The Log-logistic Weibull Distribution with Applications to Lifetime Data


  • Broderick Oluyede Georgia Southern University
  • Susan Foya Botswana International University of Science and Technology
  • Gayan Warahena-Liyanage Central Michigan University
  • Shujiao Huang University of Houston



In this paper, a new generalized distribution called the log-logistic
Weibull (LLoGW) distribution is developed and presented. This dis-
tribution contain the log-logistic Rayleigh (LLoGR), log-logistic expo-
nential (LLoGE) and log-logistic (LLoG) distributions as special cases.
The structural properties of the distribution including the hazard func-
tion, reverse hazard function, quantile function, probability weighted
moments, moments, conditional moments, mean deviations, Bonferroni
and Lorenz curves, distribution of order statistics, L-moments and Renyi
entropy are derived. Method of maximum likelihood is used to estimate
the parameters of this new distribution. A simulation study to examine
the bias, mean square error of the maximum likelihood estimators and
width of the condence intervals for each parameter is presented. Finally, real data examples are presented to illustrate the usefulness and applicability of the model.

Author Biography

Broderick Oluyede, Georgia Southern University

Broderick O. Oluyede, Ph.D.Professor and Consulting StatisticianDirector, Statistical Consulting Unit (SCU)Department of Mathematical SciencesGeorgia Southern UniversityStatesboro, GA 30460Telephone: (912) 478 5427Email: [email protected]


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How to Cite

Oluyede, B., Foya, S., Warahena-Liyanage, G., & Huang, S. (2016). The Log-logistic Weibull Distribution with Applications to Lifetime Data. Austrian Journal of Statistics, 45(3), 43–69.