The Power Lomax-Generated Family of Distributions

Konkanok  Prapasawas; Winai  Bodhisuwan; Andrei  Volodin; Sirinapa  Aryuyuen

Authors

Konkanok Prapasawas Department of Statistics, Faculty of Science, Kasetsart University, Bangkok, Thailand
Winai Bodhisuwan Department of Statistics, Faculty of Science, Kasetsart University, Bangkok, Thailand
Andrei Volodin Department of Mathematics and Statistics, University of Regina, Regina, Canada
Sirinapa Aryuyuen Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, Pathum Thani, Thailand

Keywords:

T-X family, power Lomax generated family, power Lomax-normal, power LomaxWeibull, power Lomax-beta, maximum likelihood estimation

Abstract

In this paper, a family of distributions named the power Lomax-generated family is presented. It is derived from the T-X family by using the power Lomax as its generator. Some distributions are derived from the proposed family, such as the power Lomax-normal, power Lomax-Weibull, and power Lomax-beta distributions. Various properties of the proposed family, including the quantile function, skewness, kurtosis, order statistics, and moments, are provided. The maximum likelihood (ML) method is used to estimate the parameters of the proposed distribution. Moreover, the simulation study demonstrates how well the ML method performs when estimating the parameters of some submodels in the proposed family, such as the power Lomax-Weibull distribution. Finally, real data sets are utilized to showcase the practicality of this newly established family.

References

Abramowitz M, Stegun IA. Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables. Applied mathematics series. Dover Publications, 1965. ISBN 9780486612720.

Alizadeh M, Cordeiro GM, Bastos PLG, Ghosh I. The Gompertz-G family of distributions. J Stat Theory Pract. 2017; 11(1): 179-207.

Alzaatreh A, Lee C, Famoye F. A new method for generating families of continuous distributions. Metron. 2013; 71(1): 63-79.

Alzaatreh A, Ghosh I. On the Weibull-X family of distributions. J Stat Theory Appl. 2015; 14(2): 169-183.

Aryuyuen S, Bodhisuwan W, Ngamkham T. Power Garima-generated family of distributions: properties and application. Lobachevskii J Math. 2021; 42(2): 287-299.

Elbatal IA, Helal TS, Elsehetry AM, Elshaarawy RS. Topp-Leone Weibull generated family of distributions with applications. J Bus Environ Sci. 2022; 1(1): 183-195.

Eugene N, Lee C, Famoye F. Beta-normal distribution and its applications. Commun Stat Theory. 2002; 31(4): 497-512.

Fonseca MB, Franca MGC. A influoencia da fertilidade do solo e caracterizacao da fixacao biologica de N2 para o crescimento de Dimorphandra wilsonii rizz, Master Thesis, Universidade Federal de Minas Gerais, Brazil, 2007.

Gradshteyn IS and Ryzhik IM. Table of Integrals, Series and Products. 7th ed. USA: Elsevier; 2007.

Hand DJ, Daly F, McConway K, Lunn D, Ostrowski E. A Handbook of Small Data Sets. CRC Press.

p.69.

Johnson NL, Kotz S, Balakrishnan N. Beta Distributions. In: Continuous Univariate Distributions. 2nd ed. New York, NY: John Wiley and Sons. 1994; 210-275.

Kenney JF, Keeping ES. Mathematics of Statistics. Princeton: Chapman & Hall; 1962.

Lee E, Wang J. Statistical Methods for Survival Data Analysis, 3rd ed. Wiley, New York, 2003.

Marinho PRD, Bourguignon M, Dias CRB. R-package Adequacy Model. https://cran.rproject.org/web/packages/AdequacyModel//AdequacyModel.pdf.

Moors AJ. A quantile alternative for kurtosis. J R Stat Soc. 1998; 37: 25-32.

Rady El-A, Hassanein WA, Elhaddad TA. The power Lomax distribution with an application to bladder cancer data. SpringerPlus. 2016; 5(1): 1-22.

R Core Team. R: A language and environment for statistical computing. R foundation for statistical

computing. Vienna: Austria; 2020.

Silva RB, Pereira MB, Dias CRB, Cordeiro GM. The compound class of extended Weibull power series distributions. Comput Stat Data An. 2013; 58: 352-367.

Verbeke J, Cools R. The Newton-Raphson method. Int J Math Educ Sci Technol. 1995; 26(2): 177-

Watthanawisut A, Bodhisuwan W, Supapakorn T. The beta Topp-Leone generated family of distributions and theirs applications. Thail Stat. 2022; 20(3): 489-507.

Zubair A. The Zubair-G family of distributions: properties and applications. Ann Data Sci. 2020; 7(2): 195-208.