메뉴 건너뛰기




Volumn 49, Issue 4, 2009, Pages 399-425

Domains of attraction to Tweedie distributions

Author keywords

Esscher transform; exponential tilting; natural exponential family; power variance function; Tauber theory; Tweedie domains of attraction

Indexed keywords


EID: 79451469182     PISSN: 03631672     EISSN: 15738825     Source Type: Journal    
DOI: 10.1007/s10986-009-9062-8     Document Type: Article
Times cited : (13)

References (54)
  • 7
    • 51249161499 scopus 로고
    • Characterization of the Jørgensen set in generalized linear models
    • M. Casalis and G. Letac, Characterization of the Jørgensen set in generalized linear models, Test, 3: 145-162, 1994.
    • (1994) Test , vol.3 , pp. 145-162
    • Casalis, M.1    Letac, G.2
  • 8
    • 0011627656 scopus 로고
    • On path properties of super-2 processes. II
    • Proc. Symp. Pure Math, M. G. Cranston and M. A. Pinsky (Eds.), Providence, RI: Amer. Math. Soc
    • D. A. Dawson, K. J. Hochberg, and V. Vinogradov, On path properties of super-2 processes. II, in M. G. Cranston and M. A. Pinsky (Eds.), Stochastic Analysis, Proc. Symp. Pure Math., Vol. 57, Amer. Math. Soc., Providence, RI, 1995, pp. 385-403.
    • (1995) Stochastic Analysis , vol.57 , pp. 385-403
    • Dawson, D.A.1    Hochberg, K.J.2    Vinogradov, V.3
  • 9
    • 0005456546 scopus 로고    scopus 로고
    • Stability and attraction to normality for Lévy processes at zero and infinity
    • R. A. Doney and R. A. Maller, Stability and attraction to normality for Lévy processes at zero and infinity, J. Theor. Probab., 15: 751-792, 2002.
    • (2002) J. Theor. Probab. , vol.15 , pp. 751-792
    • Doney, R.A.1    Maller, R.A.2
  • 10
    • 84862654961 scopus 로고    scopus 로고
    • The Tweedie package
    • P. Dunn, The Tweedie package, R Contributed Packages, 2008, http://cran. r-project. org/web/packages/tweedie/tweedie. pdf.
    • (2008) R Contributed Packages
    • Dunn, P.1
  • 11
    • 42949145468 scopus 로고    scopus 로고
    • Fluctuation scaling in complex systems: Taylor's law and beyond
    • Z. Eisler, I. Bartos, and J. Kertész, Fluctuation scaling in complex systems: Taylor's law and beyond, Adv. Phys., 57: 89-142, 2008.
    • (2008) Adv. Phys. , vol.57 , pp. 89-142
    • Eisler, Z.1    Bartos, I.2    Kertész, J.3
  • 14
    • 71349087408 scopus 로고    scopus 로고
    • Structural, continuity, and asymptotic properties of a branching particle system
    • K. J. Hochberg and V. Vinogradov, Structural, continuity, and asymptotic properties of a branching particle system, Lith. Math. J., 49(3): 241-270, 2009.
    • (2009) Lith. Math. J. , vol.49 , Issue.3 , pp. 241-270
    • Hochberg, K.J.1    Vinogradov, V.2
  • 17
    • 33947641216 scopus 로고
    • Introduction to the Theory of Regular Exponential Families
    • Institute of Mathematical Statistics, University of Copenhagen
    • S. Johansen, Introduction to the Theory of Regular Exponential Families, Lect. Notes, Vol. 3, Institute of Mathematical Statistics, University of Copenhagen, 1979.
    • (1979) Lect. Notes , vol.3
    • Johansen, S.1
  • 19
    • 0011377685 scopus 로고
    • Fitting Tweedie's compound Poisson model to insurance claims data
    • B. Jørgensen and M. C. P. de Souza, Fitting Tweedie's compound Poisson model to insurance claims data, Scand. Actuarial J. 69-93, 1994.
    • (1994) Scand. Actuarial J. , pp. 69-93
    • Jørgensen, B.1    de Souza, M.C.P.2
  • 20
    • 79956196197 scopus 로고    scopus 로고
    • The Lévy-Khinchine representation of the Tweedie family
    • B. Jørgensen and J. R. Martínez, The Lévy-Khinchine representation of the Tweedie family, Braz. J. Probab. Stat., 10: 225-233, 1996.
    • (1996) Braz. J. Probab. Stat. , vol.10 , pp. 225-233
    • Jørgensen, B.1    Martínez, J.R.2
  • 21
    • 0040923456 scopus 로고    scopus 로고
    • Tauber theory for infinitely divisible variance functions
    • B. Jørgensen and J. R. Martínez, Tauber theory for infinitely divisible variance functions, Bernoulli, 3: 213-224, 1997.
    • (1997) Bernoulli , vol.3 , pp. 213-224
    • Jørgensen, B.1    Martínez, J.R.2
  • 22
    • 0001046327 scopus 로고
    • Asymptotic behaviour of the variance function
    • B. Jørgensen, J. R. Martínez, and M. Tsao, Asymptotic behaviour of the variance function, Scand. J. Stat., 21: 223-243, 1994.
    • (1994) Scand. J. Stat. , vol.21 , pp. 223-243
    • Jørgensen, B.1    Martínez, J.R.2    Tsao, M.3
  • 23
    • 0032387664 scopus 로고    scopus 로고
    • Stationary time series models with exponential dispersion model margins
    • B. Jørgensen and P. X.-K. Song, Stationary time series models with exponential dispersion model margins, J. Appl. Probab., 35: 78-92, 1998.
    • (1998) J. Appl. Probab. , vol.35 , pp. 78-92
    • Jørgensen, B.1    Song, P.X.-K.2
  • 24
    • 40549116554 scopus 로고    scopus 로고
    • Diagnosis of stationarity in state space models for longitudinal data
    • B. Jørgensen and P. X.-K. Song, Diagnosis of stationarity in state space models for longitudinal data, Far East J. Theor. Stat., 19: 43-59, 2006.
    • (2006) Far East J. Theor. Stat. , vol.19 , pp. 43-59
    • Jørgensen, B.1    Song, P.X.-K.2
  • 25
    • 84862688479 scopus 로고    scopus 로고
    • Stationary state space models for longitudinal data
    • B. Jørgensen and P. X.-K. Song, Stationary state space models for longitudinal data, Can. J. Stat., 34: 1-23, 2007.
    • (2007) Can. J. Stat. , vol.34 , pp. 1-23
    • Jørgensen, B.1    Song, P.X.-K.2
  • 26
    • 0033619156 scopus 로고    scopus 로고
    • Dispersion models and longitudinal data analysis
    • B. Jørgensen and M. Tsao, Dispersion models and longitudinal data analysis, Stat. Med., 18: 2257-2270, 1999.
    • (1999) Stat. Med. , vol.18 , pp. 2257-2270
    • Jørgensen, B.1    Tsao, M.2
  • 29
    • 0023571337 scopus 로고
    • Families of discrete distributions satisfying Taylor's power law
    • A. W. Kemp, Families of discrete distributions satisfying Taylor's power law, Biometrics, 43: 693-699, 1987.
    • (1987) Biometrics , vol.43 , pp. 693-699
    • Kemp, A.W.1
  • 30
    • 0036605988 scopus 로고    scopus 로고
    • Spatial aggregation of the Colorado potato beetle described by an exponential dispersion model
    • W. S. Kendal, Spatial aggregation of the Colorado potato beetle described by an exponential dispersion model, Ecol. Model., 151: 261-269, 2002.
    • (2002) Ecol. Model. , vol.151 , pp. 261-269
    • Kendal, W.S.1
  • 31
    • 2942534600 scopus 로고    scopus 로고
    • A scale invariant clustering of genes on Human chromosome 7
    • W. S. Kendal, A scale invariant clustering of genes on Human chromosome 7, BMC Evol. Biol., 4(3), 2004, http://www. biomedcentral. com/1471-2148/4/3.
    • (2004) BMC Evol. Biol , vol.4 , Issue.3
    • Kendal, W.S.1
  • 32
    • 33847012601 scopus 로고    scopus 로고
    • Scale invariant correlations between genes and SNPs on Human chromosome 1 reveal potential evolutionary mechanisms
    • W. S. Kendal, Scale invariant correlations between genes and SNPs on Human chromosome 1 reveal potential evolutionary mechanisms, J. Theor. Biol., 245: 329-340, 2007.
    • (2007) J. Theor. Biol. , vol.245 , pp. 329-340
    • Kendal, W.S.1
  • 33
    • 0035065398 scopus 로고    scopus 로고
    • Characterization of the frequency distribution for Human hematogenous metastases: Evidence for clustering and a power variance function
    • W. S. Kendal, F. J. Lagerwaard, and O. Agboola, Characterization of the frequency distribution for Human hematogenous metastases: Evidence for clustering and a power variance function, Clin. Exp. Metastas., 18: 219-229, 2000.
    • (2000) Clin. Exp. Metastas. , vol.18 , pp. 219-229
    • Kendal, W.S.1    Lagerwaard, F.J.2    Agboola, O.3
  • 34
    • 12844266231 scopus 로고    scopus 로고
    • Some discrete exponential dispersion models: Poisson-Tweedie and Hinde-Demétrio classes
    • C. C. Kokonendji, S. Dossou-Gbété, and C. G. B. Demétrio, Some discrete exponential dispersion models: Poisson-Tweedie and Hinde-Demétrio classes, SORT, 28: 201-214, 2004.
    • (2004) Sort , vol.28 , pp. 201-214
    • Kokonendji, C.C.1    Dossou-Gbété, S.2    Demétrio, C.G.B.3
  • 36
    • 21144471046 scopus 로고
    • Stochastic processes directed by randomized time
    • M.-L. T. Lee and G. A. Whitmore, Stochastic processes directed by randomized time, J. Appl. Probab., 30: 302-314, 1993.
    • (1993) J. Appl. Probab. , vol.30 , pp. 302-314
    • Lee, M.-L.T.1    Whitmore, G.A.2
  • 37
    • 0035994039 scopus 로고    scopus 로고
    • The real powers of the convolution of a negative-binomial distribution and a Bernoulli distribution
    • G. Letac, D. Malouche, and S. Maurer, The real powers of the convolution of a negative-binomial distribution and a Bernoulli distribution, Proc. Am. Math. Soc., 130: 2107-2114, 2002.
    • (2002) Proc. Am. Math. Soc. , vol.130 , pp. 2107-2114
    • Letac, G.1    Malouche, D.2    Maurer, S.3
  • 38
    • 0009026932 scopus 로고
    • Convergence of the variance functions of natural exponential families
    • M. Mora, Convergence of the variance functions of natural exponential families, Ann. Fac. Sci. Univ. Toulouse, Sér. 5, 11: 105-120, 1990.
    • (1990) Ann. Fac. Sci. Univ. Toulouse, Sér , vol.5-11 , pp. 105-120
    • Mora, M.1
  • 39
    • 0032222992 scopus 로고    scopus 로고
    • Cramér's large deviations when the extreme conjugate distribution is heavy-tailed
    • A. V. Nagaev, Cramér's large deviations when the extreme conjugate distribution is heavy-tailed, Theory Probab. Appl., 43: 405-421, 1998.
    • (1998) Theory Probab. Appl. , vol.43 , pp. 405-421
    • Nagaev, A.V.1
  • 40
    • 11844251444 scopus 로고
    • Limit theorems that take into account large deviations for sums of positive random variables
    • A. V. Nagaev and S. S. Hodžabagjan, Limit theorems that take into account large deviations for sums of positive random variables, Lith. Math. J., 14: 149-163, 1974.
    • (1974) Lith. Math. J. , vol.14 , pp. 149-163
    • Nagaev, A.V.1    Hodžabagjan, S.S.2
  • 41
    • 0039832225 scopus 로고
    • A Poisson-folyamat egy jellemzíse (A characterization of Poisson processes)
    • A. Rényi, A Poisson-folyamat egy jellemzíse (A characterization of Poisson processes), Magyar Tud. Akad. Mat. Kutató, Int. Közl., 1: 519-527, 1956.
    • (1956) Magyar Tud. Akad. Mat. Kutató, Int. Közl. , vol.1 , pp. 519-527
    • Rényi, A.1
  • 42
    • 0004263072 scopus 로고
    • Lect. Notes Math, Berlin: Springer-Verlag
    • E. Seneta, Regularly Varying Functions, Lect. Notes Math., Vol. 508, Springer-Verlag, Berlin, 1976.
    • (1976) Regularly Varying Functions , vol.508
    • Seneta, E.1
  • 43
    • 85011436968 scopus 로고    scopus 로고
    • Fitting Tweedie's compound Poisson model to insurance claims data: Dispersion modelling
    • G. K. Smyth and B. Jørgensen, Fitting Tweedie's compound Poisson model to insurance claims data: Dispersion modelling, Astin Bull., 32: 143-157, 2002.
    • (2002) Astin Bull. , vol.32 , pp. 143-157
    • Smyth, G.K.1    Jørgensen, B.2
  • 47
    • 80052738078 scopus 로고    scopus 로고
    • On a conjecture of B. Jørgensen and A.D. Wentzell: From extreme stable laws to Tweedie exponential dispersion models
    • Can. Math. Soc. Conf. Proc. Ser, L. Gorostiza and G. Ivanoff (Eds.), Providence, RI: Amer. Math. Soc
    • V. Vinogradov, On a conjecture of B. Jørgensen and A. D. Wentzell: From extreme stable laws to Tweedie exponential dispersion models, in L. Gorostiza and G. Ivanoff (Eds.), Proceedings Volume for the International Conference on Stochastic Models in Honour of D. A. Dawson, Can. Math. Soc. Conf. Proc. Ser., Vol. 26, Amer. Math. Soc., Providence, RI, 2000, pp. 435-443.
    • (2000) Proceedings Volume for the International Conference on Stochastic Models in Honour of D.A. Dawson , vol.26 , pp. 435-443
    • Vinogradov, V.1
  • 48
    • 2342593008 scopus 로고    scopus 로고
    • On a class of Lévy processes used to model stock price movements with possible downward jumps
    • V. Vinogradov, On a class of Lévy processes used to model stock price movements with possible downward jumps, C. R. Math. Rep. Acad. Sci. Can., 24: 152-159, 2002.
    • (2002) C. R. Math. Rep. Acad. Sci. Can. , vol.24 , pp. 152-159
    • Vinogradov, V.1
  • 49
    • 84862704879 scopus 로고    scopus 로고
    • On a model for stock price movements and the power-variance family
    • V. Vinogradov, On a model for stock price movements and the power-variance family, C. R. Math. Rep. Acad. Sci. Can., 26: 102-109, 2004.
    • (2004) C. R. Math. Rep. Acad. Sci. Can. , vol.26 , pp. 102-109
    • Vinogradov, V.1
  • 50
    • 2342614803 scopus 로고    scopus 로고
    • On the power-variance family of probability distributions
    • Errata, p. 2573
    • V. Vinogradov, On the power-variance family of probability distributions, Commun. Stat. Theory Methods, 33: 1007-1029, 2004. Errata, p. 2573.
    • (2004) Commun. Stat. Theory Methods , vol.33 , pp. 1007-1029
    • Vinogradov, V.1
  • 51
    • 71349083967 scopus 로고    scopus 로고
    • Local approximations for branching particle systems
    • V. Vinogradov, Local approximations for branching particle systems, Commun. Stoch. Anal., 1: 293-309, 2007.
    • (2007) Commun. Stoch. Anal. , vol.1 , pp. 293-309
    • Vinogradov, V.1
  • 52
    • 33847366705 scopus 로고    scopus 로고
    • On infinitely divisible exponential dispersion model related to Poisson-exponential distribution
    • V. Vinogradov, On infinitely divisible exponential dispersion model related to Poisson-exponential distribution, Commun. Stat. Theory Methods, 36: 253-263, 2007.
    • (2007) Commun. Stat. Theory Methods , vol.36 , pp. 253-263
    • Vinogradov, V.1
  • 53
    • 39049138957 scopus 로고    scopus 로고
    • On approximations for two classes of Poisson mixtures
    • V. Vinogradov, On approximations for two classes of Poisson mixtures, Stat. Probab. Lett., 78: 358-366, 2008.
    • (2008) Stat. Probab. Lett. , vol.78 , pp. 358-366
    • Vinogradov, V.1
  • 54
    • 71349083488 scopus 로고    scopus 로고
    • Properties of certain Lévy and geometric Lévy processes
    • V. Vinogradov, Properties of certain Lévy and geometric Lévy processes, Commun. Stoch. Anal., 2: 193-208, 2008.
    • (2008) Commun. Stoch. Anal. , vol.2 , pp. 193-208
    • Vinogradov, V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.