Bounded risk estimation of the hazard rate function of the exponential distribution: Two-stage procedure

ABSTRACTIn this article, we consider sequential point estimation of hazard rate function of an exponential distribution () subject to the risk function given as , where 0 0 are known constants. We provide explicit formulas for the distribution of the total sample size, Nm, and of the expected value and risk of the estimator of the hazard rate function of the exponential distribution. In addition, we propose how to determine the parameter K( = K(m,A)) of the stopping variable Nm so that the risk is uniformly bounded by ω. In the end, the performances of the proposed methodology are investigated with the help of simulations and two applied examples.