Half-logistic Garhy distribution with applications to radiation and waiting-time data

In this paper, we introduce a novel flexible lifetime model, called the half-logistic Garhy distribution (HLGD), as an extension of the classical Garhy distribution. Our model maintains the structural simplicity of the Garhy distribution, yet becomes more flexible via the half-logistic generator and thus can accommodate a range of data patterns commonly observed in radiation, biomedical, and energy-related studies. Several key statistical properties of the HLGD, including its probability density and cumulative distribution functions, quantile function, moments, incomplete moments, skewness, kurtosis, and order statistics, are computed. The model parameters are fitted by means of maximum likelihood. The simulation shows that bias, relative bias, mean squared error, root mean squared error, and average confidence interval length all decrease with sample size. The usefulness of the HLGD is demonstrated by two real-world datasets involving waiting times of bank clients and cancer remission times after a combined radiation/chemotherapy treatment. The results highlight the superior fitting performance of the HLGD compared to a few competing models.