Browse > Article
http://dx.doi.org/10.29220/CSAM.2019.26.4.385

Classical and Bayesian studies for a new lifetime model in presence of type-II censoring  

Goyal, Teena (Department of Mathematics & Statistics, Banasthali Vidyapith)
Rai, Piyush K (Department of Statistics, Banaras Hindu University)
Maury, Sandeep K (Department of Mathematics & Statistics, Banasthali Vidyapith)
Publication Information
Communications for Statistical Applications and Methods / v.26, no.4, 2019 , pp. 385-410 More about this Journal
Abstract
This paper proposes a new class of distribution using the concept of exponentiated of distribution function that provides a more flexible model to the baseline model. It also proposes a new lifetime distribution with different types of hazard rates such as decreasing, increasing and bathtub. After studying some basic statistical properties and parameter estimation procedure in case of complete sample observation, we have studied point and interval estimation procedures in presence of type-II censored samples under a classical as well as Bayesian paradigm. In the Bayesian paradigm, we considered a Gibbs sampler under Metropolis-Hasting for estimation under two different loss functions. After simulation studies, three different real datasets having various nature are considered for showing the suitability of the proposed model.
Keywords
LTE distribution; Gibbs sampler; M-H algorithm; Bootstrap confidence interval; HPD interval;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Aarset MV (1987). How to identify a bathtub hazard rate, IEEE Transactions on Reliability, 36, 106-108.   DOI
2 Aryal GR and Tsokos CP (2009). On the transmuted extreme value distribution with application, Nonlinear Analysis: Theory, Methods & Applications, 71, e1401-e1407.   DOI
3 Balakrishnan N and Cohen AC (2014). Order Statistics and Inference: Estimation Methods, Elsevier.
4 Box GEP and Tiao GC (1973). Bayesian Inference in Statistical Analysis, Addison-Wesley, Massachusetts.
5 Carpenter J and Bithell J (2000). Bootstrap confidence intervals: when, which, what? A practical guide for medical statisticians, Statistics in Medicine, 19, 1141-1164.   DOI
6 Chen MH and Shao QM (1999). Monte Carlo estimation of Bayesian credible and HPD intervals, Journal of Computational and Graphical Statistics, 8, 69-92.   DOI
7 Chen Z (2000). A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function, Statistics & Probability Letters, 49, 155-161.   DOI
8 Chib S and Greenberg E (1995). Understanding the metropolis-hastings algorithm, The American Statistician, 49, 327-335.   DOI
9 Choulakian V and Stephens MA (2001). Goodness-of-fit tests for the generalized Pareto distribution, Technometrics, 43, 478-484.   DOI
10 Cohen AC (1965). Maximum likelihood estimation in theWeibull distribution based on complete and on censored samples, Technometrics, 7, 579-588.   DOI
11 Cordeiro GM, Ortega EMM, da Cunha DCC (2013). The exponentiated generalized class of distributions, Journal of Data Science, 11, 1-27.   DOI
12 Edwards W, Lindman H, and Savage LJ (1963). Bayesian statistical inference for psychological research., Psychological Review, 70, 193.   DOI
13 Davison AC and Hinkley DV (1997). Bootstrap Methods and Their Application, Cambridge university press, Cambridge.
14 Dey S, Nassar M, and Kumar D (2017). ${\alpha}$ logarithmic transformed family of distributions with application, Annals of Data Science, 4, 457-482.   DOI
15 Dey S, Nassar M, Kumar D, and Alaboud F (2019). Alpha logarithmic transformed Frechet distribution: properties and estimation, Austrian Journal of Statistics, 48, 70-93.   DOI
16 Efron B (1979). Bootstrap methods: another look at the jackknife, The Annals of Statistics, 7, 1-26.   DOI
17 Efron B (1982). The Jackknife, the Bootstrap, and other Resampling Plans, 38, Siam.
18 Efron B and Tibshirani RJ (1994). An Introduction to the Bootstrap, CRC press, Florida.
19 Evans IG and Ragab AS (1983). Bayesian inferences given a type-2 censored sample from a Burr distribution, Communications in Statistics-Theory and Methods, 12, 1569-1580.   DOI
20 Gelfand AE and Smith AFM (1990). Sampling-based approaches to calculating marginal densities, Journal of the American Statistical Association, 85, 398-409.   DOI
21 Geman S and Geman D (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.   DOI
22 Glaser RE (1980). Bathtub and related failure rate characterizations, Journal of the American Statistical Association, 75, 667-672.   DOI
23 Hastings WK (1970). Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57, 97-109.   DOI
24 Singh SK, Singh U, and Kumar M (2016). Bayesian estimation for Poisson-exponential model under progressive type-ii censoring data with binomial removal and its application to ovarian cancer data, Communications in Statistics-Simulation and Computation, 45, 3457-3475.   DOI
25 Singh U, Gupta PK, and Upadhyay SK (2005). Estimation of parameters for exponentiated-Weibull family under type-II censoring scheme, Computational Statistics & Data Analysis, 48, 509-523.   DOI
26 Graham RL, Knuth DE, and Patashnik O (1994). Concrete Mathematics: A Foundation for Computer Science (2nd ed), Addison-Wesley, Mass.
27 Gupta RC, Gupta PL, and Gupta RD (1998). Modeling failure time data by Lehman alternatives, Communications in Statistics-Theory and Methods, 27, 887-904.   DOI
28 Gupta RD and Kundu D (2001). Exponentiated exponential family: an alternative to gamma and Weibull distributions, Biometrical Journal: Journal of Mathematical Methods in Biosciences, 43, 117-130.   DOI
29 Hjorth U (1980). A reliability distribution with increasing, decreasing, constant and Bathtub-Shaped failure rates, Technometrics, 22, 99-107.   DOI
30 Kumaraswamy P (1980). A generalized probability density function for double-bounded random processes, Journal of Hydrology, 46, 79-88.   DOI
31 Kundu D and Howlader H (2010). Bayesian inference and prediction of the inverse Weibull distribution for Type-II censored data, Computational Statistics & Data Analysis, 54, 1547-1558.   DOI
32 Lawless JF (2011). Statistical Models and Methods for Lifetime Data, JohnWiley & Sons, New York.
33 Maurya SK, Kumar D, Singh SK, and Singh U (2018). One parameter decreasing failure rate distribution, International Journal of Statistics & Economics, 19, 120-138.
34 Smith AFM and Roberts GO (1993). Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods, Journal of the Royal Statistical Society. Series B (Methodological), 55, 3-23.   DOI
35 Tierney L (1994). Markov chains for exploring posterior distributions, The Annals of Statistics, 22, 1701-1728.   DOI
36 Varian HR (1975). A Bayesian approach to real estate assessment, Studies in Bayesian Econometric and Statistics in honor of Leonard J. Savage, 195-208, North Holland.
37 Leiva V, Athayde E, Azevedo C, and Marchant C (2011). Modeling wind energy flux by a Birnbaum-Saunders distribution with an unknown shift parameter. Journal of Applied Statistics, 38, 2819-2838.   DOI
38 Lindley DV (1958). Fiducial distributions and Bayes' theorem, Journal of the Royal Statistical Society. Series B (Methodological), 20, 102-107.   DOI
39 Maurya SK, Kaushik A, Singh RK, Singh SK, and Singh U (2016). A new method of proposing distribution and its application to real data, Imperial Journal of Interdisciplinary Research, 2, 1331-1338.
40 Maurya SK, Kaushik A, Singh SK, and Singh U (2017). A new class of distribution having decreasing, increasing and bathtub-shaped failure rate, Communications in Statistics-Theory and Methods, 46, 10359-10372.   DOI
41 Merovci F, Elbatal I, and Ahmed A (2013). Transmuted Generalized Inverse Weibull Distribution, arXiv preprint arXiv:1309.3268.
42 Merovci F and Puka L (2014). Transmuted Pareto distribution, ProbStat Forum, 7, 1-11.
43 Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, and Teller E (1953). Equation of state calculations by fast computing machines, The Journal of Chemical Physics, 21, 1087-1092.   DOI
44 Metropolis N and Ulam S (1949). The Monte Carlo method, Journal of the American Statistical Association, 44, 335-341.   DOI
45 Mudholkar GS and Srivastava DK (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data, IEEE Transactions on Reliability, 42, 299-302.   DOI
46 Murthy DNP, Xie M, and Jiang R (2004). Weibull Models, John Wiley & Sons, Hoboken.
47 Nadarajah S, Bakouch HS, and Tahmasbi R (2011). A generalized Lindley distribution, Sankhya B, 73, 331-359.   DOI
48 Nadarajah S and Kotz S (2006). The exponentiated type distributions, Acta Applicandae Mathematica, 92, 97-111.   DOI
49 Nelson WB (2003). Recurrent Events Data Analysis for Product Repairs, Disease Recurrences, and other Applications (Volume 10), SIAM, London.
50 Nassar M, Afify AZ, Dey S, and Kumar D (2018). A new estension ofWeibull distribution: Properties and different methods of estimation, Journal of Computational and Applied Mathematics, 335, 1-18.   DOI
51 Pappas V, Adamidis K, and Loukas S (2012). A family of lifetime distributions, International Journal of Quality, Statistics, and Reliability, 2012, 1-6.
52 Peter H (1988). Theoretical comparision of Bootstrap confidence intervals, The Annals of Statistics, 16, 927-953.   DOI
53 Robert C and Casella G (2013). Monte Carlo Statistical Methods, Springer Science & Business Media.
54 Shannon CE (1951). Prediction and entropy of printed English, Bell System Technical Journal, 30, 50-64.   DOI
55 Shaw WT and Buckley IRC (2007). The Alchemy of Probability Distribution: Beyond Gram-Charlier Cornish-Fisher Expansions, and Skew-Normal and Kurtotic-Normal Distribution (Research report).
56 Sinha SK (1987). Bayesian estimation of the parameters and reliability function of a mixture of Weibull life distributions, Journal of Statistical Planning and Inference, 16, 377-387.   DOI
57 Singh SK, Singh U, and Kumar M (2013). Estimation of Parameters of Exponentiated Pareto Model for Progressive Type-II Censored Data with Binomial Removals Using Markov Chain Monte Carlo Method, International Journal of Mathematics & Computation, 21, 88-102.