Re: Looking for a truncated "normal like" pdf fro which I can change one moment without changing the others

beliavsky_at_aol.com
Date: 01/28/05 

Date: 28 Jan 2005 08:24:56 -0800

G Frechette wrote:
> Hello sci.stat.math readers: I am looking for a probability
distribution
> function that would have the following property.
>
> 1. It has finite support.
> 2. I can change the variance while keeping all other moments the
same.
> 3. I can change the skewness while keeping all other moments the
same.
>
> It would be nice if it also looked "something like a normal" (at
least
> single peaked).
>
> Is there any hope of finding such a thing?

If x is unbounded, the logistic transform y = 1/(1+exp(-x)) will have
range (0,1). One can shift and scale the logistic transform to get any
desired range.

I don't think one can in general change one moment of a distribution
while preserving all other moments. One can specify a shape via the
skew and kurtosis and then scale and shift to get the desired mean and
variance. The Pearson http://mathworld.wolfram.com/PearsonSystem.html
and Johnson families of distributions can fit a wide range of skewness
and kurtosis values, but one may have to transform them to get finite
support.

To simulate from a symmetric, normal-like distribution, one can compute
the sum of uniform variates -- see
http://mathworld.wolfram.com/UniformSumDistribution.html . The sum of
12 uniform variates minus 6 has the same first 3 moments as the
standardized normal, and this method is sometimes used to produce
normal variates. (I don't recommend it, precisely because it has finite
support).

I wonder what Colin Rose of MathStatica has to say :).

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