On The Convolution of Gamma Random Variables With Respect To Two Parameters Majorization

Author : Afshin Ghanizadeh and U. V. Naik-Nimbalkar, (India)

Abstract                                                                           

Let  are independent random variables from a distribution function , . We survey the likelihood ratio ordering of the convolution of the gamma random variables in terms of the majorization order of the two parameters holds. For , if  and , we show that  is larger than  according to the likelihood ratio ordering. We find the useful bounds for the survival function and hazard rate function of convolution of non-identical gamma random variables.

Keywords: Convolution, likelihood ratio ordering, two-parameter majorization, gamma distribution, totally positivity.