On power series, Bell polynomials, Hardy-Ramanujan-Rademacher problem and its statistical applications

Vasily G. Voinov; Mikhail Nikulin

Kybernetika (1994)

  • Volume: 30, Issue: 3, page 343-358
  • ISSN: 0023-5954

How to cite

top

Voinov, Vasily G., and Nikulin, Mikhail. "On power series, Bell polynomials, Hardy-Ramanujan-Rademacher problem and its statistical applications." Kybernetika 30.3 (1994): 343-358. <http://eudml.org/doc/28316>.

@article{Voinov1994,
author = {Voinov, Vasily G., Nikulin, Mikhail},
journal = {Kybernetika},
keywords = {Euler polynomials; Bernoulli polynomials; Bell polynomials},
language = {eng},
number = {3},
pages = {343-358},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On power series, Bell polynomials, Hardy-Ramanujan-Rademacher problem and its statistical applications},
url = {http://eudml.org/doc/28316},
volume = {30},
year = {1994},
}

TY - JOUR
AU - Voinov, Vasily G.
AU - Nikulin, Mikhail
TI - On power series, Bell polynomials, Hardy-Ramanujan-Rademacher problem and its statistical applications
JO - Kybernetika
PY - 1994
PB - Institute of Information Theory and Automation AS CR
VL - 30
IS - 3
SP - 343
EP - 358
LA - eng
KW - Euler polynomials; Bernoulli polynomials; Bell polynomials
UR - http://eudml.org/doc/28316
ER -

References

top
  1. G. E. Andrews, The theory of partitions, Encyclopedia of Mathematics and Its Applications (Rota, ed.), Vol. 2, G.-C. Addison-Wesley, Reading 1976. (1976) Zbl0371.10001MR0557013
  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. (1977) Zbl0412.62010MR0652539
  4. Ch. A. Charalambides, On discrete distributions of order k, Ann. Inst. Statist. Math. 38A (1986), 557-568. (1986) Zbl0611.60016MR0871499
  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. (1972) Zbl0226.60017MR0317458
  6. P. C. Consul, L. R. Shenton, Some interesting properties of Lagrange distributions, Commun. Statist. 2 (1973), 263-272. (1973) MR0408069
  7. H. Gupta, Tables of Partitions, Madras 1939. (1939) Zbl0023.10901
  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. (1986) MR0857814
  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. (1991) MR1116744
  10. N. L. Johnson, S. Kotz, Discrete distributions 1969-1980, Internat. Statist. Rev. 50 (1982), 71-101. (1982) Zbl0497.62020MR0668611
  11. K. D. Ling, On binomial distributions of order k, Statist. Probab. Lett. 6 (1988), 247-250. (1988) Zbl0638.60024MR0920534
  12. P. A. Mac Mahon, Combinatorial Analysis. Part 2, London 1916. (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. (1983) 
  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. (1983) MR0709243
  15. A. N. Philippou, The negative binomial distribution of order k and some of its properties, Biometrical J. 36 (1984), 789-794. (1984) Zbl0566.60014MR0775198
  16. A. N. Philippou, On multiparameter distribution of order k, Ann. Inst. Statist. Math. 40 (1988), 3, 467-475. (1988) MR0964286
  17. J. Riordan, An Introduction to Combinatorial Analysis, John Wiley & Sons, Inc. 1958. (1958) Zbl0078.00805MR0096594
  18. J. Riordan, Combinatorial Identities, John Wiley & Sons, Inc. 1968. (1968) Zbl0194.00502MR0231725
  19. I. Schur, On Faber polynomials, Amer. J. Math. 69 (1945), 33-41. (1945) Zbl0060.20403MR0011740
  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. (1986) 
  21. V. G. Voinov, M. S. Nikulin, Unbiased Estimators and their Applications, Nauka, Moscow 1989. (English translation Kluwer 1993, to appear.) (1989) MR1007841

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.