Re: random numbers from user-defined distributions

• To: mathgroup at yoda.physics.unc.edu
• Subject: Re: random numbers from user-defined distributions
• From: jacobson at cello.hpl.hp.com
• Date: Thu, 07 Jan 93 08:31:32 -0800

```Dr. Robert B. Nachbar asks

does anyone know how to use Random with an arbitrary distribution
function? i would like to generate random numbers in the range {0, Pi}
with a probability distribution function (PDF) of Sin[x].

The standard technique is to take the inverse cumulative distribution
function and apply it to a random number in the range 0-1.

So in your case the cumulative distribution is given by

In[4]:= Integrate[Sin[xx],{xx,0,x}]/Integrate[Sin[xx],{xx,0,Pi}]

1 - Cos[x]
Out[4]= ----------
2

So your function is ArcCos[1-2 Random[]], or alternatively,
ArcCos[Random[Real,{-1,1}]]

-- David Jacobson

```

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