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Griffiths, R. C.; Milne, R. K.

A class of bivariate Poisson processes. (English) Zbl 0396.60050

J. Multivariate Anal. 8, 380-395 (1978).
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Cited in 12 Documents

MSC:

60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
62E10 Characterization and structure theory of statistical distributions
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

Keywords:

Bivariate Poisson Process; Doubly Stochastic Poisson Process; Poisson- Charlier Polynomials; Probability Generating Functional

Citations:

Zbl 0322.62016
Cite Review PDF
Full Text: DOI

References:

[1] Cox, D. R.; Lewis, P. A.W, Multivariate point processes, (Proc. Sixth Berkeley Symp. Math. Statist. Prob., 3 (1972)), 401-448 · Zbl 0267.60057
[2] Daley, D. J.; Vere-Jones, D., A summary of the mathematical theory of point processes, (Stochastic Point Processes: Statistical Analysis, Theory and Applications (1972), Wiley: Wiley New York), 299-383 · Zbl 0278.60035
[3] Kallenberg, O., (Random Measures (1975), Akademie-Verlag: Akademie-Verlag Berlin) · Zbl 0345.60031
[4] Kerstan, J.; Matthes, K.; Mecke, J., (Unbegrenzt Teilbare Punktprozesse (1974), Akademie-Verlag: Akademie-Verlag Berlin) · Zbl 0287.60057
[5] Lancaster, H. O., (The Chi-Squared Distribution (1969), Wiley: Wiley New York) · Zbl 0193.17802
[6] Lancaster, H. O., Joint probability distributions in the Meixner classes, J. Roy. Statist. Soc. Ser. B, 37, 434-443 (1975) · Zbl 0315.62009
[7] Lewis, P. A.W, (Stochastic Point Processes: Statistical Analysis, Theory and Applications (1972), Wiley: Wiley New York) · Zbl 0263.62056
[8] Meixner, J., Erzeugende Funktionen der Charlierschen Polynome, Math. Z., 44, 531-535 (1938) · JFM 64.0357.03
[9] Milne, R. K., Stochastic Analysis of Multivariate Point Processes, (Ph.D. Thesis (1971), Australian National University: Australian National University Canberra) · Zbl 0219.60028
[10] Nawrotzki, K., Eine Grenzwertsatz für homogene zufällige Punktfolgen, Math. Nachr., 24, 201-217 (1962) · Zbl 0106.33301
[11] Tyan, S-G; Derin, H.; Thomas, J. B., Two necessary conditions on the representation of bivariate distributions by polynomials, Ann. Statist., 4, 216-222 (1976) · Zbl 0322.62018
[12] Tyan, S.; Thomas, J. B., Characterization of a class of bivariate distribution functions, J. Multivar. Anal., 5, 227-235 (1975) · Zbl 0322.62016
[13] Westcott, M., The probability generating functional, J. Austral. Math. Soc., 14, 448-466 (1972) · Zbl 0251.60008
[14] Wood, R., Bivariate Distributions: Correlation in the Bivariate Poisson Distribution, (M.Sc. Thesis (1970), University of Sydney: University of Sydney Australia)
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