In this paper, we explicitly derive unbiased estimators for various functions of the rate parameter of the exponential distribution, 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. It is also noteworthy that this work corrects a general formula originally proposed by Tate, R. F. (Ann. Math. Statist., 30(2): 341-366, 1959) for constructing unbiased estimators of functions of the exponential distribution's rate parameter in the absence of a location parameter. Additionally, we establish a result demonstrating the asymptotic normality of the proposed unbiased estimators.

翻译：本文显式推导了指数分布率参数多种函数的无偏估计量，包括率参数的幂次、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。值得注意的是，本研究修正了Tate, R. F. (Ann. Math. Statist., 30(2): 341-366, 1959) 最初提出的关于在无位置参数情况下构建指数分布率参数函数无偏估计量的通用公式。此外，我们建立了一个结果，证明了所提出无偏估计量的渐近正态性。