Gompertz-modified Burr XII distribution: properties and applications

In this study, a new extension of the Gompertz distribution known as the Gompertz-modified Burr XII distribution is developed and studied. Various statistical properties of the distribution such as the reliability function, the quantile function, moments, order statistics, stochastic ordering, inequality measures, entropies, and stress-strength reliability parameter are derived. The plots of the density and hazard rate functions are obtained. The plots exhibit different kinds of nonmonotonic shapes. The maximum likelihood method of estimation is used to estimate the parameters of the distribution and Monte Carlo simulations are used to assess the consistency of the estimators. The flexibility and usefulness of the distribution are illustrated by fitting it to two different data sets. The results revealed that the distribution adequately fits the data sets.

[1]  M. S. Eliwa,et al.  Inverse Gompertz Distribution: Properties and Different Estimation Methods with Application to Complete and Censored Data , 2019 .

[2]  Walter Zucchini,et al.  Model Selection , 2011, International Encyclopedia of Statistical Science.

[3]  J. Gastwirth.  The Estimation of the Lorenz Curve and Gini Index , 1972 .

[4]  Albert C. Bemmaor.  Modeling the Diffusion of New Durable Goods: Word-of-Mouth Effect Versus Consumer Heterogeneity , 1992 .

[5]  P. E. Oguntunde,et al.  The Gompertz Fréchet distribution: Properties and applications , 2019, Cogent Mathematics & Statistics.

[6]  W. Weibull.  A Statistical Distribution Function of Wide Applicability , 1951 .

[7]  S. Ntouyas,et al.  Existence and Stability Analysis for Fractional Differential Equations with Mixed Nonlocal Conditions , 2019, Mathematics.

[8]  L. J. Bain.  Analysis for the Linear Failure-Rate Life-Testing Distribution , 1974 .

[9]  B. Gompertz,et al.  On the Nature of the Function Expressive of the Law of Human Mortality , 1825 .

[10]  The Modified Beta Gompertz Distribution: Theory and Applications , 2018, Mathematics.

[11]  C. Quesenberry,et al.  Concentration bands for uniformity plots , 1980 .

[12]  M. Alizadeh,et al.  The Beta-Gompertz Distribution , 2014, 1407.0743.

[13]  S. Tahmasebi,et al.  Gompertz-power series distributions , 2015, 1509.03595.

[14]  Lazhar Benkhelifa.  The beta generalized Gompertz distribution , 2017 .

[15]  M. Alizadeh,et al.  The Odd Log-Logistic Generalized Gompertz Distribution: Properties, Applications and Different Methods of Estimation , 2020, Communications in Mathematics and Statistics.

[16]  Charles E. Antle,et al.  Discrimination Between the Log-Normal and the Weibull Distributions , 1973 .

[17]  Ahmad M. Alshamrani,et al.  The generalized Gompertz distribution , 2013 .

[18]  Zohdy M. Nofal,et al.  Transmuted Complementary Weibull Geometric Distribution , 2014 .

[19]  The Odd Generalized Exponential Gompertz Distribution , 2015 .

[20]  Benjamin Gompertz,et al.  XXIV. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. In a letter to Francis Baily, Esq. F. R. S. &c , 1825, Philosophical Transactions of the Royal Society of London.

[21]  Giovanni Maria Giorgi,et al.  A look at the Bonferroni inequality measure in a reliability framework , 2005 .

[22]  Dina H. Abdelhady,et al.  On the Inverse Power Gompertz Distribution , 2020 .

[23]  M. A. Khan,et al.  On a modified Burr XII distribution having flexible hazard rate shapes , 2020, Mathematica Slovaca.

[24]  Zeyad M. Abdullah,et al.  Parameter Estimation and Reliability, Hazard Functions of Gompertz Burr Type XII Distribution , 2019 .

[25]  D. N. Prabhakar Murthy,et al.  A modified Weibull distribution , 2003, IEEE Trans. Reliab..

[26]  G. Cordeiro,et al.  The Gompertz-G family of distributions , 2017 .

[27]  J. Mazucheli,et al.  Unit-Gompertz Distribution with Applications , 2019 .