On unbiased estimators for functions of the rate parameter of the exponential distribution

In this paper, we explicitly derive unbiased estimators for various functions of the rate parameter of the exponential distribution in the absence of a location parameter, including powers of the rate parameter, the $q$th quantile, the $p$th moment, the survival function, the maximum, minimum, probability density function, mean past lifetime, moment generating function, and others. This work non-trivially complements established formulas for unbiased estimators of functions of parameters of the location-rate exponential distribution. Additionally, we establish a result demonstrating the asymptotic normality of the proposed unbiased estimators.