The Power M-Gaussian Distribution: An R-Symmetric Analog of the Exponential-Power Distribution

Saria Salah Awadalla (), Govind S. Mudholkar () and Ziji Yu ()
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Saria Salah Awadalla: UIC School of Public Health (SPH-PI), Division of Epidemiology and Biostatistics
Govind S. Mudholkar: University of Rochester, Department of Statistics and Biostatistics
Ziji Yu: Jazz Pharmaceuticals, Biostatistics Department

Chapter Chapter 6 in Mathematical and Statistical Applications in Life Sciences and Engineering, 2017, pp 141-157 from Springer

Abstract: Abstract The mode-centric M-Gaussian distribution, which may be considered a fraternal twin of the Gaussian distribution, is an attractive alternative for modeling non-negative, unimodal data, which are often right-skewed. In this paper, we aim to expand upon the existing theory and utility of R-symmetric distributions by introducing a three-parameter generalization of the M-Gaussian distribution, namely the Power M-Gaussian distribution. The basic distributional character of this R-symmetric analog of the exponential-power distribution will be studied extensively. Estimation of the mode, dispersion, and kurtosis parameters will be developed based on both moments and maximum likelihood methods. Simulation and real data examples will be used to evaluate the model.

Date: 2017
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DOI: 10.1007/978-981-10-5370-2_6

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