The Gamma-Weibull-G Family of Distributions with Applications

Authors

  • Broderick Oluyede Georgia Southern University
  • Shusen Pu
  • Boikanyo Makubate
  • Yuqi Qiu

DOI:

https://doi.org/10.17713/ajs.v47i1.155

Abstract

Weibull distribution and its extended families has been widely studied in lifetime applications. Based on the Weibull-G family of distributions and the exponentiated Weibull distribution, we study in detail this new class of distributions, namely, Gamma-WeibullG family of distributions (GWG). Some special models in the new class are discussed. Statistical properties of the family of distributions, such as expansion of density function, hazard and reverse hazard functions, quantile function, moments, incomplete moments, generating functions, mean deviations, Bonferroni and Lorenz curves and order statistics are presented. We also present R´enyi entropy, estimation of parameters by using method of maximum likelihood, asymptotic confidence intervals and applications using real data

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]

References

Aarset M (1987). “How to Identify Bathtub Hazard Rate.” IEEE Transactions on Reliability, 36(1), 106–108.

Bourguignon M, Silva R, Cordeiro G (2014). “The Weibull-G Family of Probability Distributions.” Journal of Data Science, (12), 53–68.

Chambers JM, Cleveland WS, Kleiner B, Tukey P (1983). Graphical Methods for Data Analysis.Wadsworth.

Chen Z (2000). “A New Two Parameter Lifetime Distribution with Bathtub Shape of Increasing Failure Rate Function.” Statistics and Probability Letters, 49, 155–161.

Cordeiro GM, Ortega E, Cunha D (2013). “The Exponentiated Generalized Class of Distributions.” Journal of Data Science, 11(11), 1–27.

Gompertz B (1895). “On The Nature of the Function Expressive of The Law of Human Mortality and The New Model of Determining The Value of Life Contingencies.” Philosophical Transactions of the Royal Society of London, 115, 513–585.

Gradshteyn IS, Ryzhik IM (2000). Tables of Integrals, Series and Products. Academic Press, San Diego.

Meeker W, Escobar L (1998). Statistical Methods for Reliability Data. John Wiley.

Nadarajah S, Cordeiro G, Ortega EMM (2015). “The Zografos and Balakhrishnan-G Family of Distributions: Mathematical Properties and Applications.” Communications in Statistics-Theory and Methods, 44, 186–215.

Nascimento ADC, Bourguignon M, Zea LM, Santos-Neto M, Silva RB, Cordeiro GM (2014). “The Gamma extended Weibull Family of Distributions.” Journal of Statistical Theory and Applications, 13, 1–16.

Nassar MM, Eissa F (2003). “On the Exponentiated Weibull Distribution.” Communications in Statistics-Theory and Methods, 32, 1317–1336.

Pal M, Ali MM, Woo J (2006). “Exponentiated Weibull Distribution.” Statistica, anno LXVI, 2.

Phani KK (1987). “A New Modified Weibull Distribution Function.” Journal of American Ceramic Society, 70, 182–184.

Renyi A (1961). “On Measure of Entropy and Information.” Berkeley Symposium on Mathematical Statistics and Probability, 1, 547–561.

Shaked M, Shanthikumar J (1994). Stochastic Orders and Their Applications. Academic Press.

Smith RM, Bain LJ (1975). “An Exponential Power life-Testing Distribution.” Communications in Statistics-Theory and Methods, 4, 469–481.

Tahir MH, Zubair M, Mansoor M, Cordeiro GM, Alizadeh M, Hamedani GG (2015). “A New Weibull-G Family of Distributions.” Hacettepe University Bulletin of Natural Sciences and Engineering, Series B: Mathematics and Statistics.

Torabi H, Montazeri HN (2012). “The Gamma-Uniform Distribution and It’s Applications.” Kybernetika, 48, 16–30.

Zografos K, Balakrishnan N (2009). “On Families of Beta- and Generalized Gamma-Generated Distribution and Associated Inference.” Stat. Method, 6, 344–362.

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Published

2018-01-30

How to Cite

Oluyede, B., Pu, S., Makubate, B., & Qiu, Y. (2018). The Gamma-Weibull-G Family of Distributions with Applications. Austrian Journal of Statistics, 47(1), 45–76. https://doi.org/10.17713/ajs.v47i1.155

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