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.