The <i>γ</i> -order generalized chi-square distribution γX12

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, [Formula: see text] and the probability density function (pdf) is evaluated. Moreover, the moment generating function (mgf) of the [Formula: see text] is evaluated and in the case of γ = 2 the mgf of the well known [Formula: see text] is obtained. The same procedure is followed for the moments of the [Formula: see text] One step forward is the evaluation of the convolution of two [Formula: see text] and therefore [Formula: see text] is obtained eventually and the corresponding pdf is evaluated. Finally examples and applications of [Formula: see text] are discussed.