A flexible laplace–gamma compound distribution for modeling reliability and risk data

Abstract In this article, we introduce a new form of compound distribution by combining Gamma and Laplace components. This new distribution is specifically designed to address the limitations of traditional models when dealing with skewed and heavy tailed data. Its flexible parameters enable precise control over tail heaviness and data concentration, making it adaptable to assorted data behavior common in finance, insurance, and engineering. Additionally its balanced decay mechanism ensures symmetrical treatment of extreme values, enhancing accuracy in modeling risks and uncertainties, ultimately supporting more robust decision-making in high-stakes environments. A detailed analysis of the unique structural properties of this newly proposed model is carried out, including probability density function (PDF), cumulative distribution function(CDF), survival function, hazard function, moments, parameter estimation, tail behavior analysis, ordered statistics, and risk measures.