       Re: TransformedDistribution, for a sum of M iid variables

• To: mathgroup at smc.vnet.net
• Subject: [mg120478] Re: TransformedDistribution, for a sum of M iid variables
• From: Paul von Hippel <paulvonhippel at yahoo.com>
• Date: Mon, 25 Jul 2011 07:28:23 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <20110721225621.9H9BM.1153349.imail@eastrmwml34> <j0b9p4\$jl1\$1@smc.vnet.net> <201107222346.TAA28623@smc.vnet.net> <4E2D4909.813B.006A.0@newcastle.edu.au>
• Reply-to: Paul von Hippel <paulvonhippel at yahoo.com>

```I meant question ii -- i.e., how do I code this in Mathematica. The problem I am trying to solve is complicated and it wouldn't be productive to lay out all its details. But a simpler version would be this: I wish to calculate the mean and variance of the distribution U+avgMF, where U is a chi-square variable and avgMF is the average of M iid F variables. I can solve this problem by hand, but I wish solve this and similar, more complicated problems using the TransformedDistribution function. Many thanks for any pointers.

________________________________
From: Barrie Stokes <Barrie.Stokes at newcastle.edu.au>
To: mathgroup at smc.vnet.net; paulvonhippel at yahoo <paulvonhippel at yahoo.com>
Sent: Sunday, July 24, 2011 7:44 PM
Subject: [mg120478] Re: TransformedDistribution, for a sum of M iid variables

Hi Paul

I for one am not clear on the exact question you are asking.

If by "Is there a convenient way to do this?" and you mean by "this" "... replace Z2 with the average of M independent variables", do you mean:

(i) how do I calculate the distribution of the average of M independent variables (a technical statistical question, the answer to which can be found an any statistics textbook), or

(ii) how do I code the whole calculation in Mathematica (a Mathematica coding/representation question).

Maybe, as with many questions posted on this group, more background details will help respondents to your question(s) give you better answers. For example, do you have a particular problem in mind (i.e., application), or are you just generally curious (always a great idea) about how to do such and similar things?

(I often think there's a monotonically increasing relation between usefulness of answer and quality of question, if I may put it like that).

Willing to help with either question ...

Cheers

Barrie

>>> On 23/07/2011 at 9:46 am, in message <201107222346.TAA28623 at smc.vnet.net>,
paulvonhippel at yahoo <paulvonhippel at yahoo.com> wrote:
> To clarify what I'm looking for, suppose I have the following
> distribution:
>
> TransformedDistribution[Z1+Sqrt[U/(n-1)]*Z2,{Z1\
> [Distributed]NormalDistribution[0,1],Z2\
> [Distributed]NormalDistribution[0,1],U\
> [Distributed]ChiSquareDistribution[n-1]}]
>
> I want to replace Z2 with the average of M independent variables that
> are distributed like Z2.
> Or I might want to replace U with the average of M independent
> variables that are distributed like U.
>
> Is there a convenient way to do this? Thanks!

```

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