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

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