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...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

In this paper, some properties of gamma-X family are discussed and a member of the family, the gamma-normal distribution, is studied in detail. The limiting behaviors, moments, mean deviations, dispersion, and Shannon entropy for the gamma-normal distribution are provided. Bounds for the...

In this paper, a quasi-negative binomial distribution (QNBD) derived from the class of generalized Lagrangian probability distributions is studied. The negative binomial distribution is a special case of QNBD. Some properties of QNBD, including the upper tail behavior and limiting distributions,...