A note on the stability of the estimation of the exponential distribution

Bounds on the uniform distance between a [chi]22n distribution and the distribution of 2[Sigma]ni = 1 Xi/[mu], where X1, X2,..., Xn are n independent, identically distributed nonnegative random variables with common mean [mu], are derived assuming that the Xi's are HNBUE or HNWUE or that a specific 'mechanism' is 'perturbing' an exponential distribution. These bounds are used to quantify the robustness of the sampling distribution of the usual test statistic for hypothesis tests on the mean of the exponential distribution to departures from exponentiality.