Shrinkage Estimation of Location Parameter for Uniform Distribution Based on k-record Values

Abstract

The outcomes of many real-life experiments are sequences of record-breaking data sets, where only observations that exceed (or only those that fall below) the current extreme value are recorded. Records are needed when it is difficult to obtain observations or when observations are being destroyed when subjected to an experimental test. Records are applied in many real-life applications, such as hydrology, industrial stress testing, demise of glaciers, crop production, meteorological analysis, sporting and athletic events, and oil and mining surveys. For instance, in the threshold modeling the observations are those that cross a certain threshold value. Effectively estimating the location parameters for equally likely (uniformly distributed) records is needed in many real-life experiments. The practice demonstrated that the widely used estimators, such as the best linear unbiased estimator (BLUE) and maximum likelihood estimator (MLE), have some defects. This manuscript improves the MLE and BLUE of the location parameters for uniformly distributed records by investigating the corresponding shrinkage estimator using prior information about the BLUE and MLE. To measure the accuracy and precision of the proposed shrinkage estimator, the bias and mean square error (MSE) of the proposed estimators are investigated that provide sufficient conditions to get unbiased estimator with minimum MSE. The numerical results demonstrated that the proposed estimator are dominating over the existing estimators.