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Title:
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On the computation of confluent hypergeometric functions for large imaginary part of parameters b and z
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Author:
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Navas Palencia, G.; Arratia Quesada, Argimiro Alejandro
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Ciències de la Computació; Universitat Politècnica de Catalunya. LARCA - Laboratori d'Algorísmia Relacional, Complexitat i Aprenentatge |
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Abstract:
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The final publication is available at http://link.springer.com/chapter/10.1007%2F978-3-319-42432-3_30 |
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Abstract:
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We present an efficient algorithm for the confluent hypergeometric functions when the imaginary part of b and z is large. The algorithm is based on the steepest descent method, applied to a suitable representation of the confluent hypergeometric functions as a highly oscillatory integral, which is then integrated by using various quadrature methods. The performance of the algorithm is compared with open-source and commercial software solutions with arbitrary precision, and for many cases the algorithm achieves high accuracy in both the real and imaginary parts. Our motivation comes from the need for accurate computation of the characteristic function of the Arcsine distribution or the Beta distribution; the latter being required in several financial applications, for example, modeling the loss given default in the context of portfolio credit risk. |
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Abstract:
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Peer Reviewed |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica
-Hypergeometric functions
-Differential equations
-Gradient methods
-Integral equations
-Statistical distributions
-Confluent hypergeometric function
-Steepest descent method
-Oscillatory integral
-Quadrature method
-Arcsine distribution
-Beta distribution
-Funcions hipergeomètriques |
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Rights:
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Document type:
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Article - Submitted version
Conference Object |
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Published by:
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Springer
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