A new method for generating families of continuous distributions

In this paper, a new method is proposed for generating families of continuous distributions. A random variable <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$X$$</EquationSource> </InlineEquation>, “the transformer”, is used to transform another random variable <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$T$$</EquationSource> </InlineEquation>, “the transformed”. The resulting family, the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$T$$</EquationSource> </InlineEquation>-<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$X$$</EquationSource> </InlineEquation> family of distributions, has a connection with the hazard functions and each generated distribution is considered as a weighted hazard function of the random variable <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$X$$</EquationSource> </InlineEquation>. Many new distributions, which are members of the family, are presented. Several known continuous distributions are found to be special cases of the new distributions. Copyright Sapienza Università di Roma 2013