gamma distributionとは 意味・読み方・使い方

名詞

gamma distribution (plural gamma distributions)

1. (probability theory, statistics) Any of a family of two-parameter continuous probability distributions, of which the common exponential distribution and chi-square distribution are special cases.
   • 1988, A. Clifford Cohen, Betty Jones Whitten, Parameter Estimation in Reliability and Life Span Models, Marcel Dekker, page 93:

     The gamma distribution is positively skewed and along with the Weibull, lognormal, and inverse Gaussian (IG) distributions is also available as a model in reliability and life-span studies.

   • 1999 [1977, Wiley], Jean Dickinson Gibbons, Ingram Olkin, Milton Sobel, Selecting and Ordering Populations: A New Statistical Methodology, SIAM, Republished unabridged and corrected, page 328,

     The ranking and selection problems in this chapter apply to populations that follow the gamma distribution. The gamma distribution model is used widely in many fields of applications, particularly in engineering and the social and physical sciences.

   • 2005, M. T. Todinov, Reliability and Risk Models: Setting Reliability Requirements, Wiley, page 36:

     The negative exponential distribution is a special case of the gamma distribution in which ${\displaystyle k=1}$. Another important special case of a gamma distribution with parameters ${\displaystyle k}$ and ${\displaystyle \theta =2}$ is the χ² distribution ${\displaystyle G(k,2)}$ with ${\displaystyle n=2k}$ degrees of freedom. […] Gamma distributions have an additivity property: the sum of two random variables following gamma distributions ${\displaystyle G(k_{1},\theta )}$ and ${\displaystyle G(k_{2},\theta )}$ is a random variable following a gamma distribution ${\displaystyle G(k_{1}+k_{2},\theta )}$ with parameters ${\displaystyle k_{1}+k_{2}}$ and ${\displaystyle \theta }$ […] .