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Volumn 73, Issue 1, 2005, Pages 35-58

Mixed Poisson distributions

Author keywords

Discrete distributions; Distribution theory; Mixing distribution; Mixtures; Overdispersion

Indexed keywords


EID: 17044422638     PISSN: 03067734     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1751-5823.2005.tb00250.x     Document Type: Article
Times cited : (268)

References (155)
  • 1
    • 38248999302 scopus 로고
    • On the uniform convergence of normalised poisson mixtures to their mixing distribution
    • Adell, J. & de la Cal, J. (1993). On the Uniform Convergence of Normalised Poisson Mixtures to their Mixing Distribution. Statistics and Probability Letters, 18, 227-232.
    • (1993) Statistics and Probability Letters , vol.18 , pp. 227-232
    • Adell, J.1    De La Cal, J.2
  • 2
    • 0347973805 scopus 로고
    • The multivariate poisson-log normal distribution
    • Aitchinson, J. & Ho, C.H. (1989). The Multivariate Poisson-Log Normal Distribution. Biometrika, 75, 621-629.
    • (1989) Biometrika , vol.75 , pp. 621-629
    • Aitchinson, J.1    Ho, C.H.2
  • 3
    • 21444433315 scopus 로고    scopus 로고
    • A general maximum likelihood analysis of overdispersion in generalized linear models
    • Aitkin, M. (1996). A General Maximum Likelihood Analysis of Overdispersion in Generalized Linear Models. Statistics and Computing, 6, 251-262.
    • (1996) Statistics and Computing , vol.6 , pp. 251-262
    • Aitkin, M.1
  • 4
    • 17044433356 scopus 로고
    • On some statistical methods connected with the mixed poisson process
    • Albrecht, P. (1982). On Some Statistical Methods Connected with the Mixed Poisson Process. Scandinavian Actuarial Journal, 9, 1-14.
    • (1982) Scandinavian Actuarial Journal , vol.9 , pp. 1-14
    • Albrecht, P.1
  • 5
    • 17044374946 scopus 로고
    • Laplace transforms, mellin transforms and mixed poisson processes
    • Albrecht, P. (1984). Laplace Transforms, Mellin Transforms and Mixed Poisson Processes. Scandinavian Actuarial Journal, 11, 58-64.
    • (1984) Scandinavian Actuarial Journal , vol.11 , pp. 58-64
    • Albrecht, P.1
  • 6
    • 17044385678 scopus 로고    scopus 로고
    • Statistical properties of poisson-lomax distribution and its application to repeated accidents data
    • Al-Awadhi, S.A. & Ghitany, M.E. (2001). Statistical Properties of Poisson-Lomax Distribution and its Application to Repeated Accidents Data. Journal of Applied Statistical Science, 10, 365-372.
    • (2001) Journal of Applied Statistical Science , vol.10 , pp. 365-372
    • Al-Awadhi, S.A.1    Ghitany, M.E.2
  • 9
    • 0004794930 scopus 로고
    • Accident statistics and the concept of accident-proneness
    • Arbous, A.G. & Kerrich, J.E. (1951). Accident Statistics and the Concept of Accident-Proneness. Biometrics, 7, 340-432.
    • (1951) Biometrics , vol.7 , pp. 340-432
    • Arbous, A.G.1    Kerrich, J.E.2
  • 10
    • 17044398046 scopus 로고
    • The distribution of doctor-patient contacts in the national health service
    • Ashford J.R. & Hunt R.G. (1974). The Distribution of Doctor-Patient Contacts in the National Health Service. Journal of the Royal Statistical Society A, 137, 347-383.
    • (1974) Journal of the Royal Statistical Society A , vol.137 , pp. 347-383
    • Ashford, J.R.1    Hunt, R.G.2
  • 12
    • 84988098076 scopus 로고
    • Multivariate distributions with generalized inverse gaussian marginals and associated poisson mixtures
    • Barndorff-Nielsen, O.E., Blaesild, P. & Seshardi, V. (1992). Multivariate Distributions with Generalized Inverse Gaussian Marginals and Associated Poisson Mixtures. Canadian Journal of Statistics, 20, 109-120.
    • (1992) Canadian Journal of Statistics , vol.20 , pp. 109-120
    • Barndorff-Nielsen, O.E.1    Blaesild, P.2    Seshardi, V.3
  • 13
    • 0009203827 scopus 로고
    • Contributions to the theory of accident proneness part II: True or false contagion?
    • Bates, G. & Neyman, J. (1952a). Contributions to the Theory of Accident Proneness Part II: True Or False Contagion? University of California Publications in Statistics, pp. 255-275.
    • (1952) University of California Publications in Statistics , pp. 255-275
    • Bates, G.1    Neyman, J.2
  • 14
    • 0009203827 scopus 로고
    • Contributions to the theory of accident proneness part I: An optimistic model of the correlation between light and severe accidents
    • Bates, G. & Neyman, J. (1952b). Contributions to the Theory of Accident Proneness Part I: An Optimistic Model of the Correlation Between Light and Severe Accidents. University of California Publications in Statistics, pp. 215-253.
    • (1952) University of California Publications in Statistics , pp. 215-253
    • Bates, G.1    Neyman, J.2
  • 16
    • 0016127679 scopus 로고
    • An improved gamma approximation to the negative binomial
    • Best, A. & Gipps, B. (1974). An Improved Gamma Approximation to the Negative Binomial. Technometrics, 16, 621-624.
    • (1974) Technometrics , vol.16 , pp. 621-624
    • Best, A.1    Gipps, B.2
  • 17
    • 0041059460 scopus 로고
    • Confluent hypergeometric distributions of discrete and continuous type with application to accident proneness
    • Bhattacharya, S.K. (1966). Confluent Hypergeometric Distributions of Discrete and Continuous Type with Application to Accident Proneness. Bulletin of the Calcutta Statistical Association, 15, 20-31.
    • (1966) Bulletin of the Calcutta Statistical Association , vol.15 , pp. 20-31
    • Bhattacharya, S.K.1
  • 18
    • 0014098757 scopus 로고
    • A result in accident proneness
    • Bhattacharya, S.K. (1967). A Result in Accident Proneness. Biometrika, 54, 324-325.
    • (1967) Biometrika , vol.54 , pp. 324-325
    • Bhattacharya, S.K.1
  • 20
    • 0141462756 scopus 로고    scopus 로고
    • Decompounding: An estimation problem for poisson random sums
    • Buchmann, B. & Grubel, R. (2003). Decompounding: an Estimation Problem for Poisson Random Sums. Annals of Statistics, 31, 1054-1074.
    • (2003) Annals of Statistics , vol.31 , pp. 1054-1074
    • Buchmann, B.1    Grubel, R.2
  • 21
    • 0015981751 scopus 로고
    • On fitting the poisson lognormal distribution to species abundance data
    • Bulmer, M.G. (1974). On Fitting the Poisson Lognormal Distribution to Species Abundance Data. Biometrics, 30, 101-110.
    • (1974) Biometrics , vol.30 , pp. 101-110
    • Bulmer, M.G.1
  • 23
    • 0012362384 scopus 로고
    • A class of non-Identifiable stochastic models
    • Cane, V. (1977). A Class of Non-Identifiable Stochastic Models. Journal of Applied Probability, 14, 475-482.
    • (1977) Journal of Applied Probability , vol.14 , pp. 475-482
    • Cane, V.1
  • 24
    • 38249005811 scopus 로고
    • Nonparametric tests for mixed poisson distributions
    • Carriere, J. (1993). Nonparametric Tests for Mixed Poisson Distributions. Insurance Mathematics and Economics, 12, 3-8.
    • (1993) Insurance Mathematics and Economics , vol.12 , pp. 3-8
    • Carriere, J.1
  • 25
    • 0002601395 scopus 로고
    • Frequency distributions models in the ecology of plankton and other organisms
    • Cassie, M. (1964). Frequency Distributions Models in the Ecology of Plankton and Other Organisms. Journal of Animal Ecology, 31, 65-92.
    • (1964) Journal of Animal Ecology , vol.31 , pp. 65-92
    • Cassie, M.1
  • 27
    • 21844493268 scopus 로고
    • Optimal rate of convergence for finite mixture models
    • Chen, J. (1995). Optimal Rate of Convergence for Finite Mixture Models. Annals of Statistics, 23, 221-233.
    • (1995) Annals of Statistics , vol.23 , pp. 221-233
    • Chen, J.1
  • 28
    • 0030529993 scopus 로고    scopus 로고
    • Fitting mixed poisson regression models using quasi-likelihood methods
    • Chen, J. & Ahn, H. (1996). Fitting Mixed Poisson Regression Models Using Quasi-Likelihood Methods. Biometrical Journal, 38, 81-96.
    • (1996) Biometrical Journal , vol.38 , pp. 81-96
    • Chen, J.1    Ahn, H.2
  • 30
    • 0000865420 scopus 로고
    • Some remarks on overdispersion
    • Cox, D. (1983). Some Remarks on Overdispersion. Biometrika, 70, 269-274.
    • (1983) Biometrika , vol.70 , pp. 269-274
    • Cox, D.1
  • 31
    • 0346833240 scopus 로고
    • A useful empirical bayes identity
    • Cressie, N. (1982). A Useful Empirical Bayes Identity. Annals of Statistics, 10, 625-629.
    • (1982) Annals of Statistics , vol.10 , pp. 625-629
    • Cressie, N.1
  • 35
    • 38248998993 scopus 로고
    • A triptych of discrete distributions related to the stable law
    • Devroye, L. (1993). A Triptych of Discrete Distributions Related to the Stable Law. Statistics and Probability Letters, 18, 349-351.
    • (1993) Statistics and Probability Letters , vol.18 , pp. 349-351
    • Devroye, L.1
  • 36
    • 0003614212 scopus 로고
    • Statistical Distributions in Scientific Work Series 4. Fairland, MD, USA: International Cooperative Publishing House
    • Douglas, J.B. (1980). Analysis with Standard Contagious Distributions. Statistical Distributions in Scientific Work Series 4. Fairland, MD, USA: International Cooperative Publishing House.
    • (1980) Analysis with Standard Contagious Distributions
    • Douglas, J.B.1
  • 39
    • 0000543853 scopus 로고
    • On a generalized class of contagious distributions
    • Feller, W. (1943). On a Generalized Class of Contagious Distributions. Annals of Mathematical Statistics, 14, 389-400.
    • (1943) Annals of Mathematical Statistics , vol.14 , pp. 389-400
    • Feller, W.1
  • 41
    • 0023287238 scopus 로고
    • Robust empirical bayes analyses of event rates
    • Gaver, D. & O'Muircheartaigh, I.G. (1987). Robust Empirical Bayes Analyses of Event Rates. Technometrics, 29, 1-15.
    • (1987) Technometrics , vol.29 , pp. 1-15
    • Gaver, D.1    O'Muircheartaigh, I.G.2
  • 42
    • 78751700927 scopus 로고
    • A note on overdispersed exponential families
    • Gelfand, A. & Dalal, S. (1990). A Note on Overdispersed Exponential Families. Biometrika, 77, 55-64.
    • (1990) Biometrika , vol.77 , pp. 55-64
    • Gelfand, A.1    Dalal, S.2
  • 44
    • 38249015663 scopus 로고
    • From the generalized gamma to the generalized negative binomial distribution
    • Gerber, H.U. (1991). From the Generalized Gamma to the Generalized Negative Binomial Distribution. Insurance Mathematics and Economics, 10, 303-309.
    • (1991) Insurance Mathematics and Economics , vol.10 , pp. 303-309
    • Gerber, H.U.1
  • 46
    • 0030328087 scopus 로고    scopus 로고
    • A parametric model for heterogeneity in paired poisson counts
    • Goutis, C. & Galbraith, R.F. (1996). A Parametric Model for Heterogeneity in Paired Poisson Counts. Canadian Journal of Statistics, 24, 569-581.
    • (1996) Canadian Journal of Statistics , vol.24 , pp. 569-581
    • Goutis, C.1    Galbraith, R.F.2
  • 48
    • 0001460902 scopus 로고
    • An inquiry into the nature of frequency distributions representative of multiple happenings with particular reference to the occurrence of multiple attacks of disease or of repeated accidents
    • Greenwood, M. & Yule, G. (1920), An Inquiry into the Nature of Frequency Distributions Representative of Multiple Happenings with Particular Reference to the Occurrence of Multiple Attacks of Disease or of Repeated Accidents. Journal of the Royal Statistical Society A, 83, 255-279.
    • (1920) Journal of the Royal Statistical Society A , vol.83 , pp. 255-279
    • Greenwood, M.1    Yule, G.2
  • 49
    • 0011473828 scopus 로고
    • On mixtures of distributions: A survey and some new results on ranking and selection
    • Gupta, S. & Huang, W.T. (1981). On Mixtures of Distributions: A Survey and Some New Results on Ranking and Selection. Sankhyā B, 43, 245-290.
    • (1981) Sankhyā B , vol.43 , pp. 245-290
    • Gupta, S.1    Huang, W.T.2
  • 50
  • 51
    • 0011960461 scopus 로고
    • Some interrelations among compound and generalized distributions
    • Gurland, J. (1957). Some Interrelations among Compound and Generalized Distributions. Biometrika, 44, 263-268.
    • (1957) Biometrika , vol.44 , pp. 263-268
    • Gurland, J.1
  • 52
    • 0006304383 scopus 로고
    • A generalized class of contagious distributions
    • Gurland, J. (1958). A Generalized Class of Contagious Distributions. Biometrics, 14, 229-249.
    • (1958) Biometrics , vol.14 , pp. 229-249
    • Gurland, J.1
  • 53
    • 0034396294 scopus 로고    scopus 로고
    • Generalized bivariate count data regression models
    • Gurmu, S. & Elder, J. (2000). Generalized Bivariate Count Data Regression Models. Economics Letters, 68, 31-36.
    • (2000) Economics Letters , vol.68 , pp. 31-36
    • Gurmu, S.1    Elder, J.2
  • 54
    • 17044436383 scopus 로고
    • On the effect of removing persons with n or more accidents from an accident prone population
    • Haight, F.A. (1965). On the Effect of Removing Persons with n or More Accidents from an Accident Prone Population. Biometrika, 52, 298-300.
    • (1965) Biometrika , vol.52 , pp. 298-300
    • Haight, F.A.1
  • 56
    • 0038404563 scopus 로고
    • On measures of the distance of a mixture from its parent distribution
    • Hall, P. (1979). On Measures of the Distance of a Mixture from its Parent Distribution. Stochastic Processes and Applications, 8, 357-365.
    • (1979) Stochastic Processes and Applications , vol.8 , pp. 357-365
    • Hall, P.1
  • 57
    • 84974381117 scopus 로고
    • A recursive procedure for calculation of some compound distributions
    • Hesselager, O. (1994). A Recursive Procedure for Calculation of Some Compound Distributions. ASTIN Bulletin, 24, 19-32.
    • (1994) ASTIN Bulletin , vol.24 , pp. 19-32
    • Hesselager, O.1
  • 58
    • 84919164679 scopus 로고    scopus 로고
    • A recursive procedure for calculation of some mixed compound poisson distributions
    • Hesselager, O. (1996). A Recursive Procedure for Calculation of Some Mixed Compound Poisson Distributions. Scandinavian Actuarial Journal, (1), 54-63.
    • (1996) Scandinavian Actuarial Journal , Issue.1 , pp. 54-63
    • Hesselager, O.1
  • 60
    • 0000489632 scopus 로고
    • The modality of some compound poisson distributions
    • Holgate, P. (1970). The Modality of Some Compound Poisson Distributions. Biometrika, 57, 666-667.
    • (1970) Biometrika , vol.57 , pp. 666-667
    • Holgate, P.1
  • 62
    • 0031439880 scopus 로고    scopus 로고
    • Analysis of overdispersed count data by mixtures of poisson variables and poisson processes
    • Hougaard, P., Lee, M.L.T. & Whitmore, G.A. (1997). Analysis of Overdispersed Count Data by Mixtures of Poisson Variables and Poisson Processes. Biometrics, 53, 1225-1238.
    • (1997) Biometrics , vol.53 , pp. 1225-1238
    • Hougaard, P.1    Lee, M.L.T.2    Whitmore, G.A.3
  • 63
    • 0038434799 scopus 로고
    • The generalized waring distribution parts I, II, III
    • (Part I) (Part II) (Part III)
    • Irwin, J. (1975). The Generalized Waring Distribution Parts I, II, III. Journal of the Royal Statistical Society A, 138, 18-31 (Part I), 204-227 (Part II), 374-384 (Part III).
    • (1975) Journal of the Royal Statistical Society A , vol.138 , pp. 18-31
    • Irwin, J.1
  • 64
    • 0042113370 scopus 로고
    • Uniqueness of a result in the theory of accident proneness
    • Johnson, N.L. (1957). Uniqueness of a Result in the Theory of Accident Proneness. Biometrika, 44, 530-531.
    • (1957) Biometrika , vol.44 , pp. 530-531
    • Johnson, N.L.1
  • 65
    • 0346587044 scopus 로고
    • Note on a uniqueness of a result in the theory of accident proneness
    • Johnson, N.L. (1967). Note on a Uniqueness of a Result in the Theory of Accident Proneness. Journal of the American Statistical Association, 62, 288-289.
    • (1967) Journal of the American Statistical Association , vol.62 , pp. 288-289
    • Johnson, N.L.1
  • 68
    • 0038644021 scopus 로고    scopus 로고
    • Ph.D. Thesis, Department of Statistics, Athens University of Economics. ISBN: 960-7929-19-5
    • Karlis, D. (1998). Estimation and Testing Problems in Poisson Mixtures. Ph.D. Thesis, Department of Statistics, Athens University of Economics. ISBN: 960-7929-19-5.
    • (1998) Estimation and Testing Problems in Poisson Mixtures
    • Karlis, D.1
  • 69
    • 17044423675 scopus 로고    scopus 로고
    • On some distributions arising from the triangular distribution
    • Department of Statistics, Athens University of Economics and Business, August 2000
    • Karlis, D. & Xekalaki, E. (2000). On some Distributions Arising from the Triangular Distribution. Technical Report 111, Department of Statistics, Athens University of Economics and Business, August 2000.
    • (2000) Technical Report , vol.111
    • Karlis, D.1    Xekalaki, E.2
  • 70
    • 0039193154 scopus 로고
    • Interrelations among generalized distributions and their components
    • Katti, S. (1966). Interrelations among Generalized Distributions and their Components. Biometrics, 22, 44-52.
    • (1966) Biometrics , vol.22 , pp. 44-52
    • Katti, S.1
  • 71
    • 0010689929 scopus 로고
    • Splitters, lumpers and species per genus
    • Kemp, A.W. (1995). Splitters, Lumpers and Species per Genus. Mathematical Scientist, 20, 107-118.
    • (1995) Mathematical Scientist , vol.20 , pp. 107-118
    • Kemp, A.W.1
  • 73
    • 0005542311 scopus 로고
    • Mixtures with a limited number of modal intervals
    • Kemperman, J.H.B. (1991). Mixtures with a Limited Number of Modal Intervals. Annals of Statistics, 19, 2120-2144.
    • (1991) Annals of Statistics , vol.19 , pp. 2120-2144
    • Kemperman, J.H.B.1
  • 74
    • 0016670934 scopus 로고
    • A generalized form of Fisher's logarithmic series
    • Kempton, R.A. (1975). A Generalized Form of Fisher's Logarithmic Series. Biometrika, 62, 29-38.
    • (1975) Biometrika , vol.62 , pp. 29-38
    • Kempton, R.A.1
  • 75
    • 17044418836 scopus 로고    scopus 로고
    • Bounds on the kolmogorov distance of a mixture from its parent distribution
    • Khaledi, B.E. & Shaked, M. (2003). Bounds on the Kolmogorov Distance of a Mixture from its Parent Distribution. Sankhyā, A, 65, 317-332.
    • (2003) Sankhyā, A , vol.65 , pp. 317-332
    • Khaledi, B.E.1    Shaked, M.2
  • 77
  • 79
    • 84988052086 scopus 로고
    • Negative binomial and mixed poisson regression
    • Lawless, J. (1987). Negative Binomial and Mixed Poisson Regression. Canadian Journal of Statistics, 15, 209-225.
    • (1987) Canadian Journal of Statistics , vol.15 , pp. 209-225
    • Lawless, J.1
  • 81
    • 84988099053 scopus 로고
    • Uniqueness of estimation and identifiability in mixture models
    • Lindsay, B. & Roeder, K. (1993). Uniqueness of Estimation and Identifiability in Mixture Models. Canadian Journal of Statistics, 21, 139-147.
    • (1993) Canadian Journal of Statistics , vol.21 , pp. 139-147
    • Lindsay, B.1    Roeder, K.2
  • 82
    • 0007263918 scopus 로고
    • Mixtures, generalized convexity and balayages
    • Lynch, J. (1988). Mixtures, Generalized Convexity and Balayages. Scandinavian Journal of Statistics, 15, 203-210.
    • (1988) Scandinavian Journal of Statistics , vol.15 , pp. 203-210
    • Lynch, J.1
  • 83
    • 12844264697 scopus 로고
    • On the compound and generalized poisson distributions
    • Maceda, B.C. (1948). On the Compound and Generalized Poisson Distributions. Annals of Mathematical Statistics, 19, 414-416.
    • (1948) Annals of Mathematical Statistics , vol.19 , pp. 414-416
    • Maceda, B.C.1
  • 84
    • 0032525501 scopus 로고    scopus 로고
    • Hierarchical bayes estimation of mortality rates for disease mapping
    • Maiti, T. (1998). Hierarchical Bayes Estimation of Mortality Rates for Disease Mapping. Journal of Statistical Planning and Inference, 69, 339-348.
    • (1998) Journal of Statistical Planning and Inference , vol.69 , pp. 339-348
    • Maiti, T.1
  • 85
    • 17044373078 scopus 로고
    • The mixed poisson process
    • McFadden, J.A. (1965). The Mixed Poisson Process. Sankhyā, A, 27, 83-92.
    • (1965) Sankhyā, A , vol.27 , pp. 83-92
    • McFadden, J.A.1
  • 88
    • 84989479529 scopus 로고
    • Overdispersed poisson regression models for studies of air pollution and human health
    • McNeney, B. & Petkau, J. (1994). Overdispersed Poisson Regression Models for Studies of Air Pollution and Human Health. Canadian Journal of Statistics, 22, 421-440.
    • (1994) Canadian Journal of Statistics , vol.22 , pp. 421-440
    • McNeney, B.1    Petkau, J.2
  • 90
    • 0344628496 scopus 로고    scopus 로고
    • Stochastic comparisons of poisson and binomial random variables with their mixtures
    • Misra, N., Singh, H. & Harner, E.J (2003). Stochastic Comparisons of Poisson and Binomial Random Variables with their Mixtures. Statistics and Probability Letters, 65, 279-290.
    • (2003) Statistics and Probability Letters , vol.65 , pp. 279-290
    • Misra, N.1    Singh, H.2    Harner, E.J.3
  • 92
    • 0013467864 scopus 로고    scopus 로고
    • Simulated maximum likelihood estimation of multivariate mixed-poisson regression models, with applications
    • Munkin, M.K. & Trivedi, P.K. (1999). Simulated Maximum Likelihood Estimation of Multivariate Mixed-Poisson Regression Models, with Applications. Econometrics Journal, 2, 29-48.
    • (1999) Econometrics Journal , vol.2 , pp. 29-48
    • Munkin, M.K.1    Trivedi, P.K.2
  • 94
    • 0021393762 scopus 로고
    • A service model in which the server is required to search for customers
    • Neuts, M.F. & Ramalhoto, M.F. (1984). A Service Model in Which the Server is Required to Search for Customers. Journal of Applied Probability, 21, 157-166.
    • (1984) Journal of Applied Probability , vol.21 , pp. 157-166
    • Neuts, M.F.1    Ramalhoto, M.F.2
  • 95
    • 0012703083 scopus 로고
    • Empirical bayes point estimation in a family of probability distributions
    • Nichols, W.G. & Tsokos, C. (1972). Empirical Bayes Point Estimation in a Family of Probability Distributions. International Statistical Review, 40, 147-151.
    • (1972) International Statistical Review , vol.40 , pp. 147-151
    • Nichols, W.G.1    Tsokos, C.2
  • 96
    • 0346723557 scopus 로고
    • Computation of probabilities of a generalized log-series and related distributions
    • Ong, S.H. (1995). Computation of Probabilities of a Generalized Log-Series and Related Distributions. Communication in Statistics-Theory and Methods, 24, 253-271.
    • (1995) Communication in Statistics-theory and Methods , vol.24 , pp. 253-271
    • Ong, S.H.1
  • 97
    • 0040655675 scopus 로고    scopus 로고
    • On a class of discrete distributions arising from the birth-death with immigration process
    • Ong, S.H. (1996). On a Class of Discrete Distributions Arising from the Birth-Death with Immigration Process. Metrika, 43, 221-235.
    • (1996) Metrika , vol.43 , pp. 221-235
    • Ong, S.H.1
  • 99
    • 0011063904 scopus 로고
    • Graphical methods for a class of discrete distributions
    • Ord, K. (1967). Graphical Methods for a Class of Discrete Distributions. Journal of the Royal Statistical Society A, 130, 232-238.
    • (1967) Journal of the Royal Statistical Society A , vol.130 , pp. 232-238
    • Ord, K.1
  • 101
    • 38249036420 scopus 로고
    • A simple proof of feller's characterization of the compound poisson distribution
    • Ospina, V. & Gerber, H.U. (1987). A Simple Proof of Feller's Characterization of the Compound Poisson Distribution. Insurance Mathematics and Economics, 6, 63-64.
    • (1987) Insurance Mathematics and Economics , vol.6 , pp. 63-64
    • Ospina, V.1    Gerber, H.U.2
  • 102
    • 0002600114 scopus 로고
    • Recursive evaluation of a family of compound distributions
    • Panjer, H. (1981). Recursive Evaluation of a Family of Compound Distributions. ASTIN Bulletin, 18, 57-68.
    • (1981) ASTIN Bulletin , vol.18 , pp. 57-68
    • Panjer, H.1
  • 103
    • 0031498199 scopus 로고    scopus 로고
    • Posterior mean identifies the prior distribution in nb and related models
    • Papageorgiou, H. & Wesolowski, J. (1997). Posterior Mean Identifies the Prior Distribution in NB and Related Models. Statistics and Probability Letters, 36, 127-134.
    • (1997) Statistics and Probability Letters , vol.36 , pp. 127-134
    • Papageorgiou, H.1    Wesolowski, J.2
  • 104
    • 0039785453 scopus 로고
    • On certain compound poisson and compound binomial distributions
    • Patil, G.P. (1964). On Certain Compound Poisson and Compound Binomial Distributions. Sankhā A, 27, 293-294.
    • (1964) Sankhā A , vol.27 , pp. 293-294
    • Patil, G.P.1
  • 105
    • 0018194168 scopus 로고
    • Weighted distributions and size-biased sampling with applications to wildlife populations and human families
    • Patil, G.P. & Rao, C.R. (1978). Weighted Distributions and Size-Biased Sampling with Applications to Wildlife Populations and Human Families. Biometrics, 34, 179-189.
    • (1978) Biometrics , vol.34 , pp. 179-189
    • Patil, G.P.1    Rao, C.R.2
  • 107
    • 0032525542 scopus 로고    scopus 로고
    • Mixed poisson distributions tail equivalent to their mixing distributions
    • Perline, R. (1998). Mixed Poisson Distributions Tail Equivalent to their Mixing Distributions. Statistics and Probability Letters, 38, 229-233.
    • (1998) Statistics and Probability Letters , vol.38 , pp. 229-233
    • Perline, R.1
  • 108
    • 0000397925 scopus 로고
    • On the distance between mixed poisson and poisson distributions
    • Pfeifer, D. (1987). On the Distance between Mixed Poisson and Poisson Distributions. Statistics and Decision, 5, 367-379.
    • (1987) Statistics and Decision , vol.5 , pp. 367-379
    • Pfeifer, D.1
  • 109
    • 0009688550 scopus 로고
    • Run of one species with respect to another in transects through plant populations
    • Pielou, E. (1962). Run of One Species with Respect to Another in Transects through Plant Populations. Biometrics, 18, 579-593.
    • (1962) Biometrics , vol.18 , pp. 579-593
    • Pielou, E.1
  • 111
    • 0007597093 scopus 로고
    • A relation between the logarithmic, poisson and negative binomial series
    • Quenouille, M.H. (1949). A Relation between the Logarithmic, Poisson and Negative Binomial Series. Biometrics, 5, 162-164.
    • (1949) Biometrics , vol.5 , pp. 162-164
    • Quenouille, M.H.1
  • 112
    • 0010929305 scopus 로고
    • A mathematical model for accident proneness
    • Rai, G. (1971). A Mathematical Model for Accident Proneness. Trabajos Estadística, 22, 207-212.
    • (1971) Trabajos Estadística , vol.22 , pp. 207-212
    • Rai, G.1
  • 113
    • 0004051359 scopus 로고
    • On discrete distributions arising out of methods of ascertainment
    • Ed. G.P. Patil. Pergamon Press and Statistical Publishing Society, Calcutta
    • Rao, C.R. (1965). On Discrete Distributions Arising out of Methods of Ascertainment. In Classical and Contagious Discrete Distributions, Ed. G.P. Patil, pp. 320-332. Pergamon Press and Statistical Publishing Society, Calcutta.
    • (1965) Classical and Contagious Discrete Distributions , pp. 320-332
    • Rao, C.R.1
  • 114
    • 0021404166 scopus 로고
    • Mixture densities, maximum likelihood and the EM algorithm
    • Redner, R. & Walker, H. (1984). Mixture Densities, Maximum Likelihood and the EM Algorithm. SIAM Review, 26, 195-230.
    • (1984) SIAM Review , vol.26 , pp. 195-230
    • Redner, R.1    Walker, H.2
  • 115
    • 17044371447 scopus 로고    scopus 로고
    • Inference based on the empirical probability generating function for mixtures of poisson distributions
    • Remillard, B. & Theodorescu, R. (2000). Inference Based on the Empirical Probability Generating Function for Mixtures of Poisson Distributions. Statistics and Decisions, 18, 349-266.
    • (2000) Statistics and Decisions , vol.18 , pp. 349-1266
    • Remillard, B.1    Theodorescu, R.2
  • 116
    • 0037408743 scopus 로고    scopus 로고
    • Improvements in the poisson approximations of mixed poisson distributions
    • Roos, B. (2003). Improvements in the Poisson Approximations of Mixed Poisson Distributions. Journal of Statistical Planning and Inference, 113, 467-483.
    • (2003) Journal of Statistical Planning and Inference , vol.113 , pp. 467-483
    • Roos, B.1
  • 117
    • 84974317675 scopus 로고
    • A model for the claim number process
    • Ruohonen, M. (1988). A Model for the Claim Number Process. ASTIN Bulletin, 18, 57-68.
    • (1988) ASTIN Bulletin , vol.18 , pp. 57-68
    • Ruohonen, M.1
  • 118
    • 0040377748 scopus 로고
    • On certain properties of a class of compound poisson distributions
    • Sankaran, M. (1969). On Certain Properties of a Class of Compound Poisson Distributions. Sankhā B, 32, 353-362.
    • (1969) Sankhā B , vol.32 , pp. 353-362
    • Sankaran, M.1
  • 119
    • 0010860259 scopus 로고
    • The discrete poisson-lindley distribution
    • Sankaran, M. (1970). The Discrete Poisson-Lindley Distribution. Biometrics, 26, 145-149.
    • (1970) Biometrics , vol.26 , pp. 145-149
    • Sankaran, M.1
  • 120
    • 0001723762 scopus 로고
    • Identifiability of mixtures of power series distributions and related characterizations
    • Sapatinas, T. (1995). Identifiability of Mixtures of Power Series Distributions and Related Characterizations. Annals of the Institute of Statistical Mathematics, 47, 447-459.
    • (1995) Annals of the Institute of Statistical Mathematics , vol.47 , pp. 447-459
    • Sapatinas, T.1
  • 122
    • 84988106736 scopus 로고
    • Finite mixtures of natural exponential families
    • Seshadri, V. (1991). Finite Mixtures of Natural Exponential Families. Canadian Journal of Statistics, 19, 437-445.
    • (1991) Canadian Journal of Statistics , vol.19 , pp. 437-445
    • Seshadri, V.1
  • 124
    • 51249183562 scopus 로고
    • Generalized hypergeometric, digamma and trigamma distributions
    • Sibuya, M. (1979). Generalized Hypergeometric, Digamma and Trigamma Distributions. Annals of the Institute of Statistical Mathematics, 31, 373-390.
    • (1979) Annals of the Institute of Statistical Mathematics , vol.31 , pp. 373-390
    • Sibuya, M.1
  • 125
    • 0002663388 scopus 로고
    • On a distribution representing sentence-length in written prose
    • Sichel, H.S. (1974). On a Distribution Representing Sentence-Length in Written Prose. Journal of the Royal Statistical Society A, 137, 25-34.
    • (1974) Journal of the Royal Statistical Society A , vol.137 , pp. 25-34
    • Sichel, H.S.1
  • 127
    • 0000570212 scopus 로고
    • On a class of skew distributions
    • Simon, P. (1955). On a Class of Skew Distributions. Biometrika, 42, 425-440.
    • (1955) Biometrika , vol.42 , pp. 425-440
    • Simon, P.1
  • 128
    • 84988120995 scopus 로고
    • Robust bayesian analysis of the binomial empirical bayes problem
    • Sivaganesan, S. & Berger, J.O. (1993). Robust Bayesian Analysis of the Binomial Empirical Bayes Problem. The Canadian Journal of Statistics, 21, 107-119.
    • (1993) The Canadian Journal of Statistics , vol.21 , pp. 107-119
    • Sivaganesan, S.1    Berger, J.O.2
  • 132
    • 0009126233 scopus 로고
    • A test for intrinsic correlation in the theory of accident proneness
    • Subrahmaniam, K. (1966). A Test for Intrinsic Correlation in the Theory of Accident Proneness. Journal of the Royal Statistical Society B, 28, 180-189.
    • (1966) Journal of the Royal Statistical Society B , vol.28 , pp. 180-189
    • Subrahmaniam, K.1
  • 134
    • 0040599241 scopus 로고
    • The identifiability of mixtures of distributions
    • Tallis, G.M. (1969). The Identifiability of Mixtures of Distributions. Journal of Applied Probability, 6, 389-398.
    • (1969) Journal of Applied Probability , vol.6 , pp. 389-398
    • Tallis, G.M.1
  • 138
    • 0001431082 scopus 로고
    • Some recent research in the analysis of mixture distributions
    • Titterington, D.M. (1990). Some Recent Research in the Analysis of Mixture Distributions. Statistics, 21, 619-641.
    • (1990) Statistics , vol.21 , pp. 619-641
    • Titterington, D.M.1
  • 139
    • 4344585241 scopus 로고    scopus 로고
    • Using mixed poisson distributions in connection with bonus-malus systems
    • Wahlin, J.F. & Paris, J. (1999). Using Mixed Poisson Distributions in Connection with Bonus-Malus Systems. ASTIN Bulletin, 29, 81-99.
    • (1999) ASTIN Bulletin , vol.29 , pp. 81-99
    • Wahlin, J.F.1    Paris, J.2
  • 140
    • 38249000686 scopus 로고
    • Critical starting points for stable evaluation of mixed poisson probabilities
    • Wang, S. & Panjer, H. (1993). Critical Starting Points for Stable Evaluation of Mixed Poisson Probabilities. Insurance Mathematics and Economics, 13, 287-297.
    • (1993) Insurance Mathematics and Economics , vol.13 , pp. 287-297
    • Wang, S.1    Panjer, H.2
  • 141
    • 84974409319 scopus 로고
    • Further results on hesselager's recursive procedure for calculation of some compound distributions
    • Wang, S. & Sobrero, M. (1994). Further Results on Hesselager's Recursive Procedure for Calculation of Some Compound Distributions. ASTIN Bulletin, 24, 160-166.
    • (1994) ASTIN Bulletin , vol.24 , pp. 160-166
    • Wang, S.1    Sobrero, M.2
  • 142
    • 0029938342 scopus 로고    scopus 로고
    • Mixed poisson regression models with covariate dependent rates
    • Wang, P., Puterman, M., Cockburn, I. & Le, N. (1996). Mixed Poisson Regression Models with Covariate Dependent Rates. Biometrics, 52, 381-400.
    • (1996) Biometrics , vol.52 , pp. 381-400
    • Wang, P.1    Puterman, M.2    Cockburn, I.3    Le, N.4
  • 143
    • 84911226380 scopus 로고
    • Mixed compound poisson distribution
    • Willmot, G.E. (1986). Mixed Compound Poisson Distribution. ASTIN Bulletin Supplement, 16, 59-79.
    • (1986) ASTIN Bulletin Supplement , vol.16 , pp. 59-79
    • Willmot, G.E.1
  • 144
    • 0013452599 scopus 로고
    • Asymptotic tail behaviour of poisson mixtures with applications
    • Willmot, G.E. (1990). Asymptotic Tail Behaviour of Poisson Mixtures with Applications. Advances in Applied Probability, 22, 147-159.
    • (1990) Advances in Applied Probability , vol.22 , pp. 147-159
    • Willmot, G.E.1
  • 145
    • 0001385525 scopus 로고
    • On recursive evaluation of mixed poisson probabilities and related quantities
    • Willmot, G.E. (1993). On Recursive Evaluation of Mixed Poisson Probabilities and Related Quantities. Scandinavian Actuarial Journal, 18, 114-133.
    • (1993) Scandinavian Actuarial Journal , vol.18 , pp. 114-133
    • Willmot, G.E.1
  • 146
    • 84950663460 scopus 로고
    • On posterior probabilities and moments in mixed poisson processes
    • Willmot, G.E. & Sundt, B. (1989). On Posterior Probabilities and Moments in Mixed Poisson Processes. Scandinavian Actuarial Journal, 14, 139-146.
    • (1989) Scandinavian Actuarial Journal , vol.14 , pp. 139-146
    • Willmot, G.E.1    Sundt, B.2
  • 147
    • 15544379729 scopus 로고
    • Chance mechanisms for the univariate generalized waring distribution and related characterizations
    • Eds. C. Taillie, G.P. Patil and B. Baldessari. The Netherlands: D. Reidel Publishing Co.
    • Xekalaki, E. (1981). Chance Mechanisms for the Univariate Generalized Waring Distribution and Related Characterizations. In Statistical Distributions in Scientific Work, Eds. C. Taillie, G.P. Patil and B. Baldessari, 4, 157-171. The Netherlands: D. Reidel Publishing Co.
    • (1981) Statistical Distributions in Scientific Work , vol.4 , pp. 157-171
    • Xekalaki, E.1
  • 148
    • 0020973982 scopus 로고
    • The univariate generalized waring distribution in relation to accident theory: Proneness, spells or contagion?
    • Xekalaki, E. (1983a). The Univariate Generalized Waring Distribution in Relation to Accident Theory: Proneness, Spells Or Contagion? Biometrics, 39, 887-895.
    • (1983) Biometrics , vol.39 , pp. 887-895
    • Xekalaki, E.1
  • 149
    • 0346339249 scopus 로고
    • Infinite divisibility, completeness and regression properties of the univariate generalized waring distribution
    • Xekalaki, E. (1983b). Infinite Divisibility, Completeness and Regression Properties of the Univariate Generalized Waring Distribution. Annals of the Institute of Statistical Mathematics, 32, 279-289.
    • (1983) Annals of the Institute of Statistical Mathematics , vol.32 , pp. 279-289
    • Xekalaki, E.1
  • 150
    • 0007039949 scopus 로고
    • The bivariate generalized waring distribution and its application to accident theory
    • Xekalaki, E. (1984a). The Bivariate Generalized Waring Distribution and its Application to Accident Theory. Journal of the Royal Statistical Society A, 147, 488-498.
    • (1984) Journal of the Royal Statistical Society A , vol.147 , pp. 488-498
    • Xekalaki, E.1
  • 151
    • 11444268919 scopus 로고
    • Models leading to the bivariate generalized waring distribution
    • Xekalaki, E. (1984b). Models Leading to the Bivariate Generalized Waring Distribution. Utilitas Mathematica, 35, 263-290.
    • (1984) Utilitas Mathematica , vol.35 , pp. 263-290
    • Xekalaki, E.1
  • 152
    • 84972874640 scopus 로고
    • The multivariate generalized waring distribution
    • Xekalaki, E. (1986). The Multivariate Generalized Waring Distribution. Communications in Statistics, 15, 1047-1064.
    • (1986) Communications in Statistics , vol.15 , pp. 1047-1064
    • Xekalaki, E.1


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