The Distribution of Sum, Product and Ratio for the Absolutely Continuous Bivariate Generalized Exponential Random Variables

Document Type : Original Article

Author

Department of Mathematical Statistics, Institute of Statistical Studies and Research, Cairo University, Egypt

Abstract

Block and  Basu  bivariate  exponential  distribution is  a  standout  amongst the  most  absolutely continuous  bivariate   technique . This idea can  be  extended to the  generalized  exponential   technique  also. In this  case  this   technique  is called  as  the  block  and  Basu  bivariate  generalized  exponential (BBBGE)  distribution . some  properties  of  BBBGE   distribution   can  be  obtained  as  the  moment  generating  function, median  and  mode .  the  exact  forms  for the   distribution  of  sum , ratio  product  of  dependent  variables  follow  the  block  and  Basu  bivariate generalized  exponential   distribution  are derived the maximum likelihood  estimation  (MLE) procedure  is  performed  for  the  parameters  of  the  BBBGE   distribution   a  numerical  illustration  performed  to  see  the  performances  of  the  MLEs 

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