a bivariate α-power transformed family: theory and application

In this paper, some general classes of bivariate semi-parametric continuous distributions are introduced. some important properties of this family of distributions will be illustrated. it is seen that the bivariate distribution corresponds to the known ali-mikhail-haq copula. hence, some important properties such as the $hbox{tp}_2$ property are justified. it will be shown that the marginals are kind of heavy tailed weighted distributions whose hazard rate functions can take variety of shapes. the behavior of the hazard rate function is mathematically illustrated. in addition, the $alpha$-power transformed distributions of a second type, which are introduced for the first time here, can be verified as special cases of the marginals. some members of the new bivariate classes are studied in details. the estimation of the parameters is illustrated by means of an efficient expectation-maximization algorithm, and some real data sets are also analyzed for illustrative purposes.