Re: Flexible probability density function
- From: beliavsky@xxxxxxx
- Date: 29 Mar 2006 14:20:29 -0800
Ramesh Rebba wrote:
Which is the most flexible probability distribution that spans from
(1) -inf to +inf
(2) zero to +inf
I am guessing Weibull could be a good choice for (2). Any ideas about (1)?
For (1), there are the
(a) Johnson and Pearson families of distributions, which both can be
fit to the first four moments of data.
(b) skewed t distribution, with at least two distinct parameterizations
-- see the links to R packages at
(i) http://cran.r-project.org/src/contrib/Descriptions/sn.html
(ii) http://cran.r-project.org/src/contrib/Descriptions/skewt.html
(c) mixture of normals (or mixture of Student t, for even more
flexibility)
For (2), note that if x has range (-inf,inf), log(x) has range (0,inf).
There is something called the "generalized lambda" distribution, that
can fit data of type (1). I have not used it myself, but it is covered
in the book "Fitting Statistical Distributions: The Generalized Lambda
Distribution and Generalized Bootstrap Methods" published in 2000.
.
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