On the Estimation of Parameters and Reliability Functions of a New Two-Parameter Lifetime Distribution based on Type II Censoring
Keywords:Maximum likelihood estimators, Bayes estimators, Non-informative prior, Lindley's approximation, Type II censoring scheme , Squared error loss function, LINEX loss function
We consider here the generalization of the Bilal distribution proposed by Abd-Elrahman (2017) by zeroing in on two measures of reliability, R(t) and P, based on type II censoring. We obtain point estimators namely, λ and θ, of the above said distribution, when both parameters of the distribution are unknown. Maximum likelihood estimators (MLEs), Bayes estimators (BEs) and Lindley’s approximation for the Bayes estimators are proposed. By using independent noninformative type of priors for the unknown parameters Bayes estimators are derived. Although the proposed estimators cannot be expressed in closed forms, these can be easily obtained through the use of numerical procedures. The performance of these estimators is studied on the basis of their mean squared error (MSE), computed separately under LINEX loss function (LLF) and squared error loss function (SELF) through Monte-Carlo simulation technique.
A. M. ABD-ELRAHMAN (2013). Utilizing ordered statistics in lifetime distributions production: A new lifetime distribution and applications. Journal of Probability and Statistical Science, 11, no. 2, pp. 153–164.
A. M. ABD-ELRAHMAN (2017). A new two-parameter lifetime distribution with decreasing, increasing or upside-down bathtub-shaped failure rate. Communications in Statistics - Theory and Methods, 46, no. 18, pp. 8865–8880.
H. AKAIKE (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, no. 6, pp. 716–723.
M. BADER, A. PRIEST (1982). Statistical aspects of fibre and bundle strength in hybrid composites. Progress in Science and Engineering of Composites, pp. 1129–1136.
J. O. BERGER (1985). Statistical Decision Theory and Bayesian Analysis. Springer, New York.
A.CHATURVEDI, S.-B. KANG, A. PATHAK (2016). Estimation and testing procedures for the reliability functions of generalized half logistic distribution. Journal of The Korean Statistical Society, 45, no. 2, pp. 314–328.
A.CHATURVEDI, T.KUMARI (2015). Estimation and testing procedures for the reliability functions of a family of lifetime distributions. InterStat. URL http://interstat. statjournals.net/YEAR/2015/abstracts/1504001.php.
A.CHATURVEDI, T.KUMARI (2017). Estimation and testing procedures for the reliability functions of a general class of distributions. Communications in Statistics - Theory and Methods, 46, no. 22, pp. 11370–11382.
A. CHATURVEDI, T. KUMARI (2019). Estimation and testing procedures of the reliability functions of generalized inverted scale family of distributions. Statistics, 53, no. 1, pp. 148–176.
A. CHATURVEDI, A. PATHAK (2012). Estimation of the reliability function for exponentiated Weibull distribution. Journal of Statistics and Applications, 7, no. 3/4, p.113.
B. GEP, G. TIAO (1973). Bayesian Inference in Statistical Analysis. Addison-Wesley, Reading.
N. JOHNSON, S. KOTZ, N. BALAKRISHNAN (1994). Continuous Univariate Distributions. John Wiley and Sons, New York, 2nd ed.
S. KOTZ, Y. LUMELSKII, M. PENSKY (2003). The Stress-Strength Model and its Generalizations: Theory and Applications. World Scientific, Singapore.
K. KUMAR, R. GARG, H. KRISHNA (2017). Nakagami distribution as a reliability model under progressive censoring. International Journal of System Assurance Engineering and Management, 8, no. 1, pp. 109–122.
J. F. LAWLESS (1982). Statistical Methods for Lifetime Data. Wiley, New York.
J. F. LAWLESS (2003). Statistical Models and Methods for Lifetime Data. Wiley, New York.
D. V. LINDLEY (1980). Approximate Bayesian methods. Trabajos de estadística y de investigación operativa, 31, no. 1, pp. 223–245.
N. R. MANN, N. D. SINGPURWALLA, R. E. SCHAFER (1974). Methods for Statistical Analysis of Reliability and Life Data. Wiley.
H. F. MARTZ, R.WALLER (1982). Bayesian Reliability Analysis. Wiley, New York.
W. NELSON (1982). Applied Life Data Analysis. John Wiley & Sons, Inc., New York.
M. Z. RAQAB, M. T. MADI, D. KUNDU (2008). Estimation of p(y < x) for the three parameter generalized exponential distribution. Communications in Statistics—Theory and Methods, 37, no. 18, pp. 2854–2864.
H. A. SCHAFFT, T. C. STATON, J. MANDEL, J. D. SHOTT (1987). Reproducibility of electromigration measurements. IEEE Transactions on Electron Devices, 34, no. 3, pp. 673–681.
G. SCHWARZ (1978). Estimating the dimension of a model. The Annals of Statistics, 6, no. 2, pp. 461–464.
P. SINGH, S. K. SINGH, U. SINGH (2008). Bayes estimator of inverse Gaussian parameters under general entropy loss function using Lindley’s approximation. Communications in Statistics — Simulation and Computation, 37, no. 9, pp. 1750–1762.
S. K. SINGH, U. SINGH, D. KUMAR (2013). Bayesian estimation of parameters of inverse Weibull distribution. Journal of Applied Statistics, 40, no. 7, pp. 1597–1607.
S. K. SINHA (1986). Reliability and Life Testing. Wiley Eastern Ltd., Delhi, India.
H. R. VARIAN (1975). A Bayesian Approach to Real Estate Assessment. North Holland, Amsterdam.
A. ZELLNER (1986). Bayesian estimation and prediction using asymmetric loss functions. Journal of the American Statistical Association, 81, no. 394, pp. 446–451.
How to Cite
Copyright (c) 2021 Statistica
This work is licensed under a Creative Commons Attribution 3.0 Unported License.