Gamma Distribution definition, formula and applications



gamma distribution by statisticalaid.com

 

Gamma Distribution

A continuous random variable X is said to have a generalised gamma distribution with parameter α and β if its probability density fumction is defined as,


Where α and β are two parameter and  α,β>0. Gamma distribution is a continuous probability distribution.

gamma distribution curve


Properties of Gamma distribution

  • Gamma distribution has two parameter  α and β.
  • Mean of Gamma distribution (variate) is α/β.
  • Variance of Gamma distribution (variate) is α/ β2
  • Characteristic function of gamma distribu­tion is .
  • Moment generating function of gamma distribution is .
  • The measure of skewness β1=.
  • Measure of kurtosisβ2= . These measures show that gamma distribution is positively skewed and leptokurtic.
  • If the value of  β=1; mean= variance, if  β>1; mean<variance and if  β<1; mean>variance.

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