Geodesic
On a trivariate Poisson distribution
Applications of Mathematics, Tome 36 (1991) no. 6, pp. 432-439

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
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.
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.
DOI : 10.21136/AM.1991.104480
Classification : 62E10, 62E15, 62F10
Keywords: trivariate Poisson distribution; recurrence relationships; estimation; information matrix; maximum likelihood; simulation; partial derivatives; determinant; asymptotic covariance matrix 
Loukas, Sotirios; Papageorgiou, H. On a trivariate Poisson distribution. Applications of Mathematics, Tome 36 (1991) no. 6, pp. 432-439. doi: 10.21136/AM.1991.104480
@article{10_21136_AM_1991_104480,
     author = {Loukas, Sotirios and Papageorgiou, H.},
     title = {On a trivariate {Poisson} distribution},
     journal = {Applications of Mathematics},
     pages = {432--439},
     year = {1991},
     volume = {36},
     number = {6},
     doi = {10.21136/AM.1991.104480},
     mrnumber = {1134920},
     zbl = {0742.62012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1991.104480/}
}
TY  - JOUR
AU  - Loukas, Sotirios
AU  - Papageorgiou, H.
TI  - On a trivariate Poisson distribution
JO  - Applications of Mathematics
PY  - 1991
SP  - 432
EP  - 439
VL  - 36
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1991.104480/
DO  - 10.21136/AM.1991.104480
LA  - en
ID  - 10_21136_AM_1991_104480
ER  - 
%0 Journal Article
%A Loukas, Sotirios
%A Papageorgiou, H.
%T On a trivariate Poisson distribution
%J Applications of Mathematics
%D 1991
%P 432-439
%V 36
%N 6
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1991.104480/
%R 10.21136/AM.1991.104480
%G en
%F 10_21136_AM_1991_104480

[1] J. T. Campbell: The Poisson correlation function. Proc. Edin. Math. Soc. 4 (1934), 18-26. | DOI | Zbl

[2] P. Ноlgate: Estimation for the bivariate Poisson distribution. Biometrika 51 (1964), 241 - 245. | DOI | MR

[3] N. L. Johnson S. Kotz: Distributions in Statistics: Discrete Distributions. Houghton Mifflin Co., Boston, 1969. | MR

[4] K. Kawamura: The structure of trivariate Poisson distribution. Kōdai Math. Sem. Rep. 28 (1976), 1-8. | DOI | MR | Zbl

[5] K. Kawamura: The structure of multivariate Poisson distribution. Kōdai Math. J. 2 (1979), 337-345. | MR | Zbl

[6] C. D. Kemp H. Papageorgiou: Bivariate Hermite distributions. Sankhyā Ser. A 44 (1982), 269-280. | MR

[7] A. S. Krishnamoorthy: Multivariate binomial and Poisson distributions. Sankhyā 11 (1951), 117-124. | MR | Zbl

[8] S. Loukas C. D. Kemp: On computer sampling from trivariate and multivariate discrete distributions. J. Statist. Comput. Simul. 17 (1983), 113-123. | DOI

[9] D. M. Mahamunulu: A note on regression in the multivariate Poisson distribution. J. Amer. Statist. Assoc. 62 (1967), 251-258. | DOI | MR | Zbl

[10] H. Papageorgiou: Bivariate "Short" distributions. Commun. Statist. - Theor. Meth. 15 (1986), 893-905. | DOI | MR | Zbl

[11] C. R. Rao: Linear Statistical Inference and its Applications. Wiley, New York, 1965. | MR | Zbl

[12] Z. Šidák: A chain of inequalities for some types of multivariate distributions. Colloquia Mathematica Societatis János Bolyai 1972, 693 - 699. | MR

[13] Z. Šidák: A chain of inequalities for some types of multivariate distributions, with nine special cases. Aplikace Matematiky 18 (1973), 110-118. | MR

[14] Z. Šidák: On probabilities in certain multivariate distributions: Their dependence on correlations. Aplikace Matematiky 18 (1973), 128-135. | MR

[15] H. Teicher: On the multivariate Poisson distribution. Skand. Actuar. 37 (1954), 1 - 9. | MR | Zbl

Cité par Sources :