The generalized Poisson distribution (GPD) has been found to be a very versatile discrete distribution with applications in various areas of study such as engineering, manufacturing, survival analysis, genetic and branching processes. In this paper, we study the estimation of generalized Poisson distribution by the method of weighted discrepancies between observed and expected frequencies. The methods of maximum likelihood (ML), minimum chi-square and the minimum discrimination information estimation are special cases of the weighted discrepancies method. A new weighting technique, the empirical weighted rates of change, for estimating the GPD parameters is discussed. It is observed that the bias under this new estimation method performs equally good or better than the ML, minimum chi-square and the weighted discrepancies methods, but its variance is the largest of all.
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