메뉴 건너뛰기




Volumn 49, Issue 2-3, 2005, Pages 389-406

Gurland's ratio for the gamma function

Author keywords

Cram r Rao inequality; Gamma function; Gurland's ratio; Inverse function; Polygamma functions

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; ESTIMATION; HARMONIC ANALYSIS; INVERSE PROBLEMS; SET THEORY;

EID: 17644371319     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2004.01.016     Document Type: Article
Times cited : (44)

References (51)
  • 1
    • 84890486698 scopus 로고
    • An inequality satisfied by the gamma function
    • J. Gurland An inequality satisfied by the gamma function Skand. Aktuarietidiskr. 39 1956 171 172
    • (1956) Skand. Aktuarietidiskr. , vol.39 , pp. 171-172
    • Gurland, J.1
  • 3
    • 0034466955 scopus 로고    scopus 로고
    • Inequalities for beta and gamma functions via some classical and new integral inequalities
    • S.S. Dragomir, R.P. Agarwal, and N.S. Barnett Inequalities for beta and gamma functions via some classical and new integral inequalities J. of Inequalities and Applications 5 2000 103 165
    • (2000) J. of Inequalities and Applications , vol.5 , pp. 103-165
    • Dragomir, S.S.1    Agarwal, R.P.2    Barnett, N.S.3
  • 4
    • 85171841264 scopus 로고
    • Some elementary inequalities relating to the gamma and incomplete gamma function
    • W. Gautschi Some elementary inequalities relating to the gamma and incomplete gamma function J. Math. and Phys. 38 1959 77 81
    • (1959) J. Math. and Phys. , vol.38 , pp. 77-81
    • Gautschi, W.1
  • 5
    • 0030587988 scopus 로고    scopus 로고
    • Logarithmic convexity and inequalities for the gamma function
    • M. Merkle Logarithmic convexity and inequalities for the gamma function J. Math. Analysis Appl. 203 1996 369 380
    • (1996) J. Math. Analysis Appl. , vol.203 , pp. 369-380
    • Merkle, M.1
  • 6
    • 0042376839 scopus 로고    scopus 로고
    • On some inequalities for the gamma and psi functions
    • H. Alzer On some inequalities for the gamma and psi functions Math. Comp. 66 1997 373 389
    • (1997) Math. Comp. , vol.66 , pp. 373-389
    • Alzer, H.1
  • 7
    • 0002164044 scopus 로고
    • On some gamma function inequalities
    • J. Dutka On some gamma function inequalities SIAM J. Math. Anal. 16 1985 180 185
    • (1985) SIAM J. Math. Anal. , vol.16 , pp. 180-185
    • Dutka, J.1
  • 8
    • 17644403240 scopus 로고
    • Inequalities for the Wallis product
    • C.J. Everett Inequalities for the Wallis product Math. Mag. 43 1970 30 33
    • (1970) Math. Mag. , vol.43 , pp. 30-33
    • Everett, C.J.1
  • 11
    • 0000695717 scopus 로고
    • A generalization of gamma distribution
    • E.W. Stacy A generalization of gamma distribution Ann. Math. Statistics 28 1962 1187 1192
    • (1962) Ann. Math. Statistics , vol.28 , pp. 1187-1192
    • Stacy, E.W.1
  • 12
    • 0029251559 scopus 로고
    • Estimation of shape parameter for generalized Gaussian distribution in subband decomposition of video
    • K. Sharifi, and A. Leon-Garcia Estimation of shape parameter for generalized Gaussian distribution in subband decomposition of video IEEE Trans. Circ. Syst. Video Techn. 5 1995 52 56
    • (1995) IEEE Trans. Circ. Syst. Video Techn. , vol.5 , pp. 52-56
    • Sharifi, K.1    Leon-Garcia, A.2
  • 13
    • 0029307221 scopus 로고
    • Comparison of generalized Gaussian and Laplacian modeling in DCT image coding
    • R.L. Joshi, and T.R. Fischer Comparison of generalized Gaussian and Laplacian modeling in DCT image coding IEEE Signal Proc. Letters 2 1995 81
    • (1995) IEEE Signal Proc. Letters , vol.2 , pp. 81
    • Joshi, R.L.1    Fischer, T.R.2
  • 15
    • 17644389308 scopus 로고
    • Rasširenie granic primenimosti nekotorih neravnenstv dlya gamma-funkcii
    • I.V. Čebaevskaya Rasširenie granic primenimosti nekotorih neravnenstv dlya gamma-funkcii Moskov. Gos. Ped. Inst. Učen. Zap. 460 1972 38 42
    • (1972) Moskov. Gos. Ped. Inst. Učen. Zap. , vol.460 , pp. 38-42
    • Čebaevskaya, I.V.1
  • 16
    • 17644398536 scopus 로고
    • On certain inequalities connected with the gamma function
    • P.P. Chakrabarty On certain inequalities connected with the gamma function Skand. Aktuarietidiskr. 1969 20 23
    • (1969) Skand. Aktuarietidiskr. , pp. 20-23
    • Chakrabarty, P.P.1
  • 17
    • 0042766966 scopus 로고
    • On an inequality for gamma function
    • D. Gokhale On an inequality for gamma function Skand. Aktuarietidiskr. 1962 210 215
    • (1962) Skand. Aktuarietidiskr. , pp. 210-215
    • Gokhale, D.1
  • 18
    • 17644366554 scopus 로고
    • An inequality satisfied by the gamma function
    • I. Olkin An inequality satisfied by the gamma function Skand. Aktuarietidiskr. 61 1958 37 39
    • (1958) Skand. Aktuarietidiskr. , vol.61 , pp. 37-39
    • Olkin, I.1
  • 19
    • 17644396786 scopus 로고
    • An improved inequality satisfied by the gamma function
    • B. Raja Rao An improved inequality satisfied by the gamma function Skand. Aktuarietidiskr. 1969 78 83
    • (1969) Skand. Aktuarietidiskr. , pp. 78-83
    • Raja Rao, B.1
  • 20
    • 17644392928 scopus 로고
    • On an inequality satisfied by the gamma function and its logarithmic derivatives
    • B. Raja Rao On an inequality satisfied by the gamma function and its logarithmic derivatives Metron 39 3-4 1981 125 131
    • (1981) Metron , vol.39 , Issue.3-4 , pp. 125-131
    • Raja Rao, B.1
  • 21
    • 17644390000 scopus 로고
    • An inequality for the gamma function using the analogue of Bhatacharyya's inequality
    • B. Raja Rao, and M.L. Garg An inequality for the gamma function using the analogue of Bhatacharyya's inequality Skand. Aktuarietidiskr. 1969 71 77
    • (1969) Skand. Aktuarietidiskr. , pp. 71-77
    • Raja Rao, B.1    Garg, M.L.2
  • 22
    • 0042766962 scopus 로고
    • An inequality satisfied by the gamma function
    • J.B. Seliah An inequality satisfied by the gamma function Canadian Math. Bull. 19 1976 85 87
    • (1976) Canadian Math. Bull. , vol.19 , pp. 85-87
    • Seliah, J.B.1
  • 23
    • 17644367257 scopus 로고
    • Further stronger gamma function inequalities
    • R. Shantaram Further stronger gamma function inequalities Skand. Aktuarietidiskr. 1968 204 206
    • (1968) Skand. Aktuarietidiskr. , pp. 204-206
    • Shantaram, R.1
  • 24
    • 0002124539 scopus 로고
    • On some analogues to the amount of information and their use in statistical estimation
    • A. Bhattacharyya On some analogues to the amount of information and their use in statistical estimation Sankhya 8 1946 1 14
    • (1946) Sankhya , vol.8 , pp. 1-14
    • Bhattacharyya, A.1
  • 25
    • 17644371753 scopus 로고
    • On some analogs of Rao-Cramer inequality and a series of inequalities satisfied by the gamma function
    • B. Raja Rao On some analogs of Rao-Cramer inequality and a series of inequalities satisfied by the gamma function Metron 42 1-2 1984 89 108
    • (1984) Metron , vol.42 , Issue.1-2 , pp. 89-108
    • Raja Rao, B.1
  • 26
    • 17644376636 scopus 로고
    • On an analogue of Bhattacharyya bound
    • M. Sankaran On an analogue of Bhattacharyya bound Biometrika 51 1964 268 270
    • (1964) Biometrika , vol.51 , pp. 268-270
    • Sankaran, M.1
  • 28
    • 84973987300 scopus 로고
    • A note on gamma function
    • (Notes) G.N. Watson A note on gamma function Proc. Edin. Math. Soc. 11 1959 7 9
    • (1959) Proc. Edin. Math. Soc. , vol.11 , pp. 7-9
    • Watson, G.N.1
  • 29
    • 84945602615 scopus 로고
    • Gurland's inequality for the gamma function
    • A.V. Boyd Gurland's inequality for the gamma function Skand. Aktuarietidiskr. 43 1961 134 135
    • (1961) Skand. Aktuarietidiskr. , vol.43 , pp. 134-135
    • Boyd, A.V.1
  • 31
    • 0042265720 scopus 로고
    • Variance bounds and orthogonal expansions in Hilbert space with an application to inequalities for gamma function and π
    • H. Ruben Variance bounds and orthogonal expansions in Hilbert space with an application to inequalities for gamma function and π J. Reine und Angew. Math. 225 1967 147 153
    • (1967) J. Reine und Angew. Math. , vol.225 , pp. 147-153
    • Ruben, H.1
  • 35
    • 0001308973 scopus 로고
    • Kolmogorov-Landau inequalities for monotone functions
    • A.M. Fink Kolmogorov-Landau inequalities for monotone functions J. Math. Anal. Appl. 90 1982 251 258
    • (1982) J. Math. Anal. Appl. , vol.90 , pp. 251-258
    • Fink, A.M.1
  • 36
    • 84968470274 scopus 로고
    • Some gamma function inequalities
    • H. Alzer Some gamma function inequalities Math. Comp. 60 1993 337 346
    • (1993) Math. Comp. , vol.60 , pp. 337-346
    • Alzer, H.1
  • 37
    • 84966216618 scopus 로고
    • On gamma function inequalities
    • J. Bustoz, and M.E.H. Ismail On gamma function inequalities Math. Comp. 47 1986 659 667
    • (1986) Math. Comp. , vol.47 , pp. 659-667
    • Bustoz, J.1    Ismail, M.E.H.2
  • 38
    • 0022721836 scopus 로고
    • Completely monotonic functions associated with the gamma function and its q-analogues
    • M.E.H. Ismail, L. Lorch, and M. Muldoon Completely monotonic functions associated with the gamma function and its q-analogues J. Math. Anal. Appl. 116 1986 1 9
    • (1986) J. Math. Anal. Appl. , vol.116 , pp. 1-9
    • Ismail, M.E.H.1    Lorch, L.2    Muldoon, M.3
  • 39
    • 0002146064 scopus 로고
    • Some monotonicity properties and characterization of the gamma function
    • M.E. Muldoon Some monotonicity properties and characterization of the gamma function Aequationes Math. 18 1978 54 63
    • (1978) Aequationes Math. , vol.18 , pp. 54-63
    • Muldoon, M.E.1
  • 40
    • 0010883342 scopus 로고
    • On an integral connected with the average order of a class of arithmetical functions
    • J. Steinig On an integral connected with the average order of a class of arithmetical functions J. Number Theory 4 1972 463 468
    • (1972) J. Number Theory , vol.4 , pp. 463-468
    • Steinig, J.1
  • 41
    • 17644421561 scopus 로고
    • Generalization of Hölder's and Minkowski's inequalities
    • D.E. Daykin, and C.J. Eliezer Generalization of Hölder's and Minkowski's inequalities Proc. Camb. Phil. Soc. 64 1968 1023 1027
    • (1968) Proc. Camb. Phil. Soc. , vol.64 , pp. 1023-1027
    • Daykin, D.E.1    Eliezer, C.J.2
  • 45
    • 0032341719 scopus 로고    scopus 로고
    • Convexity, Schur-convexity and bounds for the gamma function involving the digamma function
    • M. Merkle Convexity, Schur-convexity and bounds for the gamma function involving the digamma function Rocky Mountain J. Math. 28 3 1998 1053 1066
    • (1998) Rocky Mountain J. Math. , vol.28 , Issue.3 , pp. 1053-1066
    • Merkle, M.1
  • 46
    • 0032381142 scopus 로고    scopus 로고
    • Inequalities for the polygamma functions
    • H. Alzer, and J. Wells Inequalities for the polygamma functions SIAM J. Math. Anal. 29 6 1998 1466 1549
    • (1998) SIAM J. Math. Anal. , vol.29 , Issue.6 , pp. 1466-1549
    • Alzer, H.1    Wells, J.2
  • 47
    • 0040209543 scopus 로고    scopus 로고
    • Representation of the error term in Jensen's and some related inequalities with applications
    • M. Merkle Representation of the error term in Jensen's and some related inequalities with applications J. Math. Analysis Appl. 231 1999 76 90
    • (1999) J. Math. Analysis Appl. , vol.231 , pp. 76-90
    • Merkle, M.1
  • 49
    • 84912062631 scopus 로고
    • The gamma function inequalities of Gurland and Gautschi
    • T. Erber The gamma function inequalities of Gurland and Gautschi Skand. Aktuarietidskr. 1961 27 28
    • (1961) Skand. Aktuarietidskr. , pp. 27-28
    • Erber, T.1
  • 50
    • 17644405904 scopus 로고
    • On gamma function inequalities
    • A.W. Kemp On gamma function inequalities Skand. Aktuarietidiskr. 1973 65 69
    • (1973) Skand. Aktuarietidiskr. , pp. 65-69
    • Kemp, A.W.1
  • 51
    • 0041882790 scopus 로고
    • Note on the gamma function
    • J.G. Wendel Note on the gamma function Am. Math. Monthly 55 1948 564 653
    • (1948) Am. Math. Monthly , vol.55 , pp. 564-653
    • Wendel, J.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.