A NEW METHOD FOR ADDING A PARAMETER TO A FAMILY OF DISTRIBUTIONS WITHAPPLICATION TO THE EXPONENTIAL AND WEIBULL FAMILIES

A new way of introducing a parameter to expand a family of distributio ns is introduced and applied to yield a new two-parameter extension of the exponential distribution which may serve as a competitor to such commonly-used two-parameter families of life distributions as the Weib ull, gamma and lognormal distributions. In addition, the general metho d is applied to yield a new three-parameter Weibull distribution. Fami lies expanded using the method introduced here have the property that the minimum of a geometric number of independent random variables with common distribution in the family has a distribution again in the fam ily. Bivariate versions are also considered.