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K-distribution : ウィキペディア英語版
K-distribution
In probability and statistics, the K-distribution is a three-parameter family of continuous probability distributions.
The distribution arises by compounding two gamma distributions. In each case, a re-parametrization of the usual form of the family of gamma distributions is used, such that the parameters are:
:
*the mean of the distribution, and
:
*the usual shape parameter.
==Density==
The model is that random variable X has a gamma distribution with mean \sigma and shape parameter L, with \sigma being treated as a random variable having another gamma distribution, this time with mean \mu and shape parameter \nu. The result is that X has the following probability density function (pdf) for x>0:〔Redding (1999)〕
:f_X(x;\mu,\nu,L)= \frac} K_\alpha ( 2 \sqrt),
where \alpha = \nu-L, \beta = L + \nu - 1, \xi = L\nu/\mu , and K is a modified Bessel function of the second kind. In this derivation, the K-distribution is a compound probability distribution. It is also a product distribution:〔 it is the distribution of the product of two independent random variables, one having a gamma distribution with mean 1 and shape parameter L, the second having a gamma distribution with mean \mu and shape parameter \nu.
This distribution derives from a paper by Jakeman and Pusey (1978) who used it to model microwave sea echo. Jakeman and Tough (1987) derived the distribution from a biased random walk model. Ward (1981) derived the distribution from the product for two random variables, ''z'' = ''a'' ''y'', where ''a'' has a chi distribution and ''y'' a complex Gaussian distribution. The modulus of ''z'', ''|z|'', then has K distribution.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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