Re: how to get random numbers from a distribution

*To*: mathgroup at smc.vnet.net*Subject*: [mg81501] Re: how to get random numbers from a distribution*From*: Bill Rowe <readnewsciv at sbcglobal.net>*Date*: Wed, 26 Sep 2007 06:37:47 -0400 (EDT)

On 9/24/07 at 4:19 AM, tdoxmail at gmail.com wrote: >I am a new Mathematica user. I have a function that i use to >generate a probability distribution (eg x^2). I want a random number >generator, that should generate values from this probability >distribution only, >I know this Random function in mathematica, that can generate in >particular range, but how do i tell to generate from a particular >distribution. >I created a list of values using my probability function but not >able to integrate it with Random function so that random numnber >takes value from that list. =46irst, x^2 is not a probability distribution. For a function to be a probability distribution, integrating the function over the domain of the function must yield 1. That is, 3 x^2 over restricted to the range of 0 to 1 is a probability distribution function since In[14]:= Integrate[3*x^2, {x, 0, 1}] Out[14]= 1 =46or this particular case, inverting the cumulative distribution function is probably the simplest most direct way to get the desired distribution. That is RandomReal[]^(1/3) has the desired distribution. There are other methods to get arbitrary distributions from the uniform distribution when the inverse of the cumulative distribution function cannot be expressed as simply in closed form. A good discussion of various methods to do this can be found in the text Seminumerical Algorithms Vol 2 by Knuth. Another good reference is Mathematical Statistics for Mathematica by Colin Rose and Murray Smith. This text comes with a Mathmatica package (mathstatica) that can do what you want. Note, the currently available version of mathstatica is compatible with Mathematica version 5.2 and has not yet been updated to be compatible with version 6. -- To reply via email subtract one hundred and four