift[-1]*shift[-length(shift)] < 0)
Find the actual points of crossing, by finding the roots of Series - 0.7 and plot
shiftedF = approxfun(1:length(c1), c1-0.7)
Intersections = sapply(Lower, function(x) { uniroot(shiftedF, x:(x+1))$root })
points(Intersections, rep(0.7, length(Intersections)), pch=16, col="red")
I'm trying to log-transform the x axis of a density plot and get unexpected results. The code without the transformation works fine:
library(ggplot2)
data = data.frame(x=c(1,2,10,11,1000))
dens = density(data$x)
densy = sapply(data$x, function(x) { dens$y[findInterval(x, dens$x)] })
ggplot(data, aes(x = x)) +
geom_density() +
geom_point(y = densy)
If I add scale_x_log10(), I get the following result:
Apart from the y values having been rescaled, something seems to have happened to the x values as well -- the peaks of the density function are not quite where the points are.
Am I using the log transformation incorrectly here?
The shape of the density curve changes after the transformation because the distribution of the data has changed and the bandwidths are different. If you set a bandwidth of (bw=1000) prior to the transformation and 10 afterward, you will get two normal looking densities (with different y-axis values because the support will be much larger in the first case). Here is an example showing how varying bandwidths change the shape of the density.
data = data.frame(x=c(1,2,10,11,1000), y=0)
## Examine how changing bandwidth changes the shape of the curve
par(mfrow=c(2,1))
greys <- colorRampPalette(c("black", "red"))(10)
plot(density(data$x), main="No Transform")
points(data, pch=19)
plot(density(log10(data$x)), ylim=c(0,2), main="Log-transform w/ varying bw")
points(log10(data$x), data$y, pch=19)
for (i in 1:10)
points(density(log10(data$x), bw=0.02*i), col=greys[i], type="l")
legend("topright", paste(0.02*1:10), col=greys, lty=2, cex=0.8)
So I have a barplot in which the y axis is the log (frequencies). From just eyeing it, it appears that bars decrease exponentially, but I would like to know this for sure. What I want to do is also plot an exponential on this same graph. Thus, if my bars fall below the exponential, I would know that my bars to decrease either exponentially or faster than exponential, and if the bars lie on top of the exponential, I would know that they dont decrease exponentially. How do I plot an exponential on a bar graph?
Here is my graph if that helps:
If you're trying to fit density of an exponential function, you should probably plot density histogram (not frequency). See this question on how to plot distributions in R.
This is how I would do it.
x.gen <- rexp(1000, rate = 3)
hist(x.gen, prob = TRUE)
library(MASS)
x.est <- fitdistr(x.gen, "exponential")$estimate
curve(dexp(x, rate = x.est), add = TRUE, col = "red", lwd = 2)
One way of visually inspecting if two distributions are the same is with a Quantile-Quantile plot, or Q-Q plot for short. Typically this is done when inspecting if a distribution follows standard normal.
The basic idea is to plot your data, against some theoretical quantiles, and if it matches that distribution, you will see a straight line. For example:
x <- qnorm(seq(0,1,l=1002)) # Theoretical normal quantiles
x <- x[-c(1, length(x))] # Drop ends because they are -Inf and Inf
y <- rnorm(1000) # Actual data. 1000 points drawn from a normal distribution
l.1 <- lm(sort(y)~sort(x))
qqplot(x, y, xlab="Theoretical Quantiles", ylab="Actual Quantiles")
abline(coef(l.1)[1], coef(l.1)[2])
Under perfect conditions you should see a straight line when plotting the theoretical quantiles against your data. So you can do the same plotting your data against the exponential function you think it will follow.
This question already has answers here:
Closed 10 years ago.
Possible Duplicate:
Fitting a density curve to a histogram in R
I'd like to plot on the same graph the histogram and various pdf's. I've tried for just one pdf with the following code (adopted from code I've found in the web):
hist(data, freq = FALSE, col = "grey", breaks = "FD")
.x <- seq(0, 0.1, length.out=100)
curve(dnorm(.x, mean=a, sd=b), col = 2, add = TRUE)
It gives me an error. Can you advise me?
For multiple pdf's what's the trick?
And I've observed that the histogram seems to be plot the density (on y-y axis) instead of the number of observations.... how can I change this?
Many thanks!
It plots the density instead of the frequency because you specified freq=FALSE. It is not very fair to complain about it doing exactly what you told it to do.
The curve function expects an expression involving x (not .x) and it does not require you to precompute the x values. You probably want something like:
a <- 5
b <- 2
hist( rnorm(100, a, b), freq=FALSE )
curve( dnorm(x,a,b), add=TRUE )
To head of your next question, if you specify freq=TRUE (or just leave it out for the default) and add the curve then the curve just runs along the bottom (that is the whole purpose of plotting the histogram as a density rather than frequencies). You can work around this by scaling the expression given to curve by the width of the bins and the number of total points:
out <- hist( rnorm(100, a, b) )
curve( dnorm(x,a,b)*100*diff(out$breaks[1:2]), add=TRUE )
Though personally the first option (density scale) without tickmark labels on the y-axis makes more sense to me.
h<-hist(data, breaks="FD", col="red", xlab="xTitle", main="Normal pdf and histogram")
xfit<-seq(min(data),max(data),length=100)
x.norm<-rnorm(n=100000, mean=a, sd=b)
yfit<-dnorm(xfit,mean=mean(x.norm),sd=sd(x.norm))
yfit <- yfit*diff(h$mids[1:2])*length(loose_All)
lines(xfit, yfit, col="blue", lwd=2)