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Algorithm 939: Computation of the Marcum \(Q\)-function. (English) Zbl 1322.65046


MSC:

65D20 Computation of special functions and constants, construction of tables
33E20 Other functions defined by series and integrals
65C60 Computational problems in statistics (MSC2010)

Software:

DLMF; Algorithm 939
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Full Text: DOI arXiv

References:

[1] Ashour, S. K. and Abdel-Samad, A. I. 1990. On the computation of noncentral chisquare distribution function.Comm. Statist. Simul. Comput. 19, 4, 1279–1291. · Zbl 0850.62204 · doi:10.1080/03610919008812916
[2] Bleistein, N. 1966. Uniform asymptotic expansions of integrals with stationary point near algebraic singularity.Comm. Pure Appl. Math. 19, 353–370. · Zbl 0145.15801 · doi:10.1002/cpa.3160190403
[3] Cohen, J. D. 1988. Noncentral chi-square: Some observations on recurrence.Amer. Statist. 42, 120–122.
[4] Dyrting, S. 2004. Evaluating the noncentral chi-square distribution for the cox-ingersoll-ross process.Comput. Econ. 24, 35–50. · Zbl 1059.62013 · doi:10.1023/B:CSEM.0000038840.58451.c9
[5] Gautschi, W. 1961. Recursive computation of certain integrals.J. ACM 8, 21–40. · Zbl 0097.12201 · doi:10.1145/321052.321054
[6] Gil, A., Segura, J., and Temme, N. M. 2007.Numerical Methods for Special Functions. SIAM, Philadelphia, PA. · Zbl 1144.65016 · doi:10.1137/1.9780898717822
[7] Gil, A., Segura, J., and Temme, N. M. 2012. Efficient and accurate algorithms for the computation and inversion of the incomplete gamma function ratios.SIAM J. Sci. Comput. 34, 6, A2965–A2981. · Zbl 1259.33006 · doi:10.1137/120872553
[8] Gil, A., Segura, J., and Temme, N. M. 2013. Recent software developments for special functions in the santander-amsterdam project.Sci. Comput. Program.(To appear)
[9] Helstrom, C. W. 1992. Computing the generalized marcum q–function.IEEE Trans. Inf. Theory 38, 4, 1422–1428. · doi:10.1109/18.144731
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[11] Marcum, J. I. 1960. A statistical theory of target detection by pulsed radar.IRE Trans. Inf. Theory 6, 2, 59–267. · doi:10.1109/TIT.1960.1057560
[12] Olver, F. W. J. 1997.Asymptotics and Special Functions. A K Peters Ltd., Wellesley, MA. (Reprint of the 1974 original, Academic Press, New York.)
[13] Paris, R. B. 2010. Incomplete gamma and related functions. InNIST Handbook of Mathematical Functions. U.S. Department of Commerce, Washington, DC, 175–192.
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[15] Rice, S. O. 1968. Uniform asymptotic expansions for saddle point integrals—Application to a probability distribution occurring in noise theory.Bell. Syst. Tech. J. 47, 1971–2013. · Zbl 0177.47804 · doi:10.1002/j.1538-7305.1968.tb01099.x
[16] Robertson, G. H. 1976. Computation of the noncentral F distribution (cfar) detection.IEEE Trans. Aerospace Electron. Syst. AES-12, 5, 568–571. · doi:10.1109/TAES.1976.308257
[17] Ross, A. H. M. 1999. Algorithm for calculating the noncentral chi-square distribution.IEEE Trans. Inf. Theory 45, 4, 1327–1333. · Zbl 0958.65015 · doi:10.1109/18.761294
[18] Shnidman, D. A. 1989. The calculation of the probability of detection and the generalized marcum q-function.IEEE Trans. Inf. Theory 35, 2, 389–400. · Zbl 0677.94014 · doi:10.1109/18.32133
[19] Temme, N. M. 1986. A double integral containing the modified bessel function: Asymptotics and computation.Math. Comput. 47, 176, 683–691. · Zbl 0602.33002 · doi:10.1090/S0025-5718-1986-0856712-X
[20] Temme, N. M. 1993. Asymptotic and numerical aspects of the noncentral chi-square distribution.Comput. Math. Appl. 25, 5, 55–63. · Zbl 0768.62013 · doi:10.1016/0898-1221(93)90198-5
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