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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 has a gamma distribution with mean and shape parameter , with being treated as a random variable having another gamma distribution, this time with mean and shape parameter . The result is that has the following probability density function (pdf) for :〔Redding (1999)〕 : where and 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 , the second having a gamma distribution with mean and shape parameter . 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)』 ■ウィキペディアで「K-distribution」の詳細全文を読む スポンサード リンク
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