Estimation of the Parameters of Power Function Distribution based on Progressively Type-II Right Censoring with Binomial Removal
DOI:
https://doi.org/10.6092/issn.1973-2201/12418Keywords:
Power function distribution, Maximum likelihood distribution, Lindley approximation, Importance sampling procedure, PredictionAbstract
In this article, we proposed the estimates of unknown parameters of power function distribution in the context of progressive type-II censoring with binomial removals, where the number of units removed at each failure time follows a binomial distribution. The maximum-likelihood estimators (MLEs) for the power function parameters are derived using the expectation–maximization (EM) algorithm. EM-algorithm is also used to obtain the asymptotic variance-covariance matrix. By using the variance-covariance matrix of the MLEs, the asymptotic 950=0 confidence interval for the parameters are constructed. Bayes estimators under different loss functions are obtained using the Lindley approximation method and importance sampling procedure. We also introduced one and two sample prediction estimates and corresponding confidence intervals by using Bayesian techniques. To compare performance of the proposed estimators, we introduced simulation and real-life data studies.
References
N. BALAKRISHNAN (2007). Progressive censoring methodology: an appraisal. Test, 16, no. 2, p. 211–259.
N. BALAKRISHNAN, R. AGGARWALA (2000). Progressive Censoring: Theory, Methods, and Applications. Springer Science & Business Media, Boston.
N. BALAKRISHNAN, E. CRAMER (2014). The Art of Progressive Censoring. Statistics for Industry and Technology, Springer, New York.
R. CALABRIA, G. PULCINI (1996). Point estimation under asymmetric loss functions for left-truncated exponential samples. Communications in Statistics, Theory and Methods, 25, no. 3, pp. 585–600.
A. CHATURVEDI, N. KUMAR, K. KUMAR (2018). Statistical inference for the reliability functions of a family of lifetime distributions based on progressive type-II right censoring. Statistica, 78, no. 1, pp. 81–101.
M.-H. CHEN, Q.-M. SHAO (1999). Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics, 8, no. 1, pp. 69–92.
A. P. DEMPSTER, N. M. LAIRD, D. B. RUBIN (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B - Methodological, 39, no. 1, pp. 1–22.
S. DEY, T. KAYAL, Y. M. TRIPATHI (2018). Statistical inference for the Weighted Exponential distribution under progressive type-II censoring with binomial removal. American Journal of Mathematical and Management Sciences, 37, no. 2, pp. 188–208.
R. HASHEMI, L. AMIRI (2011). Analysis of progressive type-II censoring in the Weibull model for competing risks data with binomial removals. Applied Mathematical Sciences, 5, no. 22, pp. 1073–1087.
W. K. HASTINGS (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 357, no. 1, pp. 97–109.
D. V. LINDLEY (1980). Approximate Bayesian methods. Trabajos de Estadística y de Investigación Operativa, 31, no. 1, pp. 223–245.
M.MENICONI, D. M. BARRY (1996). The Power function distribution: a useful and Simple distribution to assess electrical component reliability. Microelectronics Reliability, 36, no. 9, pp. 1207–1212.
N. METROPOLIS, A. W. ROSENBLUTH, M. N. ROSENBLUTH, A. H. TELLER, E. TELLER (1953). Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 21, no. 6, pp. 1087–1092.
H. K. T. NG, P. S. CHAN, N. BALAKRISHNAN (2002). Estimation of parameters from Progressively censored data using EM algorithm. Computational Statistics & Data Analysis, 39, no. 4, pp. 371–386.
A. M. SARHAN, A. ABUAMMOH (2008). Statistical inference using progressively type-II censored data with random scheme. International Mathematical Forum, 35, no. 3, pp. 1713–1725.
S. K. TSE, C. YANG, H.-K. YUEN (2000). Statistical analysis of Weibull distributed lifetime data under type-II progressive censoring with binomial removals. Journal of Applied Statistics, 27, no. 8, pp. 1033–1043.
H. R. VARIAN (1975). A Bayesian approach to real estate assessment. In S. E. F. L. J. SAVAGE, A. ZELLNER (eds.), Studies in Bayesian econometric and Statistics in Honor of L. J. Savage, North-Holland Pub. Co., Amsterdam, pp. 195–208.
S.-J. WU, C.-T. CHANG (2002). Parameter estimations based on exponential progressive type-II censored data with binomial removals. International Journal of Information and Management Sciences, 13, no. 3, pp. 37–46.
S.-J. WU, C.-T. CHANG (2003). Inference in the Pareto distribution based on progressive type-II censoring with random removals. Journal of Applied Statistics, 30, no. 2, pp. 163–172.
W. YAN, S. H. I. YIMIN, B. SONG., Z.M A O. (2011). Statistical analysis of generalized exponential distribution under progressive censoring with binomial removals. Journal of Systems Engineering and Electronics, 22, no. 4, pp. 707–714.
H.-K. YUEN, S.-K. TSE (1996). Parameters estimation for Weibull distributed lifetimes under progressive censoring with random removeals. Journal of Statistical Computation and Simulation, 55, no. 1-2, pp. 57–71.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Statistica
This work is licensed under a Creative Commons Attribution 3.0 Unported License.
