How to get the pdf of a complex variable?

• To: mathgroup at smc.vnet.net
• Subject: [mg20707] How to get the pdf of a complex variable?
• From: Cheng Lee Lung <eeacheng at cityu.edu.hk>
• Date: Mon, 8 Nov 1999 02:48:49 -0500
• Organization: City University of Hong Kong
• Sender: owner-wri-mathgroup at wolfram.com

```Dear All,

I wish to use Mathematica to find the pdf of a complex variable. For a
real no. is very easily but when I try to solve the complex no., I could
not get the result as I expected. The way I get the pdf of the real no.
is straight forward. It is shown as below.

In[1]:=
<<Statistics`NormalDistribution`

In[2]:=
ndist = NormalDistribution[m, \[Sigma]]
Out[2]=
NormalDistribution[m,\[Sigma]]
In[3]:=
xnorm=PDF[ndist,x]
Out[3]=
\!\(E\^\(-\(\((\(-m\) + x)\)\^2\/\(2\ \[Sigma]\^2\)\)\)\/\(\ at \(2\
\[Pi]\)\
\[Sigma]\)\)
x above is a real no.

If z is a complex no. The pdf of the complex no. should
come out like this,
\!\(znorm = \
E\^\(-\(\((\(-m\) + z)\)\^2\/\(2\ \[Sigma]\^2\)\)\)\/\(\
\[Pi]\ \[Sigma]\^2\)\)

How can I get this result with Mathematica?

Best regards,

Anthony Cheng
EE dept. of City University of Hong Kong.
email : eeacheng at cityu.edu.hk
phone : 852-27887755
fax : 852-27887791

```

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