On sharp and highly manageable asymptotic approximations for instances of the Meijer G function

Carlos A. Coelho; Filipe J. Marques; Rui P. Alberto

doi:10.1063/1.4912754

On sharp and highly manageable asymptotic approximations for instances of the Meijer G function

Carlos A. Coelho, Filipe J. Marques, Rui P. Alberto

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Instances of the Meijer G function may be used as representations for the probability density function (p.d.f.) and cumulative density function (c.d.f.) of several distributions. However, although the Meijer G function is a very handy representation for the p.d.f. and c.d.f. of these distributions, and nevertheless prominent progress has been made in its computation, this still remains very heavy, and time consuming, even with the newer versions of symbolic and extended precision softwares, so that the development of sharp and fast approximations is a desirable goal. In this paper it is shown how extremely sharp approximations for particular instances of the Meijer G function may be based on the probability density and cumulative distribution functions of the Generalized Near-Integer Gamma distribution.

Original language	English
Title of host publication	Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014
Publisher	AIP - American Institute of Physics
Volume	1648
ISBN (Electronic)	978-0-7354-1287-3
DOIs	https://doi.org/10.1063/1.4912754
Publication status	Published - 10 Mar 2015
Event	International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014 - Rhodes, Greece Duration: 22 Sept 2014 → 28 Sept 2014

Conference

Conference	International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014
Country/Territory	Greece
City	Rhodes
Period	22/09/14 → 28/09/14

Keywords

Characteristic function
Generalized near-integer gamma distribution
Inverse mellin transform
Mellin-barnes integral
Product of independent beta random variables
Sum of independent Logbeta random variables
BETA RANDOM-VARIABLES

Access to Document

10.1063/1.4912754Licence: Unspecified

Cite this

@inproceedings{9fbbc60bdaf746179dcacf82859ba4c2,

title = "On sharp and highly manageable asymptotic approximations for instances of the Meijer G function",

abstract = "Instances of the Meijer G function may be used as representations for the probability density function (p.d.f.) and cumulative density function (c.d.f.) of several distributions. However, although the Meijer G function is a very handy representation for the p.d.f. and c.d.f. of these distributions, and nevertheless prominent progress has been made in its computation, this still remains very heavy, and time consuming, even with the newer versions of symbolic and extended precision softwares, so that the development of sharp and fast approximations is a desirable goal. In this paper it is shown how extremely sharp approximations for particular instances of the Meijer G function may be based on the probability density and cumulative distribution functions of the Generalized Near-Integer Gamma distribution.",

keywords = "Characteristic function, Generalized near-integer gamma distribution, Inverse mellin transform, Mellin-barnes integral, Product of independent beta random variables, Sum of independent Logbeta random variables, BETA RANDOM-VARIABLES",

author = "Coelho, {Carlos A.} and Marques, {Filipe J.} and Alberto, {Rui P.}",

note = "sem pdf conforme despacho; International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014 ; Conference date: 22-09-2014 Through 28-09-2014",

year = "2015",

month = mar,

day = "10",

doi = "10.1063/1.4912754",

language = "English",

volume = "1648",

booktitle = "Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014",

publisher = "AIP - American Institute of Physics",

address = "United States",

}

Coelho, CA , Marques, FJ & Alberto, RP 2015, On sharp and highly manageable asymptotic approximations for instances of the Meijer G function. in Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014. vol. 1648, 540008, AIP - American Institute of Physics, International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014, Rhodes, Greece, 22/09/14. https://doi.org/10.1063/1.4912754

On sharp and highly manageable asymptotic approximations for instances of the Meijer G function. / Coelho, Carlos A.; Marques, Filipe J.; Alberto, Rui P.
Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014. Vol. 1648 AIP - American Institute of Physics, 2015. 540008.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - On sharp and highly manageable asymptotic approximations for instances of the Meijer G function

AU - Coelho, Carlos A.

AU - Marques, Filipe J.

AU - Alberto, Rui P.

N1 - sem pdf conforme despacho

PY - 2015/3/10

Y1 - 2015/3/10

N2 - Instances of the Meijer G function may be used as representations for the probability density function (p.d.f.) and cumulative density function (c.d.f.) of several distributions. However, although the Meijer G function is a very handy representation for the p.d.f. and c.d.f. of these distributions, and nevertheless prominent progress has been made in its computation, this still remains very heavy, and time consuming, even with the newer versions of symbolic and extended precision softwares, so that the development of sharp and fast approximations is a desirable goal. In this paper it is shown how extremely sharp approximations for particular instances of the Meijer G function may be based on the probability density and cumulative distribution functions of the Generalized Near-Integer Gamma distribution.

AB - Instances of the Meijer G function may be used as representations for the probability density function (p.d.f.) and cumulative density function (c.d.f.) of several distributions. However, although the Meijer G function is a very handy representation for the p.d.f. and c.d.f. of these distributions, and nevertheless prominent progress has been made in its computation, this still remains very heavy, and time consuming, even with the newer versions of symbolic and extended precision softwares, so that the development of sharp and fast approximations is a desirable goal. In this paper it is shown how extremely sharp approximations for particular instances of the Meijer G function may be based on the probability density and cumulative distribution functions of the Generalized Near-Integer Gamma distribution.

KW - Characteristic function

KW - Generalized near-integer gamma distribution

KW - Inverse mellin transform

KW - Mellin-barnes integral

KW - Product of independent beta random variables

KW - Sum of independent Logbeta random variables

KW - BETA RANDOM-VARIABLES

UR - http://www.scopus.com/inward/record.url?scp=84939647887&partnerID=8YFLogxK

U2 - 10.1063/1.4912754

DO - 10.1063/1.4912754

M3 - Conference contribution

AN - SCOPUS:84939647887

VL - 1648

BT - Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014

PB - AIP - American Institute of Physics

T2 - International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014

Y2 - 22 September 2014 through 28 September 2014

ER -

On sharp and highly manageable asymptotic approximations for instances of the Meijer G function

Abstract

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this