## Algorithm 939

 swMATH ID: 12897 Software Authors: Gil, Amparo; Segura, Javier; Temme, Nico M. Description: Algorithm 939: computation of the Marcum Q-function. Methods and an algorithm for computing the generalized Marcum Q-function (Q μ (x,y)) and the complementary function (P μ (x,y)) are described. These functions appear in problems of different technical and scientific areas such as, for example, radar detection and communications, statistics, and probability theory, where they are called the noncentral chi-square or the noncentral gamma cumulative distribution functions. The algorithm for computing the Marcum functions combines different methods of evaluation in different regions: series expansions, integral representations, asymptotic expansions, and use of three-term homogeneous recurrence relations. A relative accuracy close to 10 -12 can be obtained in the parameter region (x,y,μ)∈[0,A]×[0,A]×[1,A],A=200, while for larger parameters the accuracy decreases (close to 10 -11 for A=1000 and close to 5×10 -11 for A=10000). Homepage: http://dl.acm.org/citation.cfm?doid=2610268.2591004 Keywords: Marcum Q-function; noncentral chi-square distribution Related Software: DLMF; GammaCHI; ncg Cited in: 8 Publications

### Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
Algorithm 939: Computation of the Marcum $$Q$$-function. Zbl 1322.65046
Gil, Amparo; Segura, Javier; Temme, Nico M.
2014
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### Cited by 10 Authors

 5 Segura, Javier 3 Gil, Amparo 3 Temme, Nico M. 1 Baricz, Árpád 1 Bisht, Nitin 1 Dias, José Carlos 1 Nunes, João Pedro Vidal 1 Singh, Sanjeev 1 Veestraeten, Dirk 1 Vijesh, V. Antony
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### Cited in 8 Serials

 1 Computer Physics Communications 1 Journal of Mathematical Analysis and Applications 1 ACM Transactions on Mathematical Software 1 Applied Mathematics and Computation 1 Studies in Applied Mathematics 1 European Journal of Operational Research 1 Integral Transforms and Special Functions 1 Applicable Analysis and Discrete Mathematics
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### Cited in 8 Fields

 6 Special functions (33-XX) 4 Probability theory and stochastic processes (60-XX) 3 Numerical analysis (65-XX) 2 Statistics (62-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX)