THE BIVARIATE EXTENSION OF AMOROSO DISTRIBUTION - David Sam Jayakumar; A Sulthan; W Samuel (Statistics and Data Science Program Study, SSMI, IPB University, in collaboration with the Forum Pendidikan Tinggi Statistika Indonesia (FORSTAT) and the Ikatan Statistisi Indonesia (ISI), 2020)
This paper introduces the bivariate extension of the amoroso distribution and its density function is expressed in terms of hyper-geometric function. The standard amoroso distribution, cumulative distribution functions, conditional distributions, and its moments are also derived. The Product moments, Co-variance, correlations, and Shannon’s differential entropy are also shown. Moreover, the generating functions such as moment, Cumulant, Characteristic functions are expressed in Fox-wright function, and the Survival, hazard, and Cumulative hazard functions are also computed. The special cases of the bivariate amoroso distribution are also discussed and nearly 780 bivariate mixtures of distributions can be derived. Finally, the two-dimensional probability surfaces are visualized for the selected special cases and we also showed the estimation of parameters by the method of maximum likelihood approach, and the constrained maximum likelihood approach is also computed by using Non-linear Programming with a numerical application