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Distribution of the Sum of Variates from Truncated Discrete Populations

Published online by Cambridge University Press:  20 November 2018

A. K. MD. Ehsanes Saleh  and
M. A. Rahim
A. K. MD. Ehsanes Saleh
Affiliation:
Carleton University, Ottawa, Ontario
M. A. Rahim
Affiliation:
Carleton University, Ottawa, Ontario
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Distributions often arise in practice where one or more values of the variate are unobserved. Various practical problems have been referred by Finney [1], David and Johnson [4], Bliss and Fisher [3]. It is of interest to know the exact distribution of the sum of variâtes from such truncated discrete population. In this paper, utilising the property of characteristic function certain general results are shown. The distribution of the sum of independent variables from a discrete population, truncated by any set of s distinct values, follows from them immediately. Using these results the exact distributions of the sum, from binomial, poisson, negative binomial and geometric population, truncated from anywhere, are derived.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 3 , September 1972 , pp. 395 - 398
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Finney, D. J., The truncated binomial distribution, Ann. of Eugenics, 14 (1949), 319-328.Google Scholar
2. Malik, H. J., Distribution of the sum of truncated binomial variates, Canad. Math. Bull. (3) 12 (1969), p. 344.Google Scholar
3. Bliss, C. I., and Fisher, R. A., Fitting the binomial distribution to biological data and note on the efficient fitting of the negative binomial, Biometrics, 9 (1953), 176-200.Google Scholar
4. David, F. N., and Johnson, N. L., The truncated poisson, Biometrics, 8 (1952), 275-285.Google Scholar
5. Rider, P. R., Truncated binomial and negative binomial distributions, Amer. Statist. Assoc. 50 (1955), 877-883.Google Scholar
6. Ehsanes Saleh, A. K. Md., Distribution of the sum of independent truncated poisson variates, Dacca Univ., Bangladesh, J. Statist. Res. (1) 4 (1970), 32-36.Google Scholar