The Distribution of Z gamma and Z* when the Distribution of the Complex Variable Z Is a Member of a Particular Family of Distributions

摘要

An eight parameter family of densities is introduced which contains several of the well-known density functions as particular cases. We reserve the functions f and g to denote this family, or one of its particular cases, in the r-theta plane and x-y plane, respectively. We will show that if the distribution of Z is determined by the eight parameter family, then the distributions of Z superscript gamma and Z* (the complex conjugate of Z) are also determined by the eight parameter family. We then obtain estimators and some properties of these estimators for some particular cases of the family. (Author)