A new discrete distribution depending on two parameters <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\alpha -1$$</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\sigma 0$$</EquationSource> </InlineEquation> is obtained by discretizing the generalized normal distribution proposed in García et al. (Comput Stat and Data Anal 54:2021–2034, <CitationRef CitationID="CR6">2010</CitationRef>), which was derived from the normal distribution by using the...</citationref></equationsource></inlineequation></equationsource></inlineequation>

Given two independent non-degenerate positive random variables X and Y, Lukacs (Ann Math Stat 26:319–324, <CitationRef CitationID="CR14">1955</CitationRef>) proved that X/(X + Y) and X + Y are independent if and only if X and Y are gamma distributed with the same scale parameter. In this work, under the assumption X/U and U are...</citationref>