A New Model of Discrete-Continuous Bivariate Distribution with Applications to Medical Data

B I Mohammed; Nicholas Makumi; Ramy Aldallal; Taysir E Dyhoum; Hassan M Aljohani

doi:10.1155/2022/1883491

A New Model of Discrete-Continuous Bivariate Distribution with Applications to Medical Data

Comput Math Methods Med. 2022 May 21:2022:1883491. doi: 10.1155/2022/1883491. eCollection 2022.

Authors

B I Mohammed^{1

2}, Nicholas Makumi³, Ramy Aldallal⁴, Taysir E Dyhoum^{5

6}, Hassan M Aljohani⁷

Affiliations

¹ Department of Mathematics, Faculty of Science, Jeddah University, 2749 Asfan Rd. Jeddah 21589, Saudi Arabia.
² Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr city, Cairo, Egypt.
³ Pan African University, Institute for Basic Sciences, Technology and Innovation (PAUSTI), Nairobi, Kenya.
⁴ College of Business Administration in Hotat Bani Tamim, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia.
⁵ Department of Mathematics, School of the Natural Sciences, Faculty of Science and Technology, University of Central Lancashire, Preston, UK.
⁶ School of Computing, Faculty of Science, Technology, Engineering and Mathematics, Arden University, Coventry, UK.
⁷ Department of Mathematics & Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia.

Abstract

The bivariate Poisson exponential-exponential distribution is an important lifetime distribution in medical data analysis. In this article, the conditionals, probability mass function (pmf), Poisson exponential and probability density function (pdf), and exponential distribution are used for creating bivariate distribution which is called bivariate Poisson exponential-exponential conditional (BPEEC) distribution. Some properties of the BPEEC model are obtained such as the normalized constant, conditional densities, regression functions, and product moment. Moreover, the maximum likelihood and pseudolikelihood methods are used to estimate the BPEEC parameters based on complete data. Finally, two data sets of real bivariate data are analyzed to compare the methods of estimation. In addition, a comparison between the BPEEC model with the bivariate exponential conditionals (BEC) and bivariate Poisson exponential conditionals (BPEC) is considered.

MeSH terms

Humans
Likelihood Functions
Models, Statistical*
Statistical Distributions