A Novel Lomax Extension with Statistical Properties, Copulas, Different Estimation Methods and Applications

• Published in: Bulletin of the Malaysian Mathematical Sciences Society Vol. 45; no. Suppl 1; pp. 85 - 120
• Main Authors: Aboraya, Mohamed, Ali, M. Masoom, Yousof, Haitham M., Ibrahim, Mohamed
• Format: Journal Article
• Language: English
• Published: Singapore Springer Nature Singapore 01-09-2022; Springer Nature B.V
• Subjects: Applications of Mathematics; Bivariate analysis; Least squares; Mathematics; Mathematics and Statistics; Maximum likelihood method; Monte Carlo simulation; Poisson distribution; Statistical analysis; Clayton copula; 62N01; 62N02; Farlie–Gumbel–Morgenstern; Lomax distribution; Ali-Mikhail-Haq copula; 62E10; Poisson distribution; Kernel density estimation; Modeling; Compounding method
• ISSN: 0126-6705; 2180-4206
• DOI: 10.1007/s40840-022-01250-y

A new compound Lomax model is proposed and analyzed. The novel distribution is derived based on compounding the zero truncated Poisson distribution and the exponentiated exponential Lomax distribution. The new density can be “monotonically left skewed,” “monotonically right skewed” and “symmetric” with various useful shapes. The new hazard rate can be “upside down bathtub-increasing,” “bathtub (
U
-shape),” “monotonically decreasing,” “increasing-constant” and “monotonically increasing.” Relevant statistical properties are derived. We briefly describe different estimation methods, namely the maximum likelihood, Cramér-von-Mises, ordinary least squares, weighted least square, Anderson–Darling, right tail Anderson–Darling and left tail Anderson–Darling. Monte Carlo simulation experiments are performed for comparing the performances of the proposed methods of estimation for both small and large samples. For facilitating the mathematical modeling of the bivariate real data sets, we derive some new corresponding bivariate distributions. Graphical simulation study is performed for assessing the finite sample behavior of the estimators using the maximum likelihood method. Two applications are provided for illustrating the applicability of the new model.