| Title:
|
On power series, Bell polynomials, Hardy-Ramanujan-Rademacher problem and its statistical applications (English) |
| Author:
|
Voinov, Vasily G. |
| Author:
|
Nikulin, Mikhail |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
30 |
| Issue:
|
3 |
| Year:
|
1994 |
| Pages:
|
343-358 |
| . |
| Category:
|
math |
| . |
| MSC:
|
05A17 |
| MSC:
|
11B68 |
| MSC:
|
11B73 |
| MSC:
|
30B10 |
| MSC:
|
33C99 |
| MSC:
|
60C05 |
| MSC:
|
62G05 |
| idZBL:
|
Zbl 0826.30002 |
| idMR:
|
MR1291936 |
| . |
| Date available:
|
2009-09-24T18:48:14Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125161 |
| . |
| Reference:
|
[1] G. E. Andrews: The theory of partitions.Encyclopedia of Mathematics and Its Applications (Rota, ed.), Vol. 2, G.-C. Addison-Wesley, Reading 1976. Zbl 0371.10001, MR 0557013 |
| Reference:
|
[2] A. Cayley: Collected mathematical papers No. 3, 9, 11, 13.Cambridge 1889-1897. |
| Reference:
|
[3] Ch. A. Charalambides: On the generalized discrete distributions and the Bell polynomials.Sankya 39B (1977), 36-44. Zbl 0412.62010, MR 0652539 |
| Reference:
|
[4] Ch. A. Charalambides: On discrete distributions of order k.Ann. Inst. Statist. Math. 38A (1986), 557-568. Zbl 0611.60016, MR 0871499 |
| Reference:
|
[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. Zbl 0226.60017, MR 0317458 |
| Reference:
|
[6] P. C. Consul, L. R. Shenton: Some interesting properties of Lagrange distributions.Commun. Statist. 2 (1973), 263-272. MR 0408069 |
| Reference:
|
[7] H. Gupta: Tables of Partitions.Madras 1939. Zbl 0023.10901 |
| Reference:
|
[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 0857814 |
| Reference:
|
[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 1116744 |
| Reference:
|
[10] N. L. Johnson, S. Kotz: Discrete distributions 1969-1980.Internat. Statist. Rev. 50 (1982), 71-101. Zbl 0497.62020, MR 0668611 |
| Reference:
|
[11] K. D. Ling: On binomial distributions of order k.Statist. Probab. Lett. 6 (1988), 247-250. Zbl 0638.60024, MR 0920534 |
| Reference:
|
[12] P. A. Mac Mahon: Combinatorial Analysis. Part 2.London 1916. |
| Reference:
|
[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. |
| Reference:
|
[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 0709243 |
| Reference:
|
[15] A. N. Philippou: The negative binomial distribution of order k and some of its properties.Biometrical J. 36 (1984), 789-794. Zbl 0566.60014, MR 0775198 |
| Reference:
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[16] A. N. Philippou: On multiparameter distribution of order k.Ann. Inst. Statist. Math. 40 (1988), 3, 467-475. MR 0964286 |
| Reference:
|
[17] J. Riordan: An Introduction to Combinatorial Analysis.John Wiley \& Sons, Inc. 1958. Zbl 0078.00805, MR 0096594 |
| Reference:
|
[18] J. Riordan: Combinatorial Identities.John Wiley \& Sons, Inc. 1968. Zbl 0194.00502, MR 0231725 |
| Reference:
|
[19] I. Schur: On Faber polynomials.Amer. J. Math. 69 (1945), 33-41. Zbl 0060.20403, MR 0011740 |
| Reference:
|
[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. |
| Reference:
|
[21] V. G. Voinov, M. S. Nikulin: Unbiased Estimators and their Applications.Nauka, Moscow 1989. (English translation Kluwer 1993, to appear.) MR 1007841 |
| . |
