A new method for adding a parameter to a family of bivariate exponential and Weibull distributions

A new way of introducing a parameter to expand a family of exponential and Weibull distributions is introduced and studied. It is applied to yield a new two-parameter extension of the bivariate exponential distribution which may serve as a competitor to such commonly used two-parameter family of the life distribution as the Weibull, gamma and lognormal distributions. The general method is applied to give a new three-parameter Weibull distribution. The families of distributions expanded by the method introduced 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 family.

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