Point estimation under asymmetric loss functions for left-truncated exponential samples

In this paper, Bayes estimates of the parameters and functions thereof in the left-truncated exponential distribution are derived. Asymmetric loss functions are used to reflect that, in most situations of interest, overestimation of a parameter does not produce the same economic consequence than underestimation. Both the non-informative prior and an informative prior on the reliability level at a prefixed time value are considered, and the statistical performances of the Bayes estimates are compared to those of the maximum likelihood ones through the risk function.