Pitman closeness results for Type-I hybrid censored data from exponential distribution

Recent work on Pitman closeness has compared estimators under Type-II censored samples from an exponential distribution. More recently, a comparison was done for Type-I censored data wherein two estimators based on two different censoring times were compared in their estimation of θ under Pitman closeness. Extending such a comparison, one may consider alternate comparisons under Type-I hybrid censoring. In this paper, we consider the comparison of three associated estimators based on three hybrid censored samples and carry out the analogous Pitman closeness comparisons. Formulas are derived for the suitable Pitman closeness probabilities and numerical results are tabulated for a variety of settings. While most of the tabulated probabilities agree with an intuition that the estimator based on larger termination time should be Pitman closer, exceptions are found.