[R] Random numbers with PDF of user-defined function

[Robert A LaBudde]

At 05:40 AM 4/29/2010, Nick Crosbie wrote:
>Hi,
>
>In S+/R, is there an easy way to generate random numbers with a
>probability distribution specified by an exact user-defined function?
>
>For example, I have a function:
>
>f(x) = 1/(365 * x), which should be fitted for values of x between 1 and
>100,000
>
>How do I generate random numbers with a probability distribution that
>exactly maps the above function?
>
>Nick

First of all, your pdf should be f(x) = 1 / [x log(100000)], if x is 
continuous.

Second, compute the cdf as F(x) = ln(x) / log(100000).

Third, compute the inverse cdf as G(p) = exp[p log(100000)]

Finally, to generate random variates, use G(u), where u is a uniform 
random variate in [0,1].

In R,

 > G<- function (p) exp(p*log(100000))
 > G(runif(5))
[1] 11178.779736  9475.748549 65939.487801 94914.354479     1.694695


================================================================
Robert A. LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral at lcfltd.com
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