A generalized class of form-invariant bivariate weighted distributions

ABSTRACT

Weighted random variables are used to model sampling methods with unequal sampling probabilities proportional to non negative weight functions, that is, when we want to study original distributions under weighted samples. Recently, Alavi and Chinipardaz [Alavi, S.M.R., Chinipardaz, R. (2009). Form-invariance under weighted sampling. Statistics. 43(1):81–90] have introduced two new classes of form-invariant bivariate weighted distributions. In this paper these classes have been generalized, under a more general weight function . The class includes some of custom continuous bivariate models. Some properties of the class are explained and maximum likelihood estimates of parameters are obtained.

Keywords:

• Bivariate weighted distributions
• form-invariance
• generalized weight function
• weighted distributions.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E10
• 62E15

Acknowledgments

The authors would like to thank the associate editor and the referees for their useful comments and suggestions on improvement of this paper. They also appreciate Dr. Abdolghafoor Khademarasoul and Dr. Abbas Emam for editing the manuscript.

Funding

The authors would like to thank Shahid Chamran University of Ahvaz for the financial support they provided.