The Zografos-Balakrishnan Odd Log-Logistic Generalized Half-Normal Distribution with Mathematical Properties and Simulations

  • Mahdieh Mozafari Department of Mathematics and Computing, Higher Education Complex of Bam, Iran
  • Mahmoud Afshari Associate Professor. Persian Gulf University, 7516913798, Iran
  • Morad Alizadeh Department of Statistics, Persian Gulf University, Bushehr, Iran
  • Hamid Karamikabir Department of Statistics, Persian Gulf University, Bushehr, Iran
DOI: https://doi.org/10.19139/soic.v7i1.649
Keywords: Zografos-Balakrishnan odd log-logistic family, Generalized half-normal family, Quantile function, Moments, Maximum likelihood, Weighted least square, Bias, Mean square error

Abstract

In this paper, A new class of distributions called the Zografos-Balakrishnan odd log-logistic Generalized half-normal (ZOLL-GHN) family with four parameters is introduced and studied. Useful representations and some mathematical properties of the new family include moments, quantile function, moment Generating function are investigated. The maximum likelihood equations for estimating the parameters based on real data are given. Different methods have been used to estimate its parameters such as maximum likelihood, Least squares, weighted least squares, Crammer-von-Misers,Anderson-Darling and right-tailed Anderson-Darling methods. We assesses the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of a simulation study. Finally, the usefulness of the family and fitness capability of this model, are illustrated by means of two real data sets.

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Published
2019-01-07
How to Cite
Mozafari, M., Afshari, M., Alizadeh, M., & Karamikabir, H. (2019). The Zografos-Balakrishnan Odd Log-Logistic Generalized Half-Normal Distribution with Mathematical Properties and Simulations. Statistics, Optimization & Information Computing, 7(1), 211-234. https://doi.org/10.19139/soic.v7i1.649
Issue
Vol 7 No 1 (2019)
Section
Research Articles
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