A NEW LIFETIME DISTRIBUTION FOR MODELING MONOTONIC DECREASING SURVIVAL PATTERNS
Keywords:
Squared Error, Linex, Entropy and Precautionary Loss, Maximum Likelihood Estimates, Asymptotically Invariant Prior, Posterior Risk functions.Abstract
One parameter inverse size biased p-dimensional Rayleigh distribution (ISBRD) is introduced for modeling lifetimes. Its distributional properties including moments are studied. Hazard function is studied under different parametric settings. Parameter estimation is done using maximum likelihood method and Bayesian approach. The risks of Bayes estimators have been obtained under different loss structures and a comparative risk analysis has been conducted empirically. Findings of simulation study are presented
Downloads
References
W.S. (1919). Rayleigh. Philosophical Magazine, 6th Series 37, p. 321-347.
Cohen, A.C. and Whitten, B.J. (1988). Parameter estimation in Reliability and
life span models, Marcel Dekker, Inc., New York, p. 96.
Fisher, R. A. (1934). The effect of methods of ascertainment upon the
estimation of frequencies, Annals of Human Genetics, Vol. 6(1), p. 13-25.
Cox, D. F. (1962). Description and measurement of rates of early mortality in
the pig, Iowa State Univ. Agr. Expt. Sta. Res. Bull. 500.
Patil, G.P. (2002). Weighted distributions, Encyclopedia of Environmetrics,
John Wiley and Sons, Vol.4, p. 2369- 2377.
Varian, H.R., (1975). A Bayesian approach to real state assessment, in studies
in Bayesian Econometrics and Statistics in honour of L.J. Savage (Fienberg,
S.E. and Zellner, A., Editors), Amsterdam: North-Holland, p. 195-208.
Zellner, A. (1986). Bayesian estimation and prediction using asymmetric loss
functions, Jour. Statist. Assoc., 81, p. 446-451.
R. V. Canfield (1970). A Bayesian approach to reliability estimation using a
loss function, IEEE Transaction on Reliability, R-19, p. 13-16.
Rojo, J. (1987). On the admissibility of cx+d with respect to the Linex loss
functions, Common., statist., T&M., 16, p. 3745-3748.
A.P. Basu and N. Ebrahimi (1991). Bayesian Approach to life testing and
reliability estimation using Asymmetric Loss Function, Journal of Statistical
Planning and Inference, 29, p. 21-31.
Soliman, A. Ahmed (2000). Comparison of Linex and quadratic Bayes
estimators for the Rayleigh distribution, Commun. Statist. Theory meth.,
(1), p. 95-107.
Calabria, R. and Pulcini (1994). An engineering approach to Bayes estimation
for the Weibull distribution, Micro-Election. Reliab. 34 (5), p. 789-802.
Norstrom, J.G. (1996). The use of precautionary loss functions in risk analysis,
IEEE Trans. Reliability, Vol. 45(3), p. 400-403.
Hartigan, J.A. (1964). Invariant prior distributions, Ann. Math. Statist. 34, p.
-845.
