A NEW ONE-PARAMETER DISTRIBUTION FOR MODELING POSITIVE SKEWNESS DATA: THE GENERIC KRISON DISTRIBUTION
Abstract
Inspired by the hyperbolic secant distribution and a specific hyperbolic trigonometric identity, we propose a new continuous distribution with one parameter, called the Generic Krison distribution. We derive its probability density function, survival function, cumulative distribution function, hazard function, quantile function, and mean excess loss function. Closed‑form expressions for the moment generating function are also provided. Statistical measures including the raw moments, mean, variance, standard deviation, median, mode, skewness, kurtosis, coefficient of variation, and index of dispersion are obtained. The distribution exhibits constant moderate positive skewness and a constant coefficient of variation, making it a natural candidate for modeling positively skewed data. The parameter is estimated by the method of maximum likelihood; because the score equation is transcendental, the estimate is obtained numerically. We compare the Generic Krison distribution with the one‑parameter Rayleigh, Lindley, and Bilal distributions across three datasets (income, survival time, mortality rate). The results demonstrate that the Generic Krison distribution performs well on all three datasets, offering a promising new tool for statistical modeling.
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