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An L-Moment Based Characterization Of The Family Of Dagum Distributions, Mohan D. Pant, Todd C. Headrick
An L-Moment Based Characterization Of The Family Of Dagum Distributions, Mohan D. Pant, Todd C. Headrick
Todd Christopher Headrick
This paper introduces a method for simulating univariate and multivariate Dagum distributions through the method of 𝐿-moments and 𝐿-correlations. A method is developed for characterizing non-normal Dagum distributions with controlled degrees of 𝐿-skew, 𝐿-kurtosis, and 𝐿-correlations. The procedure can be applied in a variety of contexts such as statistical modeling (e.g., income distribution, personal wealth distributions, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that 𝐿-moment-based Dagum distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed method also demonstrates that the estimates of 𝐿-skew, 𝐿-kurtosis, …
Weighted Simplex Procedures For Determining Boundary Points And Constants For The Univariate And Multivariate Power Methods, Todd C. Headrick, Shlomo S. Sawilowsky
Weighted Simplex Procedures For Determining Boundary Points And Constants For The Univariate And Multivariate Power Methods, Todd C. Headrick, Shlomo S. Sawilowsky
Todd Christopher Headrick
The power methods are simple and efficient algorithms used to generate either univariate or multivariate non-normal distributions with specified values of (marginal) mean, standard deviation, skew, and kurtosis. The power methods are bounded as are other transformation techniques. Given an exogenous value of skew, there is an associated lower bound of kurtosis. Previous approximations of the boundary for the power methods are either incorrect or inadequate. Data sets from education and psychology can be found to lie within, near or outside the boundary of the power methods. In view of this, we derived necessary and sufficient conditions using the Lagrange …