In this paper, classical as well as Bayesian estimation of stress strength reliability of Dagum distribution under progressive type-II censored sample is done. Maximum likelihood estimators (MLEs) of are also obtained along with asymptotic, bootstrap-p (boot-p) and bootstrap-t (boot-t) confidence intervals. Bayes estimators of along with highest posterior density (HPD) credible intervals based on informative and non-informative priors are also obtained. Symmetric as well as asymmetric loss functions are considered for the Bayesian estimation. Monte Carlo simulation study is carried out to check the performance of estimators. Real life data sets are considered for illustration purpose.
AhmedA. (2015). Estimation of R = P [Y < X] for the three parameter dagum distribution. Journal of Statistics: Advances in Theory and Applications, 13(2), 167–178.
2.
AhmedE.A. (2014). Bayesian estimation based on progressive type-II censoring from two-parameter bathtub-shaped lifetime model: An Markov chain Monte Carlo approach. Journal of Applied Statistics, 41(4), 752–768.
3.
AroraS.MahajanK.K., & KumariR. (2019). Bayes estimators for the reliability and hazard rate functions of Topp-Leone distribution using Type-II censored data. Communications in Statistics – Simulation and Computation. doi: 10.1080/03610918.2019.1602646.
4.
BadarM.G., & PriestA.M. (1982). Statistical aspects of Fiber and bundle strength in hybrid composites. In: HayashiT.KawatanK.UmekawaS., Eds. Progress in science and engineering composites. Tokyo: ICCM-IV; pp. 1129–1136.
5.
BalakrishnanN., & AggarwalaR. (2000). Progressive Censoring: Theory, Method and Applications. Birkhauser and Publishers, Boston, MA.
6.
BalakrishnanN., & SandhuR.A. (1995) A simple simulation algorithm for generating progressive Type II censored samples. The American Statistician, 49(2), 229–230.
7.
CalabriaR., & PulciniG. (1996). Point estimation under asymmetric loss function for left truncated exponential samples. Communications in Statistics-Theory and Methods, 25(3), 585–600.
8.
ChenM.H., & ShaoQ.M. (1999). Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics, 8(1), 69–92.
9.
CohenA.C. (1963). Progressively censored samples in life testing. Technometrics, 5(3), 327–339.
10.
DagumC. (1977). A new model for personal income distribution: Specification and estimation. Economic Applique, 30(3), 413–437.
11.
DeyS., & DeyT. (2014). On progressively censored generalized inverted exponential distribution. Journal of Applied Statistics, 41(12), 2557–2576.
12.
DeyS.Al-ZahraniB., & BasloomS. (2017). Dagum distribution: Properties and different methods of estimation. International Journal of Statistics and Probability, 6(2), 74–92.
13.
Díaz-FrancésE., & MontoyaJ.A. (2013). The simplicity of likelihood based inferences for P(X<Y) and for the ratio of means in the exponential model. Statistical Papers, 54(2), 499–522.
14.
DommaF. (2002). L’andamento della Hazard function nel modello di Dagum a tre parametri. Quaderni di Statistica, 4, 1–12.
15.
DommaF.GiordanoS., & ZengaM.M. (2011). Maximum likelihood estimation in Dagum distribution with censored sample. Journal of Applied Statistics, 38(12), 2971–2985.
16.
DommaF.LatorreG., & ZengaM. (2011). Reliability studies of the Dagum distribution. Working Paper No. 207, Department of Quantitative Methods for Economics and Business, University of Milan – Bicocca, Italy.
17.
DubeM.GargR., & KrishnaH. (2016). On progressively first failure censored Lindley distribution. Computational Statistics, 31(1), 139–163.
18.
EfronB. (1982). The jackknife, the bootstrap and other re-sampling plans, CBMS-NSF Regional Conference Series in Applied Mathematics Society. Philadelphia: SIAM 38.
19.
FernandezJ.A. (2004). On estimating exponential parameters with general type-II progressive censoring. Journal of Statistical Planning and Inference, 121(1), 135–147.
20.
GunasekeraS. (2015). Generalized inferences of R=Pr(X>Y) for Pareto distribution. Statistical Papers, 56(2), 333–351.
21.
HallP. (1988). Theoretical comparison of bootstrap confidence intervals. Annals of Statistics, 16(3), 927–953.
22.
HastingsW.K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), 97–109.
23.
JiangL., & WongA.C.M. (2008). A note on inference for P(X<Y) for right truncated exponentially distributed data. Statistical Papers, 49(4), 637–651.
24.
KimC., & ChungY. (2006). Bayesian estimation of P(Y<X) from Burr-type X model containing spurious observations. Statistical Papers, 47(4), 643–651.
25.
KleiberC. (2008). A guide to the Dagum distributions. In Modeling Income Distributions and Lorenz Curves, 97–117. Springer New York.
26.
KrishnaH., & KumarK. (2013). Reliability estimation in generalized inverted exponential distribution with progressively type II censored sample. Journal of Statistical Computation and Simulation, 83(6), 1007–1019.
27.
KumariR.MahajanK.K., & AroraS. (2019). Bayesian Estimation of Stress Strength Reliability using Upper Record Values from Generalised Inverted Exponential Distribution. International Journal of Mathematical, Engineering and Management Sciences, 4(4), 882–894.
28.
KunduD., & GuptaR.D. (2006). Estimation of R = P (Y < X) for Weibull distributions. IEEE Transactions on Reliability, 55(2), 270–280.
29.
MetropolisN.RosenbluthA.W.RosenbluthM.N., & TellerA.H. (1953). Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 21(6), 1087–1092.
30.
NadarM., & KızılaslanF. (2014). Classical and Bayesian estimation of P(X<Y) using upper record values from Kumaraswamy’s distribution. Statistical Papers, 55(3), 751–783.
31.
OluyedeB.O., & YeY. (2014). Weighted Dagum and related distributions. Afrika Matematika, 25(4), 1125–1141.
32.
RastogiM.K.TripathiY.M., & WuS.J. (2012). Estimating the parameters of a bathtub-shaped distribution under progressive type-II censoring. Journal of Applied Statistics, 39(11), 2389–2411.
33.
ShahzadM.N., & AsgharZ. (2013). Comparing TL-Moments, L-Moments and Conventional Moments of Dagum Distribution by Simulated data. Revista Colombiana de Estadistica, 36(1), 79–93.
34.
TianY.ZhuQ., & TianM. (2014). Inference for mixed generalized exponential distribution under progressively type-II censored samples. Journal of Applied Statistics, 41(3), 660–676.
