Abstract
In the present work we consider a new probability density function (P.D.F) with r-confluent hypergeometric function. Special cases are considered, which include gamma, Weibull and inverse gausssian distributions. In order to study certain statistical properties, we introduce a new generalized gamma function together with its incomplete forms. We derive the basic functions associated with this P.D.F.: the mean, moments, expected values, moment generating function, hazard rate function, and mean residue life function. Several special cases for inverse gaussian, Weibull and gamma distributions are given. In the graphical representations of P.D.F. and hazard rate function, the role of shape and scale parameters is reflected.
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