On a family of distributions obtained by the transformation of the gamma distribution

Abstract

The distribution of y=e ^-1where I is distributed as a gamma random variable is considered(Grassia. 1977). It is shown that this transformed Family of distributions covers a wide region in the (√β₁,β₂) plane. The moments of this Family of distributions are easily calculated. The fitting of data to this family of distributions is illustrated with a numerical example and the resulting fit is compared with the Johnson's S_B distribution fit.

Keywords:

• gamma distribution
• logarithmic transformation
• johnson's S_B distribution
• data fitting