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

In: Mathematical and Statistical Applications in Life Sciences and Engineering

Author

Listed:
  • 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)

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.

Suggested Citation

  • Saria Salah Awadalla & Govind S. Mudholkar & Ziji Yu, 2017. "The Power M-Gaussian Distribution: An R-Symmetric Analog of the Exponential-Power Distribution," Springer Books, in: Avishek Adhikari & Mahima Ranjan Adhikari & Yogendra Prasad Chaubey (ed.), Mathematical and Statistical Applications in Life Sciences and Engineering, chapter 0, pages 141-157, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-5370-2_6
    DOI: 10.1007/978-981-10-5370-2_6
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