Geodesic
On power series, Bell polynomials, Hardy-Ramanujan-Rademacher problem and its statistical applications
Kybernetika, Tome 30 (1994) no. 3, pp. 343-358
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Classification : 05A17, 11B68, 11B73, 30B10, 33C99, 60C05, 62G05 
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Voinov, Vasily G.; Nikulin, Mikhail. On power series, Bell polynomials, Hardy-Ramanujan-Rademacher problem and its statistical applications. Kybernetika, Tome 30 (1994) no. 3, pp. 343-358. http://geodesic.mathdoc.fr/item/KYB_1994_30_3_a13/

[1] G. E. Andrews: The theory of partitions. Encyclopedia of Mathematics and Its Applications (Rota, ed.), Vol. 2, G.-C. Addison-Wesley, Reading 1976. | MR | Zbl

[2] A. Cayley: Collected mathematical papers No. 3, 9, 11, 13. Cambridge 1889-1897.

[3] Ch. A. Charalambides: On the generalized discrete distributions and the Bell polynomials. Sankya 39B (1977), 36-44. | MR | Zbl

[4] Ch. A. Charalambides: On discrete distributions of order k. Ann. Inst. Statist. Math. 38A (1986), 557-568. | MR | Zbl

[5] P. C. Consul, L. R. Shenton: Use of Lagrange expansion for generating discrete generalized probability distributions. SIAM. J. Appl. Math. 23 (1972), 2, 239-272. | MR | Zbl

[6] P. C. Consul, L. R. Shenton: Some interesting properties of Lagrange distributions. Commun. Statist. 2 (1973), 263-272. | MR

[7] H. Gupta: Tables of Partitions. Madras 1939. | Zbl

[8] K. Hirano: Some properties of the distribution of order k. In: Fibonacci Numbers and their Applications (A. N. Philippou and A. F. Horodam, eds.), Reidel, Dordrecht 1986, pp. 43-53. | MR

[9] H. Hirano S. Aki N. Kashiwagi, H. Kiboki: On Ling's binomial and negative binomial distributions of order k. Statist. Probab. Lett. 11 (1991), 503-509. | MR

[10] N. L. Johnson, S. Kotz: Discrete distributions 1969-1980. Internat. Statist. Rev. 50 (1982), 71-101. | MR | Zbl

[11] K. D. Ling: On binomial distributions of order k. Statist. Probab. Lett. 6 (1988), 247-250. | MR | Zbl

[12] P. A. Mac Mahon: Combinatorial Analysis. Part 2. London 1916.

[13] A. N. Philippou: The Poisson and compound Poisson distribution of order k and some of their properties. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. 130 (1983), 175-180.

[14] A. N. Philippou C. Georghiou, G. N. Philippou: A generalized geometric distribution and some of its properties. Statist. Probab. Lett. 1 (1983), 171-175. | MR

[15] A. N. Philippou: The negative binomial distribution of order k and some of its properties. Biometrical J. 36 (1984), 789-794. | MR | Zbl

[16] A. N. Philippou: On multiparameter distribution of order k. Ann. Inst. Statist. Math. 40 (1988), 3, 467-475. | MR

[17] J. Riordan: An Introduction to Combinatorial Analysis. John Wiley \& Sons, Inc. 1958. | MR | Zbl

[18] J. Riordan: Combinatorial Identities. John Wiley \& Sons, Inc. 1968. | MR | Zbl

[19] I. Schur: On Faber polynomials. Amer. J. Math. 69 (1945), 33-41. | MR | Zbl

[20] V. G. Voinov R. Neymann, M. S. Nikulin: The Lagrange's method of evaluation of quantiles and noncentrality parameters of probability distributions. Theory Probab. Appl. 31 (1986), 1, 185-187.

[21] V. G. Voinov, M. S. Nikulin: Unbiased Estimators and their Applications. Nauka, Moscow 1989. (English translation Kluwer 1993, to appear.) | MR