Summary
This paper predicts the order statistics in the future sample in terms of order statistics in the earlier sample in a life test based on the exponential model. The sizes of the samples are either fixed or random variables, having the Poisson distribution. For the prediction purpose, predictive distributions are obtained. Three situations are considered such as (a) both the sample sizes are random (b) size of one sample is fixed while that of the other is a random variable (c) both sizes are fixed. For each of these three cases, Bayesian Prediction Regions (BPR) are obtained, and also, the variance of these predictive distributions for all these three situations, is put in closed forms.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Buhrman, J.M. (1973) On order statistics when sample size has a binomial distribution. Statistica Neerlandica, Vol. 27, pp. 125–126.
Consul, P.C. (1984) On the distribution of order statistics for a random sample size. Statistica Neerlandica, Vol. 38, no. 4., pp. 249–256.
Dunsmore, I.R. (1974) The Bayesian predictive distribution in life testing models. Technometries, Vol. 16, pp. 455–460.
Gupta, D. and Gupta, R.C. (1984) On the distribution of order statistics for a random sample size. Statistica Neerlandica, Vol. 38, pp. 13–19.
Kaminsky, Kenneth S. and Nelson, Paul I. (1975) Best linear unbiased prediction of order statistics in location and scale families. J. American Statistical Association, Vol. 70, pp. 145–150.
Lawless, J.F. (1971) A prediction problem concerning samples from the exponential distribution with application to life testing. Technometrics, Vol. 13, pp. 725–270.
Lingappaiah, G.S. (1973) Prediction in exponential life testing. Canadian J. of Statistics, Vol. 1, pp. 113–117.
Lingappaiah, G.S. (1974) Prediction in samples from the gamma distribution as applied to life testing. The Australian J. of Statistics, Vol. 1, pp. 113–117.
Lingappaiah, G.S. (1978) Bayesian approach to the prediction problem in the exponential population. IEEE Trans. Reliability, Vol. R-27, pp. 222–225.
Lingappaiah, G.S. (1979) Bayesian approach to the prediction problem in complete and censored samples from the gamma and exponential populations. Communications in Statistics, Vol. A8, pp. 1403–1424.
Lingappaiah, G.S. (1981) Sequential life testing with spacings. Exponential model. IEEE Trans. Reliability, Vol. R-30, pp. 370–374.
Lingappaiah, G.S. (1984) Bayesian prediction regions for the extreme order statistics. Biometrische Zeitschrift (Biometrical Journal), Vol. 26, pp. 49–56.
Lingappaiah, G.S. (1985) A study of shifting models in life tests via Bayesian approach using semi or used priors. (SOUPS) Annals of Institute of Statistical Mathematics, Vol. 37, pp. 151–163.
Padgett, W.J. (1982) An approximate prediction interval for the mean of the future observations from the inverse gaussian distribution. J. of Statistical Computation and Simulation, Vol. 14, pp. 191–199.
Raghunandan, K. and Patil, S.A. (1972) On order statistics from random sample size. Statistica Neerlandica, Vol. 26, pp. 121–126.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Plenum Press, New York
About this chapter
Cite this chapter
Lingappaiah, G.S. (1987). Bayes Inference in Life Tests When Samples Sizes are Fixed or Random. In: Viertl, R. (eds) Probability and Bayesian Statistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1885-9_34
Download citation
DOI: https://doi.org/10.1007/978-1-4613-1885-9_34
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-9050-6
Online ISBN: 978-1-4613-1885-9
eBook Packages: Springer Book Archive