The paper presents the probability density of parameter estimators when N independent variables are observed, each of them distributed according to the exponential low (with some parameters to be estimated). The number N is supposed to be small. Typically, such an experimental situation arises in problems of software reliability, another case is a small sample in the GLIM modeling. The considered estimator is defined by the maximum of the posterior probability density; it is equal to the maximum likelihood estimator when the prior is uniform. The exact density is obtained, and its approximation is discussed in accordance with some information-geometric considerations.
