Re: random variable

*To*: mathgroup at smc.vnet.net*Subject*: [mg102836] Re: random variable*From*: Mark Fisher <particlefilter at gmail.com>*Date*: Sun, 30 Aug 2009 06:04:31 -0400 (EDT)*References*: <200908280943.FAA11851@smc.vnet.net> <h7b0ak$i7$1@smc.vnet.net>

On Aug 29, 6:36 am, "Tony Harker" <a.har... at ucl.ac.uk> wrote: > 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:bdai... at yahoo.com] > ]-> Sent: 28 August 2009 10:43 > ]-> To: mathgr... at smc.vnet.net > ]-> Subject: 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? > ]-> > ]-> > ]-> > ]-> > > As a follow up, since the pdf is log concave, you can use "adaptive rejection sampling". See http://www.amsta.leeds.ac.uk/~wally.gilks/adaptive.rejection/web_page/Welcome.html I don't know if there is an implementation in Mathematica. --Mark

**References**:**random variable***From:*omar bdair <bdairmb@yahoo.com>