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Title: Mean of exponential distributions: Estimation from sums of unequal size samples Authors:  Jorge Buescu - University of Lisbon (Portugal)
Miguel Casquilho - FCIENCIAS-ID (Portugal) [presenting]
Abstract: The sums of unequal size samples are frequently measured and recorded in numerous industrial, manufacturing, and related activities, for Quality control reasons or supplier-customer security. While the also common, particular case of equal size samples is routine, the treatment of sums of unequal size samples seems to be absent in the literature. We address the estimation of the parameter of an adopted Exponential distribution of the individual items that underlie the samples, for the said circumstances where the sample sums are measured, thus, adding no further effort or cost to data collection. After having formerly solved the analogous problem for Gaussian items, we present the estimation of the single parameter of the Exponential, its mean, with point estimation and confidence intervals. The point estimation was derived by means of the Maximum Likelihood method. As in the Gaussian case, it gives a weighted average of the measured sample averages; and the confidence intervals are obtained computationally by Monte Carlo simulation. All these computations are freely available for direct use on our web pages, for proposed data or other supplied by the user.