Estimation and prediction based on record statistics in the presence of an outlier

Abstract

A single outlier sequence in which the distribution of the first observation differs from the others is considered and the properties of record statistics extracted from such sequence are studied. The problem of estimating the model parameters is discussed in the proportional hazard rate model. The maximum likelihood estimator and the uniformly minimum variance unbiased estimator are obtained for the special case of exponential distribution. The best linear unbiased (invariant) estimator is also derived for the location-scale family of distributions and their efficiencies are calculated. The problems of predicting the future records and reconstructing the past records are investigated. Various predictors and reconstructors are presented and some of their properties are stated. The precision of the obtained predictors are compared based on both the mean squared prediction error and Pitman’s measure of closeness criteria. Finally, an example with real data is given to illustrate the results.