Main Article Content
The article presents an extension of the Gompertz-Makeham distribution using the Lomax generator of probability distributions. This generalization of the Gompertz-Makeham distribution provides a more skewed and flexible compound model called Lomax Gompertz-Makeham distribution. The paper derives and discusses some Mathematical and Statistical properties of the new distribution. The unknown parameters of the new model are estimated via the method of maximum likelihood estimation. In conclusion, the new distribution is applied to two real life datasets together with two other related models to check its flexibility or performance and the results indicate that the proposed extension is more flexible compared to the other two distributions considered in the paper based on the two datasets used.
Gompertz B. On the nature of a function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philo. Trans. Royal Soci. 1825;115:513-585.
Marshall A, Olkin I. Life distributions. Structure of nonparametric, semiparametric and parametric families. Springer, New York; 2007.
Golubev A. Does Makeham make sense? Biogerontology. 2004;5:159-167.
Johnson NL, Kotz S, Balakrishnan N. Continuous univariate distributions, 2 Edn. John Wiley and Sons, New York. 1995;2.
Dey S, Moala FA, Kumar D. Statistical properties and different methods of estimation of Gompertz distribution with application. Revista Colombianade Estadstica. 2017;40(1):165-203.
Eugene N, Lee C, Famoye F. Beta-normal distribution and it applications. Comm. in Stat.: Theo. and Meth. 2002;31:497-512.
Shaw WT, Buckley IR. The alchemy of probability distributions: beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map. Research Report; 2007.
Zografos K, Balakrishnan N. On families of beta- and generalized gamma generated distributions and associated inference. Stat. Meth. 2009;63:344–362.
Cordeiro GM, De Castro M. A new family of generalized distributions. J. Stat. Comp. Sim. 2011;81:883-898.
Alexander C, Cordeiro GM, Ortega EMM, Sarabia JM. Generalized beta-generated distributions. Comp. Stat. Data Analy. 2012;56:1880–1897.
Risti´c MM, Balakrishnan N. The gamma-exponentiated exponential distribution. J. Stat. Comp. Sim. 2012;82:1191–1206.
Torabi H, Montazari NH. The gamma-uniform distribution and its application. Kybernetika. 2012;48:16–30.
Amini M, Mirmostafaee SMTK, Ahmadi J. Log-gamma-generated families of distributions. Stat.; 2012.
Alzaghal A, Lee C, Famoye F. Exponentiated T-X family of distributions with some applications. Int. J. Prob. Stat. 2013;2:31–49.
Hassan AS, Elgarhy M. A new family of exponentiated Weibull-generated distributions. Int. J. of Math. & Its Appl. 2016;4:135–148.
Alzaatreh A, Famoye F, Lee C. Weibull-Pareto distribution and its applications. Comm. Stat. Theo. Meth. 2013;42:1673–1691.
Bourguignon M, Silva RB, Cordeiro GM. The Weibull-G family of probability distributions. J. Data Sci. 2014;12:53-68.
Torabi H, Montazari NH. The logistic-uniform distribution and its application. Comm. Stat.: Sim. and Comp. 2014;43:2551–2569.
Alzaatreh A, Famoye F, Lee C. The gamma-normal distribution: Properties and applications. Comp. Stat. Data Analy. 2014;69:67–80.
Cordeiro GM, Ortega EMM, Popovic BV, Pescim RR. The Lomax generator of distributions: Properties, minification process and regression model. Appl. Math. Comp. 2014;247:465-486.
Cordeiro GM, Ortega EMM, Ramires TG. A new generalized Weibull family of distributions: Mathematical properties and applications. J. Stat. Distr. Appl. 2015;2:13.
Alizadeh M, Cordeiro GM, de Brito E, Demetrio CGB. The beta Marshall-Olkin family of distributions. J. of Stat. Dist. Appl. 2015;2(4):1–18.
Tahir MH, Cordeiro GM, Alzaatreh A, Mansoor M, Zubair M. The logistic-X family of distributions and its applications. Comm. Stat.: Th. and Meth. 2016;45(24):7326-7349.
Tahir MH, Zubair M, Mansoor M, Cordeiro GM, Alizadeh M. A new Weibull-G family of distributions. Hac. J. Math. Stat. 2016;45(2):629-647.
Cakmakyapan S, Ozel G. The Lindley family of distributions: Properties and applications. Hacettepe Journal of Mathematics and Statistics. 2016;46:1-27.
Alizadeh M, Cordeiro GM, Pinho BLG, Ghosh I. The Gompertz-G family of distributions. J. of Stat. Theo. and Pract. 2017;11(1):179–207.
Gomes-Silva F, Percontini A, De Brito E, Ramos MW, Venancio R, Cordeiro GM. The odd Lindley-G family of distributions. Austrian J. of Stat. 2017;46:65-87.
Chukwu AU, Ogunde AA. On Kumaraswamy Gompertz Makeham distribution. American J. Math. Stat. 2016;6(3):122-127.
El-Bar AMTA. An extended Gompertz-Makeham distribution with application to lifetime data. Comm. Stat.: Sim. Comp. 2017;1-22.
Riffi MI, Hamdan MS. Cubic transmuted Gompertz-Makeham distribution. European J. Adv. Eng. Techn. 2018;5(12):1001-1010.
Riffi MI. A generalized transmuted Gompertz-Makeham distribution. J. Sci. Eng. Res. 2018;5(8):252-266.
Venegas O, Iriarte YA, Astorga JM, Gomez HW. Lomax-Rayleigh distribution with an application. Appl. Math. Inf. Sci. 2019;13(5):741-748.
Omale A, Yahaya A, Asiribo OE. On properties and applications of Lomax-Gompertz distribution. Asian J. Prob. Stat. 2019;3(2):1-17.
Ieren TG, Oyamakin SO, Yahaya A, Chukwu AU, Umar AA, Kuje S. On making an informed choice between two Lomax-based continuous probability distributions using lifetime data. Asian J. Prob. Stat. 2018;2(2):1-11.
Ieren TG, Kuhe AD. On the properties and applications of Lomax-exponential distribution. Asian J. Prob. Stat. 2018;1(4):1-13.
Hyndman RJ, Fan Y. Sample quantiles in statistical packages. The American Stat. 1996;50(4):361-365.
Jodra P. On order statistics from the Gompertz-Makeham distribution and the Lambert W function. Math. Mod. Anal. 2013;18(3):432-445.
Kenney JF, Keeping ES. Mathematics of Statistics, 3 Edn, Chapman & Hall Ltd, New Jersey; 1962.
Moors JJ. A quantile alternative for kurtosis. J. of the Royal Stat. Society: Series D. 1988;37:25–32.
R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria; 2019.
Dumonceaux R, Antle CE. Discrimination between the log-normal and the Weibull distributions. Technometrics. 1973;15(4):923–926.
Khan MS, King R, Hudson IL. Transmuted Kumaraswamy distribution. Statistics in Transition. 2016;17(2):183-210.
Nichols MD, Padgett WJ. A bootstrap control chart for Weibull percentiles. Quality Reliability Engineering Int. 2016;22:141-151.
Cordeiro GM, Lemonte AJ. The ß-Birnbaum-Saunders distribution: An improved distribution for fatigue life modeling. Comp. Stat. Data Anal. 2011;55:1445-1461.
Al-Aqtash R, Lee C, Famoye F. Gumbel-weibull distribution: Properties and applications. J. Modern Appl. Stat. Meth. 2014;13:201-225.
Afify AZ, Nofal WM, Butt NS. Transmuted complementary weibull geometric distribution. Pakistan J. Stat. Operat. Res. 2014;10:435-454.
Oguntunde PE, Balogun OS, Okagbue HI, Bishop SA. The Weibull-exponential distribution: Its properties and applications. J. Appl. Sci. 2015;15(11):1305-1311.
Ieren TG, Yahaya A. The Weimal distribution: Its properties and applications. J. Nigeria Ass. Math. Physics. 2017;39:135-148.
Afify MZ, Yousof HM, Cordeiro GM, Ortega EMM, Nofal ZM. The Weibull Frechet distribution and its applications. J. Appl. Stat. 2016;1-22.