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A generalized class of form-invariant bivariate weighted distributions

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  • S. M. R. Alavi

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 w(x1,x2,β1,β2)=[v1(x1)]β1[v2(x2)]β2$w(x_1,x_2, \beta _1,\beta _2)=[v_1(x_1)]^{\beta _1}[v_2(x_2)]^{\beta _2}$. The class includes some of custom continuous bivariate models. Some properties of the class are explained and maximum likelihood estimates of parameters are obtained.

Suggested Citation

  • S. M. R. Alavi, 2017. "A generalized class of form-invariant bivariate weighted distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(5), pages 2193-2201, March.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:5:p:2193-2201
    DOI: 10.1080/03610926.2015.1035395
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