메뉴 건너뛰기




Volumn 346, Issue 2, 2008, Pages 395-402

Properties of the probability density function of the non-central chi-squared distribution

Author keywords

Hoppe's formula; Modified Bessel function; Monotone form of l'Hospital's rule; Non central chi squared distribution; Tur n type inequality

Indexed keywords


EID: 45049083719     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2008.05.074     Document Type: Article
Times cited : (34)

References (23)
  • 1
    • 84968483625 scopus 로고
    • Computation of modified Bessel functions and their ratios
    • Amos D.E. Computation of modified Bessel functions and their ratios. Math. Comp. 28 (1974) 239-251
    • (1974) Math. Comp. , vol.28 , pp. 239-251
    • Amos, D.E.1
  • 5
    • 11944251241 scopus 로고    scopus 로고
    • Log-concave probability and its applications
    • Bagnoli M., and Bergstrom T. Log-concave probability and its applications. Econom. Theory 26 2 (2005) 445-469
    • (2005) Econom. Theory , vol.26 , Issue.2 , pp. 445-469
    • Bagnoli, M.1    Bergstrom, T.2
  • 6
    • 46149122293 scopus 로고    scopus 로고
    • Á. Baricz, Functional inequalities involving Bessel and modified Bessel functions of the first kind, Expo. Math. (2008), doi:10.1016/j.exmath.2008.01.001
    • Á. Baricz, Functional inequalities involving Bessel and modified Bessel functions of the first kind, Expo. Math. (2008), doi:10.1016/j.exmath.2008.01.001
  • 7
    • 34247121302 scopus 로고    scopus 로고
    • Inequalities involving modified Bessel functions of the first kind II
    • Baricz A., and Neuman E. Inequalities involving modified Bessel functions of the first kind II. J. Math. Anal. Appl. 332 1 (2007) 265-271
    • (2007) J. Math. Anal. Appl. , vol.332 , Issue.1 , pp. 265-271
    • Baricz, A.1    Neuman, E.2
  • 8
    • 84972535477 scopus 로고
    • Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
    • Cheeger J., Gromov M., and Taylor M. Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds. J. Differential Geom. 17 (1982) 15-53
    • (1982) J. Differential Geom. , vol.17 , pp. 15-53
    • Cheeger, J.1    Gromov, M.2    Taylor, M.3
  • 9
    • 0011316882 scopus 로고
    • The generalized Banach match-box problem: Application in disc storage management
    • Goczyla K. The generalized Banach match-box problem: Application in disc storage management. Acta Appl. Math. 5 1 (1986) 27-36
    • (1986) Acta Appl. Math. , vol.5 , Issue.1 , pp. 27-36
    • Goczyla, K.1
  • 10
    • 0009389702 scopus 로고
    • Isoperimetric inequalities in Riemannian manifolds
    • Asymptotic Theory of Finite Dimensional Spaces, Springer, Berlin
    • Gromov M. Isoperimetric inequalities in Riemannian manifolds. Asymptotic Theory of Finite Dimensional Spaces. Lecture Notes in Math. vol. 1200 (1986), Springer, Berlin 114-129
    • (1986) Lecture Notes in Math. , vol.1200 , pp. 114-129
    • Gromov, M.1
  • 11
    • 3042796336 scopus 로고
    • The Student t-distribution of an odd degree of freedom is infinitely divisible
    • Grosswald E. The Student t-distribution of an odd degree of freedom is infinitely divisible. Ann. Probab. 4 (1976) 680-683
    • (1976) Ann. Probab. , vol.4 , pp. 680-683
    • Grosswald, E.1
  • 12
    • 0346937063 scopus 로고
    • Bessel functions and the infinite divisibility of the Student t-distribution
    • Ismail M.E.H. Bessel functions and the infinite divisibility of the Student t-distribution. Ann. Probab. 5 4 (1977) 582-585
    • (1977) Ann. Probab. , vol.5 , Issue.4 , pp. 582-585
    • Ismail, M.E.H.1
  • 13
    • 0000302645 scopus 로고
    • Special functions, Stieltjes transforms and infinite divisibility
    • Ismail M.E.H., and Kelker D.H. Special functions, Stieltjes transforms and infinite divisibility. SIAM J. Math. Anal. 80 (1979) 884-901
    • (1979) SIAM J. Math. Anal. , vol.80 , pp. 884-901
    • Ismail, M.E.H.1    Kelker, D.H.2
  • 14
    • 84966208808 scopus 로고
    • An infinitely divisible distribution involving modified Bessel functions
    • Ismail M.E.H., and Miller K.S. An infinitely divisible distribution involving modified Bessel functions. Proc. Amer. Math. Soc. 85 2 (1982) 233-238
    • (1982) Proc. Amer. Math. Soc. , vol.85 , Issue.2 , pp. 233-238
    • Ismail, M.E.H.1    Miller, K.S.2
  • 16
    • 0035995563 scopus 로고    scopus 로고
    • The curious history of Faá di Bruno's formula
    • Johnson W.P. The curious history of Faá di Bruno's formula. Amer. Math. Monthly 109 (2002) 217-234
    • (2002) Amer. Math. Monthly , vol.109 , pp. 217-234
    • Johnson, W.P.1
  • 17
    • 45049086724 scopus 로고    scopus 로고
    • 2 distribution, Statist. Probab. Lett., submitted for publication
    • 2 distribution, Statist. Probab. Lett., submitted for publication
  • 18
    • 0005582809 scopus 로고    scopus 로고
    • L'Hospital type rules for oscillation, with applications
    • Article 33, 24 pp. (electronic)
    • Pinelis I. L'Hospital type rules for oscillation, with applications. J. Inequal. Pure Appl. Math. 2 3 (2001) Article 33, 24 pp. (electronic)
    • (2001) J. Inequal. Pure Appl. Math. , vol.2 , Issue.3
    • Pinelis, I.1
  • 19
    • 27844498408 scopus 로고    scopus 로고
    • Monotonicity properties of the relative error of a Padé approximation for Mills' ratio
    • Article 20, 8 pp. (electronic)
    • Pinelis I. Monotonicity properties of the relative error of a Padé approximation for Mills' ratio. J. Inequal. Pure Appl. Math. 3 2 (2002) Article 20, 8 pp. (electronic)
    • (2002) J. Inequal. Pure Appl. Math. , vol.3 , Issue.2
    • Pinelis, I.1
  • 20
    • 27844504363 scopus 로고    scopus 로고
    • L'Hospital type rules for monotonicity: Applications to probability inequalities for sums of bounded random variables
    • Article 7, 9 pp. (electronic)
    • Pinelis I. L'Hospital type rules for monotonicity: Applications to probability inequalities for sums of bounded random variables. J. Inequal. Pure Appl. Math. 3 1 (2002) Article 7, 9 pp. (electronic)
    • (2002) J. Inequal. Pure Appl. Math. , vol.3 , Issue.1
    • Pinelis, I.1
  • 21
    • 10844237920 scopus 로고    scopus 로고
    • L'Hospital rules for monotonicity and the Wilker-Anglesio inequality
    • Pinelis I. L'Hospital rules for monotonicity and the Wilker-Anglesio inequality. Amer. Math. Monthly 111 (2004) 905-909
    • (2004) Amer. Math. Monthly , vol.111 , pp. 905-909
    • Pinelis, I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.