A bivariate inverse Weibull distribution: properties, concomitant of order statistics, extropy’s measure

Document Type : Original Article

Authors

1 Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt.

2 Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt

3 Mathematics Department, Faculty of Science, Zagazig Univesity

4 Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

Abstract

This paper embarks on a comprehensive investigation of the Cambanis bivariate inverse Weibull (CAMBIW) distribution, meticulously delving into its inherent statistical properties and adaptability across diverse scenarios. Section 2 delves into the marginal and conditional distributions, regression curves, covariances, and correlations of the CAMBIW distribution, providing a thorough understanding of its behavior. It further extends the analysis to the study of concomitants of order statistics (OSs) derived from CAMBIW data, examining their moments to gain deeper insights into their characteristics. Building upon this foundation, Section 3 delves into the concept of extropy, deriving and discussing its application for both the inverse Weibull (IW) and CAMBIW distributions, offering valuable tools for measuring information content. Section 4 follows suit, exploring the concept of weighted extropy and its derivation for both IW and CAMBIW distributions, providing an additional layer of analysis. To solidify the understanding of the model's practical value and real-world relevance, Section 5 presents a meticulously chosen bivariate dataset and demonstrates the CAMBIW distribution's effectiveness through its respectable performance, highlighting its potential as a valuable tool for statistical analysis across various fields.

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