Pareto-Rayleigh (PR) distribution (a member of Pareto-X family proposed in ) is considered here to study. The estimated values of the model parameters are derived by the maximum likelihood estimation process. Different important properties of the introduced distribution are obtained. Four real-life applications are studied from various fields to evaluate the applicability of proposed PR model. An exclusive simulation has been conducted to observe the performance of the estimation technique. Finally, it is shown that the better fitness of newly developed model than others chosen models selected in this study.
Rana MS, Shahbaz MQ, Rahman MM. Pareto-Weibull Distribution with Properties and Applications: A Member of Pareto-X Family. Pakistan Journal of Statistics and Operation Research. 2022; 18(1): 121-132.
Steiner P. XXV. Vilfredo Pareto et l’e ́conomie politique walrasienne. Nouvelle histoire de la pense ́e e ́conomique. La De ́couverte. 1993; 2: 498-521.
Akinsete A, Famoye F, Lee C. The beta-Pareto distribution. Statistics. 2008; 42(6): 547-563.
Alzaatreh A, Famoye F, Lee C. Gamma-Pareto distribution and its applications. Journal of Modern Applied Statistical Methods. 2012; 11(1): 7.
Bourguignon M, Silva RB, Zea LM, Cordeiro GM. The Kumaraswamy Pareto distribution. J. Stat. Theory Appl. 2013; 12(2): 129-144.
Alzaatreh A,Famoye F,Lee C.Weibull-Paretodistributionanditsapplications.Communications in Statistics Theory and Methods. 2013; 42(9): 1673-1691.
Tahir MH, Cordeiro GM, Alzaatreh A, Mansoor M, Zubair M. A new Weibull–Pareto distribution: properties and applications. Communications in Statistics-Simulation and Computation. 2016; 45(10): 3548-3567.
Al-Kadim, KA, Mohammed, BDA. Rayleigh pareto distribution. Journal of University of Babylon for Pure and Applied Sciences. 2018; 26(1): 84-95.
Rahman MM, Al-Zahrani B, Shahbaz MQ. Cubic transmuted Pareto distribution. Annals of Data Science. 2020; 7(1): 91-108.
Benatmane C, Zeghdoudi H, Shanker R, Lazri N. Composite Rayleigh-Pareto distribution: Application to real fire insurance losses data set. Journal of Statistics and Management Systems. 2021; 24(3): 545-557.
Alzaatreh A, Lee C, Famoye F. A new method for generating families of continuous distributions. Metron. 2013; 71(1): 63-79.
Waseem N, Bashir S. On generating T-X family of Pareto-exponential distribution with properties and applications. International Journal of Applied Mathematics & Statistics. 2019; 58(3): 90-106.
G Prasad, R Subba Rao, RRL Kantam. Limited Failure Censored Life Test Sampling Plan: Pareto-Rayleigh Model. International Journal of Engineering and Technology, IJET. 2018; 136–140.
Zwillinger D, Jeffrey A. Table of integrals, series, and products. Elsevier. 2007.
Ebeling CE. An introduction to reliability and maintainability engineering. Tata McGraw-Hill Education. 2004.
Carpenter M. Survival analysis: a self-learning text. Taylor & Francis. 1997.
Aryal GR, Tsokos CP. Transmuted Weibull distribution: A generalization of the Weibull probability distribution. European Journal of pure and applied mathematics. 2011; 4(2): 89-102.
Al-Kadim KA Mahdi AA. Exponentiated transmuted exponential distribution. Journal of University of Babylon for Pure and Applied Sciences. 2018; 26(2): 78-90.
Mohammed AS, Ugwuowo FI. The trunsmuted exponential-exponential distribution with application to breast cancer data. Pak. J. Statist. 2021; 37(1): 1-18.
Ijaz M, Asim SM. Lomax exponential distribution with an application to real-life data. PloS one. 2019; 14(12): e0225827.
Murthy and Xie, Jiang. Weibull model. 2004; John Wiley and Sons
Vijay R, Sundaresan R, Maiya MP, Murthy SS, Fu Y, Klein HP, Groll M. Characterisation of Mg–x wt. FeTi (x= 5–30) and Mg–40 wt. FeTiMn hydrogen absorbing materials prepared by mechanical alloying. Journal of alloys and compounds. 2004; 384(1-2): 283-295.
Kim CS, Djamaludin I, Murthy DNP. Warranty and discrete preventive maintenance. Reliability Engineering and System Safety. 2004; 84(3): 301-309.
Choulakian V, Stephens MA. Goodness-of-fit tests for the generalized Pareto distribution. Technometrics. 2001; 43(4): 478-484.
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