메뉴 건너뛰기




Volumn 197, Issue 3, 1996, Pages 825-854

Length biasing and laws equivalent to the log-normal

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0030080253     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1996.0056     Document Type: Article
Times cited : (32)

References (31)
  • 2
    • 0000905932 scopus 로고
    • The q-gamma and q-beta functions
    • 2. R. Askey, The q-gamma and q-beta functions, Appl. Anal. 8 (1978), 125-141.
    • (1978) Appl. Anal. , vol.8 , pp. 125-141
    • Askey, R.1
  • 3
    • 0001582431 scopus 로고
    • Ramanujan's extensions of the gamma and beta functions
    • 3. R. Askey, Ramanujan's extensions of the gamma and beta functions, Amer. Math. Monthly 87 (1980), 346-358.
    • (1980) Amer. Math. Monthly , vol.87 , pp. 346-358
    • Askey, R.1
  • 4
    • 0002934080 scopus 로고
    • Orthogonal polynomials and theta functions
    • 4. R. Askey, Orthogonal polynomials and theta functions, Proc. Sympos. Pure Math. 49 (1989), 299-321.
    • (1989) Proc. Sympos. Pure Math. , vol.49 , pp. 299-321
    • Askey, R.1
  • 5
    • 0011691502 scopus 로고
    • The limits of sequences of iterated overshoot distribution functions
    • 5. P. van Beek and J. Braat, The limits of sequences of iterated overshoot distribution functions, Stochastic Process. Appl. 1 (1973), 307-316.
    • (1973) Stochastic Process. Appl. , vol.1 , pp. 307-316
    • Van Beek, P.1    Braat, J.2
  • 6
    • 0001301538 scopus 로고
    • A characterization and a class of distribution functions for the Stieltjes-Wigert polynomials
    • 6. T. S. Chihara, A characterization and a class of distribution functions for the Stieltjes-Wigert polynomials, Canad. Math. Bull. 13 (1970), 529-532.
    • (1970) Canad. Math. Bull. , vol.13 , pp. 529-532
    • Chihara, T.S.1
  • 7
    • 0018737488 scopus 로고
    • On generalized Stieltjes-Wigert and related orthogonal polynomials
    • 7. T. S. Chihara, On generalized Stieltjes-Wigert and related orthogonal polynomials, J. Comput. Appl. Math. 5 (1979), 291-297.
    • (1979) J. Comput. Appl. Math. , vol.5 , pp. 291-297
    • Chihara, T.S.1
  • 8
    • 0011691724 scopus 로고
    • Orthogonal Laurent-polynomials and continued fractions associated with log-normal distributions
    • 8. S. C. Cooper, W. B. Jones, and W. J. Thron, Orthogonal Laurent-polynomials and continued fractions associated with log-normal distributions, J. Comput. Appl. Math. 32 (1990), 39-46.
    • (1990) J. Comput. Appl. Math. , vol.32 , pp. 39-46
    • Cooper, S.C.1    Jones, W.B.2    Thron, W.J.3
  • 11
    • 0001240798 scopus 로고
    • Existence of quasi-stationary distributions. A renewal dynamic approach
    • 11. P. A. Ferrari, H. Kesten, S. Martinez, and P. Picco, Existence of quasi-stationary distributions. A renewal dynamic approach, Ann. Probab. 23 (1995), 501-521.
    • (1995) Ann. Probab. , vol.23 , pp. 501-521
    • Ferrari, P.A.1    Kesten, H.2    Martinez, S.3    Picco, P.4
  • 13
    • 85029965190 scopus 로고    scopus 로고
    • Convergence of sequences of transformations of distribution functions and some moment problems
    • (G. P. Patil et al., Eds.), Reidel, Dordrecht
    • 13. W. L. Harkness, Convergence of sequences of transformations of distribution functions and some moment problems, "Statistical Distributions in Scientific Work, Vol. 1" (G. P. Patil et al., Eds.), pp. 203-211, Reidel, Dordrecht.
    • Statistical Distributions in Scientific Work, Vol. 1 , vol.1 , pp. 203-211
    • Harkness, W.L.1
  • 14
    • 84972495994 scopus 로고
    • Convergence of transformations of distribution functions
    • 14. W. L. Harkness and R. Shantaram, Convergence of transformations of distribution functions, Pacific J. Math. 31 (1969), 403-415.
    • (1969) Pacific J. Math. , vol.31 , pp. 403-415
    • Harkness, W.L.1    Shantaram, R.2
  • 16
    • 0011677790 scopus 로고
    • The lognormal distribution and strong non-uniqueness of the moment problem
    • 16. R. Leipnik, The lognormal distribution and strong non-uniqueness of the moment problem, Theoret. Probab. Appl. 26 (1981), 850-852.
    • (1981) Theoret. Probab. Appl. , vol.26 , pp. 850-852
    • Leipnik, R.1
  • 17
    • 38249004693 scopus 로고
    • A probabilistic generalization of Taylor's theorem
    • 17. W. A. Massey and W. Whitt, A probabilistic generalization of Taylor's theorem, Probab. Statist. Lett. 16 (1993), 51-54.
    • (1993) Probab. Statist. Lett. , vol.16 , pp. 51-54
    • Massey, W.A.1    Whitt, W.2
  • 18
    • 0003009316 scopus 로고
    • The q-analogue of the Laguerre polynomials
    • 18. D. S. Moak, The q-analogue of the Laguerre polynomials, J. Math. Anal. Appl. 81 (1981), 20-47.
    • (1981) J. Math. Anal. Appl. , vol.81 , pp. 20-47
    • Moak, D.S.1
  • 19
    • 0642270418 scopus 로고    scopus 로고
    • Characterization by invariance under length-biasing and random scaling
    • to appear
    • 19. A. G. Pakes, Characterization by invariance under length-biasing and random scaling, J. Statist. Inf. Planning, to appear.
    • J. Statist. Inf. Planning
    • Pakes, A.G.1
  • 21
    • 84985560541 scopus 로고
    • Length-biasing, characterization of laws, and the moment problem
    • 21. A. G. Pakes and R. Khattree, Length-biasing, characterization of laws, and the moment problem, Austral. J. Statist. 34 (1992), 307-322.
    • (1992) Austral. J. Statist. , vol.34 , pp. 307-322
    • Pakes, A.G.1    Khattree, R.2
  • 23
    • 0022187414 scopus 로고
    • Orthogonal polynomials and some q-beta integrals of Ramanujan
    • 23. P. I. Pastro, Orthogonal polynomials and some q-beta integrals of Ramanujan, J. Math. Anal. Appl. 112 (1985), 517-540.
    • (1985) J. Math. Anal. Appl. , vol.112 , pp. 517-540
    • Pastro, P.I.1
  • 24
    • 0001792773 scopus 로고
    • Weighted distributions arising out of methods of ascertainment: What population does a sample represent?
    • (A. C. Atkinson and S. E. Fienberg, Eds.), Springer-Verlag, New York
    • 24. C. R. Rao, Weighted distributions arising out of methods of ascertainment: What population does a sample represent? in "A Celebration of Statistics: The ISI Centenary Volume," pp. 543-569, (A. C. Atkinson and S. E. Fienberg, Eds.), Springer-Verlag, New York, 1985.
    • (1985) A Celebration of Statistics: The ISI Centenary Volume , pp. 543-569
    • Rao, C.R.1
  • 25
    • 51249187674 scopus 로고
    • A limit theorem for a certain transform of sums of random variables
    • 25. R. Shantaram and W. L. Harkness, A limit theorem for a certain transform of sums of random variables, Ann. Inst. Statist. Math. 22 (1970), 181-184.
    • (1970) Ann. Inst. Statist. Math. , vol.22 , pp. 181-184
    • Shantaram, R.1    Harkness, W.L.2
  • 26
    • 0011681082 scopus 로고
    • On a certain class of limit distributions
    • 26. R. Shantaram and W. L. Harkness, On a certain class of limit distributions, Ann. Math. Statist. 43 (1972), 2067-2071.
    • (1972) Ann. Math. Statist. , vol.43 , pp. 2067-2071
    • Shantaram, R.1    Harkness, W.L.2
  • 28
    • 0001095135 scopus 로고
    • Distribution functions invariant under residual-lifetime and length-biased sampling
    • 28. Y. Vardi, L. A. Shepp, and B. F. Logan, Distribution functions invariant under residual-lifetime and length-biased sampling, Z. Wahrsceinlichkeitstheorie verw. Gebiete, 56 (1981), 415-426.
    • (1981) Z. Wahrsceinlichkeitstheorie Verw. Gebiete , vol.56 , pp. 415-426
    • Vardi, Y.1    Shepp, L.A.2    Logan, B.F.3
  • 29
    • 0022023316 scopus 로고
    • The renewal-process stationary-excess operator
    • 29. W. Whitt, The renewal-process stationary-excess operator, J. Appl. Probab. 22 (1985), 156-167.
    • (1985) J. Appl. Probab. , vol.22 , pp. 156-167
    • Whitt, W.1
  • 30
    • 0011562928 scopus 로고
    • Joint simulation of backward and forward recurrence times in a renewal process
    • 30. B. B. Winter, Joint simulation of backward and forward recurrence times in a renewal process, J. Appl. Probab. 26 (1989), 404-407.
    • (1989) J. Appl. Probab. , vol.26 , pp. 404-407
    • Winter, B.B.1
  • 31
    • 84988099626 scopus 로고
    • A product-limit estimator for use with length-biased data
    • 31. B. B. Winter and A. Földes, A product-limit estimator for use with length-biased data, Canad. J. Statist. 16 (1988), 337-355.
    • (1988) Canad. J. Statist. , vol.16 , pp. 337-355
    • Winter, B.B.1    Földes, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.