Generate samples from a normal distribution

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Kash022
Kash022 2016-11-25
回答： Image Analyst 2016-11-25
Hello,
I have a Gaussian mixture distribution which looks as attached. I now want to sample and generate 1000 samples from this and plot their histogram. I tried using randi function but it does not work. Please let me know how to do this.
y = randi(my_pdf,100); %%my_pdf is my distribution
Thanks!
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Kash022
Kash022 2016-11-25
编辑：Kash022 2016-11-25
Its a gaussian mixture distribution with different means. This is the code snippet used to generate it.
clear all;
XX= [-2:0.01:20];
some_rand_noise = 0.1;
my_pdf = zeros(1,length(XX));
for k = 1:256
for ii=1:256
val(ii) = hw(bitxor(ii-1,k-1))+hw(k-1); %%hw is a function used to generate hamming weights i.e no of ones %%%
my_pdf = my_pdf + normpdf(XX,val(ii),some_rand_noise);
end
end
figure();plot(XX,my_pdf/256); hold on;
Image Analyst
Image Analyst 2016-11-25
Please supply the hw function so we can run your code.

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回答（3 个）

Image Analyst
Image Analyst 2016-11-25
If you have that function already, then use inverse transform sampling: https://en.wikipedia.org/wiki/Inverse_transform_sampling. In short, compute the CDF of your function and use rand() to pick a value.
I attach an example of how I used it for the Rayleigh distribution.
CarrotCakeIsYum
CarrotCakeIsYum 2016-11-25
randi will generate rando integers.
To generate a random sample from a vector, use randsample. see:
help randsample
I'd imagine you'd want:
y = randsample(my_pdf,100);
To plot a histogram use the 'hist' command.
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Kash022
Kash022 2016-11-25
thanks! but how do I do this for different means? as you can see in my attachment, I have different means,for each of them I need to generate the samples and then plot their histogram. Thanks!
CarrotCakeIsYum
CarrotCakeIsYum 2016-11-25
Sorry I don't follow... your population will only have one mean!
For the JPEG you've posted, the mean will be at 7.5 (since it is a symmetrical distribution).

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Image Analyst
Image Analyst 2016-11-25
Maybe use randn() to get a list of a few million numbers taken from those 13 distributions (call randn thirteen times), then pick one of the values at random.

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