R help - Apr 2010 - Random numbers with PDF of user-defined function

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

This email and any attachments may contain information t...{{dropped:15}}

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
Least Cost Formulations, Ltd.            URL: http://lcfltd.com/
824 Timberlake Drive                     Tel: 757-467-0954
Virginia Beach, VA 23464-3239            Fax: 757-467-2947

"Vere scire est per causas scire"

On 29/04/2010 5:40 AM, 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?
>   
You can use sample() with the prob argument set to the values of f(x).  
You probably want replace=TRUE as well.

Duncan Murdoch
> Nick
>
> This email and any attachments may contain information t...{{dropped:15}}
>
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