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Mathematical and Statistical Applications in Life Sciences and Engineering pp 141–157Cite as

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

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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.

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Author information

Authors and Affiliations

  1. Division of Epidemiology and Biostatistics, UIC School of Public Health (SPH-PI), Chicago, IL, 60612-4394, USA

    Saria Salah Awadalla

  2. Department of Statistics and Biostatistics, University of Rochester, Rochester, NY, 14612, USA

    Govind S. Mudholkar

  3. Biostatistics Department, Jazz Pharmaceuticals, 3180 Porter Drive, Palo Alto, CA, 94304, USA

    Ziji Yu

Authors
  1. Saria Salah Awadalla
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  2. Govind S. Mudholkar
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  3. Ziji Yu
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Corresponding author

Correspondence to Saria Salah Awadalla .

Editor information

Editors and Affiliations

  1. Department of Pure Mathematics, University of Calcutta, Kolkata, West Bengal, India

    Avishek Adhikari

  2. IMBIC, Kolkata, West Bengal, India

    Mahima Ranjan Adhikari

  3. Department of Mathematics and Statistics, Concordia University, Montreal, Québec, Canada

    Yogendra Prasad Chaubey

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Awadalla, S.S., Mudholkar, G.S., Yu, Z. (2017). The Power M-Gaussian Distribution: An R-Symmetric Analog of the Exponential-Power Distribution. In: Adhikari, A., Adhikari, M., Chaubey, Y. (eds) Mathematical and Statistical Applications in Life Sciences and Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-10-5370-2_6

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