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Using the fact that Gaussian(λ=σ) is an approximation of Poisson(λ), I want to compute an approximation of Poisson noise using only uniform random numbers without using factorials.
There are two things I have no clue.
How to approximate gaussian noise from uniform noise.
How to approximate Poisson noise with Gaussian noise when λ is small.
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I'm new to solving big -O and analysis questions and I'm slightly confused on this problem. excuse me if my math is wrong but f(n) <= Cg(n) in this case n(2^n) = f(n) and 2^2n = g(n)
boiling it down I get n/2^n <= C after working it out.
im lost on how to find n0 and C, I assume n0 is 1 as it is usually the case, but im uncertain of C, i assume its 2 but im not sure how to show so.
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The probability density function of a Bates distribution random variable X is
To get cdf you need to integrate pdf
I got the following cdf function:
And Inverse function:
But this function generates wrong variates.
What am I doing wrong?
Thanks.
The inverse of a sum is not the sum of the inverses.
The Bates distribution with parameter n is the distribution of the average of n random numbers distributed according to the uniform distribution on (0, 1). So you can simply simulate the uniform distribution and take the average.
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For a school project I have to determine a function u(t) of time. I have derived an expression of the following form:
(https://i.stack.imgur.com/vNrYb.png)
with a,b,c,d constants (not necessarily integers). I have figured out that this problem is only solvable with numerical integration with initial condition u(0)=u_0, yet I don't know how to do this particular problem.
I have looked at all the numerical integration methods I have learnt so far, but they all seem to apply for polynomials or for functions where you know the function evaluations at specific points.
There are lots of ways to calculate an approximate value for u(t), some simple but requiring a lot of iterations, and more complex requiring fewer iterations. Assuming a,b,c,d are real numbers, and u_0 = u(0) then for t > 0, one could just split the interval between 0 and t into N sub-intervals and calculate
u_(i+1) = u_i + (du/dt)(t_i)*t/N
where t_i = i*t/N
then,
u_N = u(t).
If N is not sufficiently large, the result will be inaccurate. To obtain a satisfactory N is more art than science. Just printing the results for increasing N should give you an idea of how large N needs to be to obtain the level of accuracy you need. Adding higher order terms (d^2u/dt^2 etc.) can sometimes improve speed and accuracy.
You can't numerically integrate anything unless you have values for all those constants.
I don't know what numerical integration schemes you looked at, but I think Euler's method or Runga-Kutta would both be worth trying.
You don't say which language you want to use. Python would be a fine choice. So would Java. Lots of libraries to help.
Wolfram Alpha has a closed-form solution here. It's a separable, non-linear ODE. You'll need to know hypergeometric functions to evaluate.
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So - edited because some of us thought that this question is off-topic.
I need to build spline (approximation) on 100 points in one of environments listed in tags. But I need it with exact number of intervals (maximum of 6 intervals - separate equations - in whole domain). Packages / libraries in R and Maxima which I know let me for building spline on this points but with 25-30 intervals (separate equations). Does anyone know how to build spline with set number of intervals without coding whole algorithm all over again?
What you're looking for might be described as "local regression" or "localized regression"; searching for those terms might turn up some hits.
I don't know if you can find exactly what you've described. But implementing it doesn't seem too complicated: (1) Split the domain into N intervals (say N=10). For each interval, (2) make a list of the data in the interval, (3) fit a low-order polynomial (e.g. cubic) to the data in the interval using least squares.
If that sounds interesting to you, I can go into details, or maybe you can work it out yourself.
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Suppose I have an Arabic character hand-drawn in Thuluth font, as in:
http://arabicletters.info/wp-content/uploads/1.jpg
I was thinking of a way I can recreate the same shape but at a much greater height, whilst leaving the other characteristics intact (stroke width, thickness, the relation of where the curving starts to happen to the height) which then got me curious about a way of finding its mathematical representation and play with it until I can get what I want or any other shape for that matter. Is there a math sub-specialty that can help with this? and for this particular problem, can it be solved using programs like Adobe Illustrator or AutoCAD?
Forgive the noobness.
I don't think deduce is the right word.
You can get what you want if you add sufficient points and do Bezier spline fits to match the letters.
There might be a way to automate the process of adding points, but the "sufficient" criterion is tricky. And then you'd have to tell how to connect points with splines.
Sounds like you're trying to reproduce optical character recognition in Arabic.