Stirling distributions and Stirling numbers of the second kind. Computational problems in statistics

François Hennecart

Kybernetika (1994)

  • Volume: 30, Issue: 3, page 279-288
  • ISSN: 0023-5954

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Hennecart, François. "Stirling distributions and Stirling numbers of the second kind. Computational problems in statistics." Kybernetika 30.3 (1994): 279-288. <http://eudml.org/doc/28315>.

@article{Hennecart1994,
author = {Hennecart, François},
journal = {Kybernetika},
keywords = {minimum variance unbiased estimator; asymptotics; recurrence relations; left-truncated generalized Poisson distribution; modified power series distributions; sufficiency; completeness; modified Stirling numbers of the second kind; identities; relations},
language = {eng},
number = {3},
pages = {279-288},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Stirling distributions and Stirling numbers of the second kind. Computational problems in statistics},
url = {http://eudml.org/doc/28315},
volume = {30},
year = {1994},
}

TY - JOUR
AU - Hennecart, François
TI - Stirling distributions and Stirling numbers of the second kind. Computational problems in statistics
JO - Kybernetika
PY - 1994
PB - Institute of Information Theory and Automation AS CR
VL - 30
IS - 3
SP - 279
EP - 288
LA - eng
KW - minimum variance unbiased estimator; asymptotics; recurrence relations; left-truncated generalized Poisson distribution; modified power series distributions; sufficiency; completeness; modified Stirling numbers of the second kind; identities; relations
UR - http://eudml.org/doc/28315
ER -

References

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  1. S. Berg, Some properties and applications of the ratio of Stirling numbers of the second kind, Scand. J. Statist. 2 (1975), 91-94. (1975) MR0386083
  2. W. W. Bleick, P. C. C. Wang, Asymptotics of Stirling numbers of the second kind, Proc. Amer. Math. Soc. 42 (1974), 575-580. (Correction, Proc. Amer. Math. Soc. 48 (1974), 518.) (1974) Zbl0278.41034MR0330867
  3. Ch. Charalambides, Minimum variance unbiased estimation for a class of left- truncated discrete distributions, Sankyã Ser. A 36 (1974), 397-418. (1974) Zbl0312.62027MR0386113
  4. Ch. Charalambides, The generalized Stirling and C-numbers, Sankyã Ser. A 36 (1974), 419-436. (1974) Zbl0313.62014MR0386114
  5. Ch. Charalambides, The distributions of sufficient statistic of truncated generalized logarithmic series, Poisson and negative binomial distributions, Canad. J. Statist. 2 (1974), 261-275. (1974) MR0400495
  6. Ch. Charalambides, J. Singh, A review of the Stirling numbers, their generalizations and statistical applications, Comm. Statist. Theory Methods 17 (1988), 8, 2533-2595. (1988) Zbl0696.62025MR0955350
  7. L. Comtet, Advanced Combinatorics, Reidel, Dordrecht 1974. (1974) Zbl0283.05001MR0460128
  8. R. C. Gupta, Distribution of the sum of decapited generalized Poisson variables, Sankyã Ser. B 36 (1974), 212-214. (1974) MR0391342
  9. R. C. Gupta, Minimum variance unbiased estimation in a modified power series distributions and some of its applications, Comm. Statist. A -- Theory Methods 6 (1977), 977-991. (1977) MR0518866
  10. P. N. Jani, Minimum variance unbiased estimation for some left-truncated modified power series distributions, Sankyã Ser. B 39 (1977), 258-278. (1977) Zbl0394.62015MR0652703
  11. P. N. Jani, New numbers appearing in minimum variance unbiased estimation for decapited generalized, negative binomial and Poisson distributions, J. Indian Statist. Assoc. 16 (1978), 41-48. (1978) MR0529348
  12. A. Kumar, A note on minimum variance estimators of power series distributions, Comm. Statist. (A) -- Theory Methods 9 (1980), 549-556. (1980) MR0561555
  13. A. Kumar, P. C. Consul, Minimum variance unbiased estimation for modified power series distributions, Comm. Statist. (A) -- Theory Methods 9(A) (1980), 1261-1275. (1980) MR0578556
  14. L. Moser, M. Wyman, Stirling numbers of the second kind, Duke Math. J. 25 (1958), 29-43. (1958) Zbl0079.09102MR0091964
  15. M. Nikulin, Some recent results on chi-squared tests, Queen's Papers in Pure and Appl. Math. (1991), No. 86. (1991) Zbl0752.62038MR1098501
  16. F. W. J. Olver, Asymptotics and Special Functions, Academic Press, New York 1974. (1974) Zbl0308.41023MR0435697
  17. G. P. Patil, Minimum variance unbiased estimation and certain problems of additive number theory, Ann. Math. Statist., 34 (1963), 1050-1056. (1963) Zbl0116.37203MR0155388
  18. J. Roy, S. K. Mitra, Unbiased minimum variance estimation in a class of discrete distributions, Sankyã 18 (1957), 371-378. (1957) Zbl0084.14901MR0092320
  19. J. Singh, A note on the Stirling distribution of the second kind, Commun. Statist. 4 (1975), 753-759. (1975) Zbl0307.62010MR0388609
  20. R. F. Tate, R. L. Goen, Minimum variance unbiased estimation for a truncated Poisson distribution, Ann. Math. Statist. 29 (1959), 755-765. (1959) MR0093849
  21. N. M. Temme, Asymptotic estimates ot Stirling numbers, Stud. Appl. Math. 89 (1993), 233-243. (1993) MR1223774
  22. V. G. Voinov, On Jani's paper on minimum variance unbiased estimation for a left-truncated modified power series distribution, Sankyã Ser. B 48 (1986), 144-150. (1986) MR0887688
  23. V. Voinov, M. Nikulin, Unbiased Estimators and Their Applications, Kluwer Academic Publishers, Dordrecht 1993. (1993) Zbl0832.62019MR1472739
  24. S. W. Joshi, C. J. Park, Minimum variance unbiased estimation for truncated power series distributions, Sankyã Ser. A 36 (1974), 305-314. (1974) MR0386121

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