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.

翻译：本文在无位置参数的情况下，显式推导了指数分布率参数多种函数的无偏估计量，包括率参数的幂、第$q$分位数、第$p$阶矩、生存函数、最大值、最小值、概率密度函数、平均剩余寿命、矩母函数等。这项工作非平凡地补充了已有关于位置-率指数分布参数函数无偏估计量的公式体系。此外，我们建立了一个结果，证明了所提出的无偏估计量具有渐近正态性。