On Hybrid Censored Inverse Lomax Distribution: Application to the Survival Data
DOI:
https://doi.org/10.6092/issn.1973-2201/5993Keywords:
Parameters estimation, hybrid censoring, MCMC methodAbstract
In this paper, we proposed the estimation procedures to estimate the unknown parameters, reliability and hazard functions of Inverse Lomax distribution. The mathematical expressions for maximum likelihood and Bayes estimators are derived in presence of hybrid censoring scheme. In most of the cases, it has been seen that maximum likelihood and Bayes estimators of the parameters are not appear in explicit form. Hence, Newton-Raphson (N-R) method has been used to draw the maximum likelihood estimates of the parameters. The Bayes estimators are obtained under Jeffrey's non-informative prior for both shape and scale using Markov Chain Monte Carlo (MCMC) technique. Further, we have also constructed the 95% asymptotic confidence interval based on maximum likelihood estimates (MLEs) and highest posterior density (HPD) credible intervals based on MCMC samples. Finally, two data sets have been used to demonstrate the proposed methodology.References
A. BANERJEE, D. KUNDU (2008). Inference based on type-ii hybrid censored data from a weibull distribution. IEEE Trans. Reliab., 57, pp. 369–378.
B. CHANDRASEKAR, T. L. ALEXANDER, N. BALAKRISHNAN (2002). Equivariant estimation for parameters of lomax distributions based type-ii progressively censored samples. Communications in Statistics: Theory and Methods, 31, no. 10, pp. 1675–1686.
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.
S. CHEN, G. K. BHATTACHARYA (1988). Exact con dence bounds for an exponential parameter under hybrid censoring. Comm. Statist. Theory and Method, 17, pp. 1857–1870.
A. CHILDS, B. CHANDRASEKHAR, N. BALAKRISHNAN, D. KUNDU (2003). Exact likelihood inference based on type-i and type-ii hybrid censored samples from the exponential distribution. Ann. Instit. Statist. Math., 55, pp. 319–330.
N. DRAPER, I. GUTTMAN (1987). Bayesian analysis of hybrid life tests with exponential failure times. Ann. Inst. Statist. Math., 39, pp. 219–225.
S. DUBE, B. PRADHAN, D. KUNDU (2011). Parameter estimation of the hybrid censored log-normal distribution. J. Statist. Comput. Simul., 81, pp. 275–287.
N. EBRAHIMI (1990). Estimating the parameter of an exponential distribution from hybrid life test. J. Statist. Plann. Inference., 23, pp. 255–261.
B. EPSTEIN (1954). Truncated life test in exponential case. Ann. Math. Statistics, 25, pp. 555–564.
K. FAIRBANKS, R. MADSON, R. DYKSTRA (1982). A confidence interval for an exponential parameter from a hybrid life test. J. Amer. Statist. Assoc., 77, pp. 137–140.
S. GEMAN, A. GEMAN (1984). Stochastic relaxation, gibbs distributions and the bayesian restoration of images. IEEE Trans. Pattern Analysis and Machine Intelligence, 6, pp. 721–740.
R. D. GUPTA, D. KUNDU (1998). Hybrid censoring schemes with exponential failure distribution. Communications in Statistics: Theory and Method, 27, pp. 3065–3083.
W. K. HASTINGS (1970). Monte carlo sampling methods using Markov chains and their applications. Biometrika, 57, no. 1.
C. KLEIBER (2004). Lorenz ordering of order statistics from log-logistic and related distributions. Journal of Statistical Planning and Inference, 120, pp. 13–19.
C. KLEIBER, S. Kotz (2003). Statistical size distributions in economics and actuarial sciences. John Wiley & Sons, Inc., Hoboken, New Jersey.
D. KUNDU, B. PRADHAN (2009). Estimating the parameters of the generalized exponential distribution in presence of hybrid censoring. Communications in Statistics: Theory and Method, 38, pp. 2030–2041.
E. T. LEE, J. W. WANG (2003). Statistical Methods for Survival Data Analysis. 3rd ed.,Wiley, NewYork.
MIL-STD-781-C (1977). Reliability design qualification and production acceptance test, exponential distribution. U.S. Government Printing Office, Washington, D.C.
J. RAHMAN, M. ASLAM, S. ALI (2013). Estimation and prediction of inverse lomax model via bayesian approach. Caspian Journal of Applied Sciences Research, 2(3), pp. 43–56.
S. K. SINGH, U. SINGH, D. KUMAR (2012). Bayes estimators of the reliability function and parameters of inverted exponential distribution using informative and non-informative priors. Journal of Statistical computation and simulation, 83, no. 12, pp. 2258–2269.
A. F. M. SMITH, G. O. ROBERTS (1993). Bayesian computation via the gibbs sampler and related markov chain monte carlo methods. Journal of the Royal Statistical Society Series B, 55, no. 1.
S. UPADHYAY, N. VASISHTA, A. SMITH (2001). Bayes inference in life testing and reliability via markov chain monte carlo simulation. Sankhya A, 63, pp. 15–40.
A. S. YADAV, S. K. SINGH, U. SINGH (2016). Bayesian estimation of lomax distribution under type-ii hybrid censored data using lindley's approximation method. Int. Journal of data science, x, no. x,xxxx.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2016 Statistica
This journal is licensed under a Creative Commons Attribution 3.0 Unported License (full legal code).
Authors accept to transfer their copyrights to the journal.
See also our Open Access Policy.
