Geodesic
On the Distribution of Sum of Independent Positive Binomial Variables
Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 151-152

Voir la notice de l'article provenant de la source Cambridge University Press

Let X 1, X 2, ..., X n be n independent and identically distributed random variables having the positive binomial probability function 1 where 0 < p < 1, and T = {1, 2, ..., N}. Define their sum as Y=X 1 + X 2 + ... +X n . The distribution of the random variable Y has been obtained by Malik [2] using the inversion formula for characteristic functions. It appears that his result needs some correction. The purpose of this note is to give an alternative derivation of the distribution of Y by applying one of the results, established by Patil [3], for the generalized power series distribution. 
Ahuja, J. C. On the Distribution of Sum of Independent Positive Binomial Variables. Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 151-152. doi: 10.4153/CMB-1970-035-7
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[1] 1. Feller, W., An introduction to probability theory and its applications, Wiley, New York, 1 (third edition), 1968. Google Scholar

[2] 2. Malik, H. J., Distribution of the sum of truncated binomial variates. Canad. Math. Bull. 12 (1969), 334-336. Google Scholar

[3] 3. Patil, G. P., Minimum variance unbiased estimation and certain problems of additive number theory, Ann. Math. Statist. 34 (1963), 1050-1056. Google Scholar

[4] 4. Pearson, K., Tables of the incomplete beta function, Cambridge Univ. Press, London 1934. Google Scholar

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