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>

In this paper an alternative to the usual credibility premium that arises for weighted balanced loss function is considered. This is a generalized loss function which includes as a particular case the weighted quadratic loss function traditionally used in actuarial science. From this function...