Summary
This paper deals with the problem of prediction of the order statistics in a future sample. Underlying model is exponential. Outlier is present in the sample drawn and the sample size is considered a random variable. Firstly, an outlier of type πδ in the exponential model, is trated. Actual predictive distribution of the order satstistics is obtained. As an extension, two sample problem is also taken up. Finally, an outlier of type π+δ is dealt and now the predictive distribution is expressed in terms of hypergeometric functions.
Similar content being viewed by others
References
BALAKRISHNAN, N. (1987): «Two identities involving order statistics in the presence of an outlier»,Communications in Statistics-A (Theory and Methods), Vol. 16, pp. 2385–2389.
BARNETT, V., and LEWIS T. (1984):Outliers in Statistical data, Edition II, John Wiley & Sons, New York, N.Y.
CONSUL, P. C. (1984): «On the distribution of order statistics for a random sample size»,Statistica Neerlandica, Vol. 38, pp. 249–256.
DUNSMORE, I. R. (1974): «The Bayesian Predictive distribution in Life Testing models»,Technometrics Vol. 16, pp. 455–460.
ERDELYI, et al. (1954):Higher Transcendental functions, Vol. I, McGraw-Hill Co., N.Y.
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.
KITAGAWA, G. (1984): «Bayesian analysis of outliers via Akaike’s predictive likelihood of a model»,Communications in Statistics-B (Cimulation and computation), Vol. 13, pp. 107–126.
LINGAPPAIAH, G. S. (1973): «Prediction in exponential life testing»,Canadian Journal of Statistics, Vol. 1, pp. 113–117.
LINGAPPAIAH, G. S. (1974): «Prediction in the samples from the Gamma distribution as applied to life testing»,The Australian Journal of Statistics, Vol. 16, pp. 30–32.
LINGAPPAIAH, G. S. (1976): «Effect of outliers on the estimation of parameters»,Metrika, Vol. 23 pp. 27–30.
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. (1985a): «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.
LINGAPPAIAH, G. S. (1984): «Bayesian prediction regions for the extreme order statistics»,Biometrische Zeitschrift (Biometrical Journal), Vol. 26, pp. 49–56.
LINGAPPAIAH, G. S. (1985b): «Inferences in samples from the exponential populations when the sample sizes are variables»,METRON, Vol. 43, pp. 175–186.
LINGAPPAIAH, G. S. (1986): «Prediction problem in samples from a gamma population when sample sizes are random variables; a Bayesian approach»,Journal of Indian Association for Productivity, Quality and Reliability, Vol. 11, pp. 25–34.
SINHA, S. K. (1973): «Life Testing and Reliability Estimation for Non-homogeneous Data—A Bayesian Approach»,Communications in Statistics, Vol. 2, pp. 235–253.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lingappaiah, G.S. Bayesian inference in life tests based on exponential model with outliers when sample size is a random variable. TDE 5, 27–37 (1990). https://doi.org/10.1007/BF02863536
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02863536