A Method for Simulating Burr Type III and Type XII Distributions through L-Moments and L-Correlations

This paper derives the Burr Type III and Type XII family of distributions in the contexts of univariate L-moments and the L-correlations. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of L-skew, L-kurtosis, and L-correlations. The procedure...

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Bibliographic Details
Published in:ISRN applied mathematics 2013-12, Vol.2013
Main Authors: Pant, Mohan D., Headrick, Todd C.
Format: Article
Language:English
Subjects:
Advantages
Bias
Confidence intervals
Estimates
Kurtosis
Monte Carlo simulation
Software reliability
Statistics
Studies
Online Access:Get full text
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Summary:This paper derives the Burr Type III and Type XII family of distributions in the contexts of univariate L-moments and the L-correlations. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of L-skew, L-kurtosis, and L-correlations. The procedure can be applied in a variety of settings such as statistical modeling (e.g., forestry, fracture roughness, life testing, operational risk, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that L-moment-based Burr distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed procedure also demonstrates 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 correlations in terms of relative bias and relative efficiency—most notably when heavy-tailed distributions are of concern.
ISSN:2090-5564
2090-5572
DOI:10.1155/2013/191604