Abstract
We derive the distribution of the sum ofn independent doubly truncated Poisson variables not necessarily identically distributed. This distribution is called a D-distribution. Its p.d.f. can be expressed in terms of a D-number and an incomplete exponential function which are both defined in this paper. We investigate the relationship between these numbers and distributions, and use these relationships to derive recurrence relations and other properties of the D-distribution. A minimum variance unbiased estimates of the p.d.f. of this D-distribution is also obtained. Some example are included at the end to illustrate the use of this D-distribution.
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Huang, M.L., Fung, K.Y. D-distribution and its applications. Statistical Papers 34, 143–159 (1993). https://doi.org/10.1007/BF02925536
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DOI: https://doi.org/10.1007/BF02925536