| Title:
|
On a trivariate Poisson distribution (English) |
| Author:
|
Loukas, Sotirios |
| Author:
|
Papageorgiou, H. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
36 |
| Issue:
|
6 |
| Year:
|
1991 |
| Pages:
|
432-439 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A four parameter trivariate Poisson distribution is considered. Recurrences for the probabilities and the partial derivatives of the probabilities with respect to the parameters are derived. Solutions of the maximum likelihood equations are obtaired and the determinant of their asymptotic covariance matrix is given. Applications of the maximum likelihood estimation technique to simulated data sets are also examined. (English) |
| Keyword:
|
trivariate Poisson distribution |
| Keyword:
|
recurrence relationships |
| Keyword:
|
estimation |
| Keyword:
|
information matrix |
| Keyword:
|
maximum likelihood |
| Keyword:
|
simulation |
| Keyword:
|
partial derivatives |
| Keyword:
|
determinant |
| Keyword:
|
asymptotic covariance matrix |
| MSC:
|
62E10 |
| MSC:
|
62E15 |
| MSC:
|
62F10 |
| idZBL:
|
Zbl 0742.62012 |
| idMR:
|
MR1134920 |
| DOI:
|
10.21136/AM.1991.104480 |
| . |
| Date available:
|
2008-05-20T18:42:35Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104480 |
| . |
| Reference:
|
[1] J. T. Campbell: The Poisson correlation function.Proc. Edin. Math. Soc. 4 (1934), 18-26. Zbl 0009.02801, 10.1017/S0013091500024135 |
| Reference:
|
[2] P. Ноlgate: Estimation for the bivariate Poisson distribution.Biometrika 51 (1964), 241 - 245. MR 0172374, 10.1093/biomet/51.1-2.241 |
| Reference:
|
[3] N. L. Johnson S. Kotz: Distributions in Statistics: Discrete Distributions.Houghton Mifflin Co., Boston, 1969. MR 0268996 |
| Reference:
|
[4] K. Kawamura: The structure of trivariate Poisson distribution.Kōdai Math. Sem. Rep. 28 (1976), 1-8. Zbl 0349.60013, MR 0428381, 10.2996/kmj/1138847374 |
| Reference:
|
[5] K. Kawamura: The structure of multivariate Poisson distribution.Kōdai Math. J. 2 (1979), 337-345. Zbl 0434.60019, MR 0553239 |
| Reference:
|
[6] C. D. Kemp H. Papageorgiou: Bivariate Hermite distributions.Sankhyā Ser. A 44 (1982), 269-280. MR 0688806 |
| Reference:
|
[7] A. S. Krishnamoorthy: Multivariate binomial and Poisson distributions.Sankhyā 11 (1951), 117-124. Zbl 0044.13502, MR 0044789 |
| Reference:
|
[8] S. Loukas C. D. Kemp: On computer sampling from trivariate and multivariate discrete distributions.J. Statist. Comput. Simul. 17 (1983), 113-123. 10.1080/00949658308810648 |
| Reference:
|
[9] D. M. Mahamunulu: A note on regression in the multivariate Poisson distribution.J. Amer. Statist. Assoc. 62 (1967), 251-258. Zbl 0147.37802, MR 0216613, 10.1080/01621459.1967.10482905 |
| Reference:
|
[10] H. Papageorgiou: Bivariate "Short" distributions.Commun. Statist. - Theor. Meth. 15 (1986), 893-905. Zbl 0613.62021, MR 0832086, 10.1080/03610928608829158 |
| Reference:
|
[11] C. R. Rao: Linear Statistical Inference and its Applications.Wiley, New York, 1965. Zbl 0137.36203, MR 0221616 |
| Reference:
|
[12] Z. Šidák: A chain of inequalities for some types of multivariate distributions.Colloquia Mathematica Societatis János Bolyai 1972, 693 - 699. MR 0370927 |
| Reference:
|
[13] Z. Šidák: A chain of inequalities for some types of multivariate distributions, with nine special cases.Aplikace Matematiky 18 (1973), 110-118. MR 0315842 |
| Reference:
|
[14] Z. Šidák: On probabilities in certain multivariate distributions: Their dependence on correlations.Aplikace Matematiky 18 (1973), 128-135. MR 0314197 |
| Reference:
|
[15] H. Teicher: On the multivariate Poisson distribution.Skand. Actuar. 37 (1954), 1 - 9. Zbl 0056.35801, MR 0077050 |
| . |
