Document Type : Original Paper
Authors
1 Dept. of Statistics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran
2 Dept. Statistics, Mathematical Sciences and computer college, Shahid Chamran university of Ahvaz, Ahvaz, Iran
Abstract
We introduce a method to generate a new class of lifetime models based on the bounded distributions such that the defined models are exclusively a special case of the new class. A new subfamily, Generalized Alpha Power (GAP) is discussed and some stochastic orders in this subfamily are investigated to identify the proposed method effect. The performance of the maximum likelihood estimators based on the simulation is studied and in the end, the importance and flexibility of the new family for the models are illustrated by a real data set. Our results indicate that using the proposed method substantially improves the fitness of any G-family model and can be extended to any real data set. Finally, the GAPTW regression model is applied to the kidney infection data.
Keywords
- Cordeiro GM, De Castro M. A new family of generalized distributions. J. Stati. Comput. Simul.. 2011;81:883-898.
- Dey S, Sharma, VK, Mesfioui M. A new extension of Weibull distribution with application to lifetime data. Ann. Data. Sci. 2017;4:31–61.
- Keilson J, Sumita U. Uniform stochastic ordering and related inequalities. Canad. J. Stat. 1982;10:181-I98.
- Muller A, Stoyan D. Comparison Methods for Stochastic Models and Risks. 2002;Wiley, New York.
- Li X, Zuo MJ. Preservation of stochastic orders for random minima and maxima, with applications. Naval Res. Log. 2004;51:332-344.
- Zhao P. Some new results on convolutions of heterogeneous gamma random variables. J. Multivar. Anal. 2011;102:958-976.
- Mahdy M. Stochastic ordering and reliability analysis of inactivity lifetime with a cold standby. Am J. Math. Manag. Sci. 2018;DOI: 10.1080/01966324.2018.1502702.
- Shaked M and Shanthikumar JG. Stochastic orders. 2007; Springer, Berlin, Germany.
- Belzunce F. An introduction to the theory of stochastic orders. Estadistica. 2010;26,4-18.
- Belzunce F, Martínez-Riquelme C., Mulero J. An Introduction to Stochastic Orders. Elsevier Ltd; 2016.
- Giovagnoli A, Wynnb H.P. Stochastic orderings for discrete random variables. Stat. Probab. Lett. 2008;78:2827–2835.
- Yu Y. Stochastic ordering of exponential family distributions and their mixtures. J. Appl. Probab. 2009;46:244-254.
- Klenke A, Mattner L. Stochastic ordering of classical discrete distributions. Adv. Appl. Probab. 2010;42:392-410.
- Pan X, Qiu G, Hu T. Stochastic orderings for elliptical random vectors. J. Multivar. Anal. 2016;148:83-88.
- Raeisi M and Yari G. Some dependencies, stochastic orders and aging properties in an extended additive hazards model. J. Sci. Technol. Transaction A: Science. 2018;42:745–752.
- Catana, LI, Raducan A. Stochastic order for a multivariate uniform distributions family. 2020; 8, DOI: 10.3390/math8091410.
- Jones M. Kumaraswamy’s distribution: A beta-type distribution with some tractability advantages. Methodol. 2009;6:70–81.
- Eugene N, Lee C, Famoye F. Beta-normal distribution and its application. Stat. Theory. Methods. 2002;31:497–512.
- Famoye F, Lee C, Olumolade O. The beta-Weibull distribution. Stat. Theory. Appl. 2005;4:121–136.
- Nadarajah S, Kotz S. The beta-exponential distribution reliability, engineering and system safety. Eng. Syst. Saf. 2006;91:689–697.
- Akinsete A, Famoye F, Lee C. The Beta-Pareto distribution. 2008;42:547-563.
- Paranaiba PF, Ortega EMM, Cordeiro GM, Pescim RR. The beta Burr XII distribution with application to lifetime data. Comput. Stat. Data. Anal. 2011;55:1118-1136.
- Cordeiro GM, Ortega, EMM, Nadarajah S. The Kumaraswamy Weibull distribution with application to failure data. Franklin Institute. 2010;81:1399-1429.
- Pascoa AR, Ortega EMM, and Cordeiro GM. The Kumaraswamy generalized gamma distribution with application in survival analysis. Methodol 2011;8:411–433.
- Cordeiro GM, Pescim RR, Ortega, EMM. The Kumaraswamy generalized half-normal distribution for skewed positive data. Data. Sci. 2012;10: 195-224.
- Dey S, Nassar M, Kumar D. Alpha power transformed inverse Lindley distribution: A distribution with an upside-down bathtub-shaped hazard function. J. Comput. Appl. Math. 2019;348:130-45.
- Hassan AS, Elgarhy M, Mohamd RE and Alrajhi S. On the Alpha Power transformed power Lindley distribution. J. Probab. Stat. 2019;Article ID 8024769, 13 pages.
- McGilchrist CA and Aisbett CW. Regression with frailty in survival analysis. Biometrics. 1991;47(2):461-466.
- Erbay A, Ergonul O, Stoddard JS and Samore MH. Recurrent catheter-related bloodstream infections: risk factors and outcome. Int. J. Infect. Dis. 2006;10:396-400.
- Delistefani F, Wallbach M, Müller GA, Koziolek MK and Grupp C. Risk factors for catheter-related infections in patients receiving permanent dialysis catheter. BMC. Nephrol. 2019;20:199.
- Hanagal DD and Dabade AD. Comparison of Shared Frailty Models for Kidney Infection Data under Exponential Power Baseline Distribution. Commun. Stat.Theory. Methods. 2015;44: 5091–5108.
- Mahdavi A and Kundu D. A new method for generating distributions with an application to exponential distribution. Commun. Stat. Theory. Methods. 2017;46:6543-6557.
- Lehmann EL and Casella, G. The Theory of Point Estimation. 1998; Springer, USA.
|
|
- Mrsevi M. Convexity of the inverse function. Teach. Math. 2008;11:21-24.
- Boyd S, Vandenberghe L. Convex Optimization. Cambridge University Press; 2009.
- Nadarajah S, Kotz S. Strength modeling using Weibull distributions. J. Mech. Sci. Technol. 2008;22:1247-125.
- Mudholkar G, Srivastava D, Freimer M. The exponentiated Weibull family: A reanalysis of the bus-motor-failure data. 1995;37:436–445.
)