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MathGroup Archive 2007

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Re: RandomArray from user defined distribution?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73344] Re: RandomArray from user defined distribution?
  • From: "Ray Koopman" <koopman at sfu.ca>
  • Date: Tue, 13 Feb 2007 06:57:32 -0500 (EST)
  • References: <eqpdv5$eip$1@smc.vnet.net>

On Feb 12, 2:02 am, rob <r... at piovere.com> wrote:
> I'd like to use the RandomArray to produce some data from
> what I think is a Poisson distribution in t
> P[t] = a^2 t Exp[-a*t]  where a is mean, sigma.
>
> I see one can use RandomArray to produce sample data from a
> lot of continuous distributions but the Poisson isn't among
> them (it's only available in the discrete form).
>
> I've made a bunch of crippled attempts to force my P[t] to
> put out examples but have failed. Any suggestions? Thanks.

P[t] is the pdf of a continuous random variable on {0,Infinity},
but its mean is 2/a and its variance is 2/a^2.

In[1]:= P[t] = a^2 t Exp[-a*t];

In[2]:= Assuming[a > 0, Integrate[P[t],{t,0,Infinity}]]
Out[2]= 1

In[3]:= Assuming[a > 0, Integrate[t P[t],{t,0,Infinity}]]
Out[3]= 2/a

In[4]:= Assuming[a > 0, Integrate[(t-2/a)^2 P[t],{t,0,Infinity}]]
Out[4]= 2/a^2

It's certainly not a Poisson distribution. What are you trying to do?



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