Cambanis-type Bivariate Uniform Distribution: Properties and Moment Estimation

Koshti, Rohan Dilip; Kamalja, Kirtee Kiran

doi:10.21608/cjmss.2023.246513.1026

Cambanis-type Bivariate Uniform Distribution: Properties and Moment Estimation

Document Type : Original Article

Authors

¹ Department of Statistics, School of Mathematical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon, India

² Department of Statistics, School of Mathematical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon, India.

10.21608/cjmss.2023.246513.1026

Abstract

The families of distributions are crucial in statistical modeling, offering a versatile foundation for a variety of applications. The development of bivariate distributions with specific marginal distributions and correlation coefficients is of considerable interest due to its wide-ranging relevance in real-world situations. The range of correlation between variables is an important characterization of the family. The variety of methods of construction of bivariate/multivariate distributions are developed in the literature. The Cambanis family is an important class of multivariate distributions with a wide range of correlation than the traditional families. In this paper, we consider a Cambanis-type bivariate uniform distribution and develop key statistical properties of the Cambanis-type bivariate uniform distribution. We obtain moment estimators of parameters for Cambanis-type bivariate uniform distribution. To evaluate the performance of the estimators, we develop an algorithm to simulate samples from the Cambanis-type bivariate uniform distribution and implement it in the R software. We perform a simulation study to present the performance of moment estimator.

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