A new distribution with four parameters: Properties and applications

Abstract

In this paper, a new lifetime distribution called compounded geometric-mixture exponential distribution is proposed by compounding the mixture exponential and geometric distribu-tions. Some properties of the new distribution such as survival function, hazard function, mo-ments, Lorenz and Bonferroni curves, etc. are obtained. The estimations of four parameters of the new model are studied by several methods. A Monte Carlo simulation study is performed to understand the behavior of estimators. Two real data applications are also provided.

Keywords

• Compound Distributions
• Estimation
• Geometric
• Distribution
• Mixture Exponential Distribution

References

1. REFERENCES
2. [1] Karakaya K, Kınacı I, Kus C, Akdogan Y. A new family of distributions. Hacettepe J Math Stat 2017;46:303−314. [CrossRef]
3. [2] Tanış C, Saracoglu B, Kus C, Pekgor A, Karakaya K. Transmuted lower record type Frechet distribu-tion with lifetime regression analysis based on type I-censored data. J Stat Theory Appl 2021;20:86−96. [CrossRef]
4. [3] Kınacı I, Kus C, Karakaya K, Akdogan Y. APT-pareto distribution and its properties. Cumhuriyet Sci J 2019;40:378−387. [CrossRef]
5. [4] Karakaya K, Kınacı I, Kus C, Akdogan Y. On the DUS-kumaraswamy distribution. Istatistik J Turkish Stat Assoc 2021;13:29−38.
6. [5] Tanıs C, Saracoglu B. On the record-based trans-muted model of Balakrishnan and He based on weibull distribution. Commun Stat Simul 2022;51:1−21.
7. [6] Adamidis K, Loukas S. A lifetime distribution with decreasing failure rate. Statist Probab Lett 1998;39:35−42. [CrossRef]
8. [7] Kus C. A new lifetime distribution. Comput Stat Data Anal 2007;51:4497−4509. [CrossRef]

9. [8] Tahmasbi R, Rezaei S. A two-parameter lifetime distribution with decreasing failure rate. Comput Statist Data Anal 2008;52:3889−3901. [CrossRef]
10. [9] Bakouch HS, Ristic MM, Asgharzadeh A, Esmaily L, Al-Zahrani BM. An exponentiated exponential binomial distribution with application. Stat Probab Lett. 2012;82:1067−1081. [CrossRef]
11. [10] Barreto-Souza W, Morais AL, Cordeiro GM. The Weibull-geometric distribution. J Stat Comput Simul 2011;81:645−657. [CrossRef]
12. [11] Gupta RC, Huang J. The Weibull-Conway-Maxwell-Poisson distribution to analyze survival data. J Comput Appl Math 2017;311:171−182. [CrossRef]
13. [12] Nekoukhou V, Bidram H. A new generalization of the Weibull-geometric distribution with bath-tub failure rate. Commun Stat Theory Methods 2017;46:4296−4310. [CrossRef]
14. [13] Shi D, Lu W. A new compounding life distribu-tion: the Weibull-Poisson distribution. J Appl Stat 2012;39:21−38. [CrossRef]
15. [14] Canuto C, Hussaini MY, Quarteroni A, Zang TA. Spectral Methods: Fundamentals in Single Domains. 1st ed. New York: Springer-Verlag; 2006. [CrossRef]
16. [15] Bonferroni CE. Elmenti di statistica generale. Firenze: Libreria Seber; 1930. [Italian]
17. [16] Shaked M, Shanthikumar JG. Stochastic Orders. 1st ed. New York: Springer; 2007. [CrossRef]
18. [17] Lee E, Wang J. Statistical methods for survival data analysis. 1st ed. New York: Wiley and Sons; 2003.[CrossRef]
19. [18] Ghitany ME, Atieh B, Nadarajah S. Lindley distri-bution and its application. Math Comput Simul 2008;78:493−506. [CrossRef]
20. [19] Afify A, Yousof H, Nadarajah S. The beta trans-muted-H family for lifetime data. Stat Interface 2017;10:505−520. [CrossRef]