Document Zbl 0388.60052

Morgenstern’s bivariate distribution and its application to point processes. (English) Zbl 0388.60052

J. Math. Anal. Appl. 65, 247-256 (1978).

Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0388.60052

MSC:

60G55	Point processes (e.g., Poisson, Cox, Hawkes processes)
60J10	Markov chains (discrete-time Markov processes on discrete state spaces)
62H10	Multivariate distribution of statistics

Cite Review PDF

Full Text: DOI

References:

[1]	Bartlett, M. S., The spectral analysis of point processes, J. Roy. Statist. Soc. Ser. B, 25, 264-296 (1963) · Zbl 0124.08504
[2]	Cox, D. R.; Miller, H. D., The Theory of Stochastic Processes (1965), Methuen: Methuen London · Zbl 0149.12902
[3]	Daley, D. J., Stochastically monotone Markov chains, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 10, 305-317 (1968) · Zbl 0177.45604
[4]	Farlie, D. J.G, The performance of some correlation coefficients for a general bivariate distribution, Biometrika, 47, 307-323 (1960) · Zbl 0102.14903
[5]	Gumbel, E. J., Distributions a plusieurs variables dont les marges sont données, C. R. Acad. Sci. Paris, 246, 2717-2719 (1958) · Zbl 0084.35803
[6]	Gumbel, E. J., Bivariate exponential distributions, J. Amer. Statist. Assoc., 55, 698-707 (1960) · Zbl 0099.14501
[7]	Gumbel, E. J., Bivariate logistic distributions, J. Amer. Statist. Assoc., 56, 335-349 (1961) · Zbl 0099.14502
[8]	Jensen, D. R., A note on positive dependence and the structure of bivariate distributions, SIAM J. Appl. Math., 20, 479-752 (1971) · Zbl 0226.60024
[9]	Johnson, N. L.; Kotz, S., Distributions in Statistics: Continuous Multivariate Distributions (1972), Wiley: Wiley New York · Zbl 0248.62021
[10]	Kagan, Ya. Ya, A probablistic description of the seismic regime (in Russian), Fiz. Zemli, 4, 1023 (1973)
[11]	English translation in Phys. Solid Earth4; English translation in Phys. Solid Earth4
[12]	Kendall, D. G., Stochastic processes and population growth, J. Roy. Statist. Soc. Ser. B, 11, 230-264 (1949) · Zbl 0038.08803
[13]	Lampard, D. G., A stochastic process whose successive intervals between events from a first order Markov chain (I), J. Appl. Prob., 5, 648-668 (1968) · Zbl 0185.46201
[14]	Lehmann, E. L., Some concepts of dependence, Ann. Math. Statist., 37, 1137-1153 (1966) · Zbl 0146.40601
[15]	Lewis, P. A.W, A branching Poisson process model for the analysis of computer failure patterns, J. Roy. Statist. Soc. Ser. B, 26, 398-456 (1964) · Zbl 0132.39204
[16]	Morgenstern, D., Einfache Beispiele zweidimen-sionaler Verteilungen, Mitt. Math. Statist., 8, 234-235 (1956) · Zbl 0070.36202
[17]	O’Brien, G. L., A note on comparisons of Markov processes, Ann. Math. Statist., 43, 365-368 (1972) · Zbl 0241.60056
[18]	O’Brien, G. L., The comparison method for stochastic processes, Ann. Prob., 3, 80-88 (1975) · Zbl 0302.60037
[19]	Runnenburg, J. Th, On the Use of Markov Processes in One-Server Waiting Time Problems and renewal Theory, Ph.D. Thesis (1960), Amsterdam · Zbl 0092.34204
[20]	Vere-Jones, D., Stochastic models for earthquake occurrences, J. Roy. Statist. Soc. Ser. B, 32, 1-62 (1970) · Zbl 0201.27702
[21]	Wold, H., Sur les processus stationnaries ponctuels, (Colloq. Internat. C.N.R.S., 13 (1948)), 75-86 · Zbl 0035.21101
[22]	Wold, H., On stationary point processes and Markov chains, Skand. Akt., 31, 229-240 (1948) · Zbl 0041.25103

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.