Abstract
A new generalized gamma distribution is defined involving a parameter δ = λ − 1; λ ≥ 0 in the Kobayashi's (1991) function Γλ(m,n). The parameter δ will relax the restriction on the parameter λ > 0 in all probability distributions using Kobayashi's (1991) type functions. The hazard rate function of this distribution has the property of monotonicity and that of bathtub. The trend of density function and statistical properties are studied for generalized gamma distribution. With the help of a real life data set the fitting of the distribution is shown. A new Weibull type distribution is also considered and the hazard rate function of this distribution also has both the properties namely bathtub and monotonicity.
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