Simulating Burr Type VII Distributions through the Method of 𝐿�-moments and 𝐿�-correlations

Abstract

Burr Type VII, a one-parameter non-normal distribution, is among the less studied distributions, especially, in the contexts of statistical modeling and simulation studies. The main purpose of this study is to introduce a methodology for simulating univariate and multivariate Burr Type VII distributions through the method of 𝐿-moments and 𝐿-correlations. The methodology can be applied in statistical modeling of events in a variety of applied mathematical contexts and Monte Carlo simulation studies. Numerical examples are provided to demonstrate that 𝐿-moment-based Burr Type VII distributions are superior to their conventional moment-based analogs in terms of distribution fitting and estimation. Simulation results presented in this study also demonstrate that the estimates of 𝐿-skew, 𝐿-kurtosis, and 𝐿-correlation are substantially superior to their conventional product-moment based counterparts of skew, kurtosis, and Pearson correlation in terms of relative bias and relative efficiency when distributions with greater departure from normality are used.