Based on the definition of the γ-order generalized normal, the γ-order generalized standard normal is obtained, and applications are referred. We proceed on the definition of the γ-order generalized chi-square, γX12 and the probability density function (pdf) is evaluated. Moreover, the moment generating function (mgf) of the γX12 is evaluated and in the case of γ = 2 the mgf of the well known X12 is obtained. The same procedure is followed for the moments of the γX12. One step forward is the evaluation of the convolution of two γX12 and therefore γXn2 is obtained eventually and the corresponding pdf is evaluated. Finally examples and applications of γXn2 are discussed.
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Kitsos et al. (2024) studied this question.
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