Half Logistic Zeghdoudi Distribution: Statistical Properties, Estimation, Simulation and Applications

In this study, we introduce a new extension of the Zeghoudi distribution (ZD), which is an innovative modification of the ZD. The new proposed model is known as the half-logistic Zeghdoudi distribution (HLZD). This updated distribution simplifies the original ZD while increasing flexibility and accuracy when modeling data. The HLZD exhibits a variety of statistical properties, including right skewed, reduced, and unimodal probability density functions, skewness, kurtosis moments, incomplete moments, and order statistics. We use the maximum likelihood standard parameter estimation technique as well as a full simulation exercise to demonstrate the HLZD’s efficacy and dependability. Furthermore, applying the HLZD to two real-world failure time/chemotherapy datasets demonstrates its utility. It is capable of outperforming well-known models such as generalized exponential, exponentiated generalized XLindley, power exponentiated Lindley, exponential, exponentiated generalized Lindley, XLindley, Weibull power Lindley, Weibull Lindley, half logistic new-Weibull Pareto, half logistic Weibull, half logistic exponential, half logistic Rayleigh, half logistic Pareto, and power Lindley distributions.