Bivariate Generalized Half-Logistic Distribution: Properties and Its Application in Household Financial Affordability in KSA

Abstract

The generalized half-logistic distribution is ideal to fit the lifetime of some products, such as ball bearings and electrical insulation. In this paper, we aim to extend this scope by creating a motivated bivariate version. We thus introduce the bivariate generalized half-logistic distribution using the Farlie Gumbel Morgenstern (FGM) copula, which is called the FGM bivariate generalized half-logistic distribution (FGMBGHLD for short). In particular, the FGMBGHLD finds application in describing bivariate lifetime datasets that have weak correlations between variables. Some statistical properties and functions of our new distribution, such as the product moments, moment generating function, reliability function, and hazard rate function, are derived. We discuss the maximum likelihood estimation method of the FGMBGHLD parameters. As an application of the FGMBGHLD in reliability, we consider the stress–strength model when the stress and strength random variables are dependent. We also derive the point and interval estimates of the stress–strength coefficient. Finally, we use the data from the household income and expenditure survey of KSA 2018 for Saudi households by administrative region to demonstrate the practicability of the proposed model. A comparison with a modern bivariate Weibull distribution is performed.