How do I genenate random (or pseudo random) numbers from a list with a specified distribution

How do I generate random numbers from a list, with the condition that the numbers must have a given distribution?

What Ive done so far:

I was able to generate random numBers with a normal distribution with

y = 2 + .2*randn(10000,1)

Now I want to pick 3 samples from these numbers with size 50 each, each having normal, lognormal and exponential distributions. How will I do it?

Thanks in advance

Answer 1

[Walter Roberson]

Usually you cannot do that. Suppose for example that the list was just 0's and 1's representing flips of a coin. You are not going to be able to get an exponential distribution from such a list.

[Oleg Komarov]

@Raymundo: maybe you're trying to sample from a given distribution by taking the inverse cdf of a uniform [0 1]?

[Walter Roberson]

I agree, that would make much more sense to do.

[Raymundo Addun]

Dear Oleg and Walter,

No, not really interested in the uniform distribution. I just thought it might be possible to have a sample distribution (the 50 cases) different from a population distribution (the 10000 cases). Ok, if I cannot chose the distribution Id like to have in the sample, can I at least have a sample ¨not equal¨ in distribution as the population with a given significance level of equality (in a normality test for example)?

ray

[Walter Roberson]

Sub-selections are more likely than not to have a different mean. But getting the mean different _enough_ to be significant might be difficult; my intuition is that it would sometimes be impossible, but I would need to think about that more.

[Walter Roberson]

What if you "reverse engineer" kstest2() in order to determine how you would have to subsample in order to get a sufficiently high confidence for your purposes?

[Oleg Komarov]

@Raymundo: the uniform distribution is just a trick to sample from any distribution you chose since it enters the cdf from the y axes and returns the values on x axes according to the distribution you've chosen: http://en.wikipedia.org/wiki/Inverse_transform_sampling

[Raymundo Addun]

Oleg: its easy to generate a sample with a given distribution even without using the CDF inverse method. I really am not sure how might I solve my problem using the CDF inverse. Could you elaborate your idea . I already have a normally distributed population generated through the randn command.

Answer 2

[Laura Proctor]

Although you won't be able to generate the numbers from the exact data you have in y, you can still generate numbers using the data to gather the parameters, like so:

[muhat,sigmahat] = normfit(y)
rn = muhat*ones(50,1) + chol(sigmahat)*randn(50,1);

parmhat = lognfit(y);
rl = lognrnd(parmhat(1),parmhat(2),50,1);

muhat = expfit(y);
re = exprnd(muhat,50,1)

Here's a link to all the random number generator functions.

[Walter Roberson]

Though this does break the fundamental premise of the question that the numbers must be generated "from a list" (i.e., a given list of values must be sub-selected from to achieve the given distribution.)

[Raymundo Addun]

indeed, i need a sample from the list.