A New Extension of the Generalized Half Logistic Distribution with Applications to Real Data

Mustapha Muhammad; Lixia Liu

doi:10.3390/e21040339

journal article Open Access Mar 28, 2019

A New Extension of the Generalized Half Logistic Distribution with Applications to Real Data

Mustapha Muhammad Lixia Liu

Entropy Vol. 21 No. 4 pp. 339 · MDPI AG

View at Publisher Save 10.3390/e21040339

Abstract

In this paper, we introduced a new three-parameter probability model called Poisson generalized half logistic (PoiGHL). The new model possesses an increasing, decreasing, unimodal and bathtub failure rates depending on the parameters. The relationship of PoiGHL with the exponentiated Weibull Poisson (EWP), Poisson exponentiated Erlang-truncated exponential (PEETE), and Poisson generalized Gompertz (PGG) model is discussed. We also characterized the PoiGHL sub model, i.e the half logistic Poisson (HLP), based on certain functions of a random variable by truncated moments. Several mathematical and statistical properties of the PoiGHL are investigated such as moments, mean deviations, Bonferroni and Lorenz curves, order statistics, Shannon and Renyi entropy, Kullback-Leibler divergence, moments of residual life, and probability weighted moments. Estimation of the model parameters was achieved by maximum likelihood technique and assessed by simulation studies. The stress-strength analysis was discussed in detail based on maximum likelihood estimation (MLE), we derived the asymptotic confidence interval of R = P ( X 1 < X 2 ) based on the MLEs, and examine by simulation studies. In three applications to real data set PoiGHL provided better fit and outperform some other popular distributions. In the stress-strength parameter estimation PoiGHL model illustrated as a reliable choice in reliability analysis as shown using two real data set.

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Details

Published: Mar 28, 2019
Vol/Issue: 21(4)
Pages: 339
License: View

Authors

M

Mustapha Muhammad

College of Mathematics and Information Sciences, Hebei Normal University, Shijiazhuang 050024, China

L

Lixia Liu

College of Mathematics and Information Sciences, Hebei Normal University, Shijiazhuang 050024, China

Funding

Key Fund of Department of Education of Hebei Province Award: ZD2018065

Cite This Article

Mustapha Muhammad, Lixia Liu (2019). A New Extension of the Generalized Half Logistic Distribution with Applications to Real Data. Entropy, 21(4), 339. https://doi.org/10.3390/e21040339

A New Extension of the Generalized Half Logistic Distribution with Applications to Real Data

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