Re: random variable
- To: mathgroup at smc.vnet.net
- Subject: [mg103054] Re: [mg102833] random variable
- From: omar bdair <bdairmb at yahoo.com>
- Date: Sat, 5 Sep 2009 05:38:11 -0400 (EDT)
- References: <200908280943.FAA11851@smc.vnet.net> <28A3460B9CB94660BE9B0EF0E222E8E2@laertes>
Hi, I think the rejection method is the best. But the steps mentioned in the algorithm below are hard to perform because generating random sample from g(x) is in fact our problem. Please send me an example which illustrates what is mentioned. And if any body can help me in performing the 5 steps as a sketch Mathematica program, please send me this sketch. Another question: Is it possible to call every generated random variable by h[i], say, i=1,2,...,n. This step is important because I want to use these random variables in the future computations. Omar Bdair ________________________________ From: Tony Harker <a.harker at ucl.ac.uk> To: omar bdair <bdairmb at yahoo.com>; mathgroup at smc.vnet.net Sent: Friday, August 28, 2009 2:51:07 PM Subject: [mg103054] RE: [mg102833] random variable The best bet is probably the rejection method. Suppose the required distribution is p(x). We generate random numbers according to some distribution q(x) which need not be normalised (but should be normalisable, that is, have a finite integral over the domain of interest) with q(x)>=p(x) for all x -- ideally q(x) should be a distribution that has the same general shape as p(x), but in extremis we can just use a uniform distribution. This function q(x) is called the comparison function. The one thing we need to be able to do with q(x) is to generate samples from it (hence common choices are the uniform and the normal distribution) Then the procedure is as follows: a) Select a point from the distribution q(x). This gives a value of x. b) Select a value y from a uniform distribution between 0 and q(x). c) If y lies below p(x), accept the value of x, otherwise reject it. d) Repeat until the required number of x values have been accumulated. Obviously the closer the comparison function q(x) is to the required distribution p(x) the more likely step (c) is to accept the point, and the less 'wasteful' the process is. Tony ]-> -----Original Message----- ]-> From: omar bdair [mailto:bdairmb at yahoo.com] ]-> Sent: 28 August 2009 10:43 ]-> To: mathgroup at smc.vnet.net ]-> Subject: [mg102833] random variable ]-> ]-> I want to ask, how can I generate a random vaiable from ]-> some probability density functions which are not ]-> well-known? I mean, if we have some pdf which is not ]-> normal, binomial, weibull, ... but the only thing I know ]-> that it is a log-concave function, then how can I generate ]-> a number of random variables? ]-> ]-> ]-> ]->