Multivariate random sums appear in many scientific fields, most notably in actuarial science, where they model both the number of claims and their sizes. Unfortunately, they pose severe inferential problems. For example, their density function is analytically intractable, in the general case,...

This paper introduces a novel three-parameter skew-log-logistic distribution. The research involves the development of a new random variable based on Azzalini and Capitanio's (2013) proposition. Additionally, various statistical properties of this distribution are explored. The paper presents a...

This study focuses on estimating reliability P[YX], where Y has a Zeghdoudi distribution with parameter a, X has a Zeghdoudi distribution with one outlier present and parameter c, and the remaining (n - 1) random variables are from a Zeghdoudi distribution with parameter b, in order for X and Y...

This study proposes a new discrete distribution in the mixed Poisson paradigm to obtain a distribution that provides a better fit to skewed and dispersed count observation with excess zero. The cubic transmutation map is used to extend the exponential distribution, and the obtained continuous...