       RE: help in generating a gaussian random variable

• To: mathgroup at smc.vnet.net
• Subject: [mg35512] RE: [mg35488] help in generating a gaussian random variable
• From: "DrBob" <majort at cox-internet.com>
• Date: Wed, 17 Jul 2002 02:09:02 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Maybe this is what you want.  "count" will keep track of how many times
Y is evaluated, which is very important:

<< Statistics`ContinuousDistributions`
X = NormalDistribution[5, 10];
x := Random[X]
count = 0;
Y := (count++; NormalDistribution[0, Evaluate@x])
y := Random[Y]
y
count

-6.07805
1

<< Graphics`Graphics`
Histogram[y & /@ Range]

101

Histogram[RandomArray[Y, 100]]

102

The first Histogram argument draws 100 X samples and, for each of them,
one Y sample.  The second Histogram argument draws one X sample and then
100 Y samples.  The second depicts a Gaussian variable; the first does
not (too much kurtosis) -- but maybe it's what you want.

z = y & /@ Range;
#[z] & /@ {Mean, StandardDeviation, Skewness, Kurtosis}
z = RandomArray[Y, 100000];
#[z] & /@ {Mean, StandardDeviation, Skewness, Kurtosis}

{-0.0490017, 11.2665, 0.0387603, 9.00383}

{-0.0808581, 20.4408, 0.0101782, 2.97761}

Here's another output for the same input cell:

{0.0359718, 11.1685, 0.0436788, 8.29863}

{0.00507702, 13.7293, 0.00278272, 3.00732}

The second method gives a variable variance, but the first does not.

Bobby Treat

-----Original Message-----
From: Salman Durrani [mailto:dsalman at itee.uq.edu.au]
To: mathgroup at smc.vnet.net
Subject: [mg35512] [mg35488] help in generating a gaussian random variable

Hi

I need to generate a Gaussian random variable y having mean =0 and
variance
=x.

The variance x is itself a gaussian random variable having a known mean
and
variance.
e.g. mean of x =5;
variance of x = 10;

Can anyone suggest how to use this information to generate y ?

thanks

Salman

```

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