New properties and representations for members of the power-variance family.I

Vladimir Vinogradov, Richard B. Paris, Olga Yanushkevichiene

Research output: Contribution to journalArticle

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Abstract

We derive new Wright-function representations for the densities of the generating measures of most representatives of the power-variance family of distributions. For all members of this family, we construct new saddlepoint-type approximations having an arbitrary fixed number of refining terms. To this end, we derive new, “exponentially small,” Poincaré series for a subclass of the Wright functions whose coefficients are expressed in terms of the Zolotarev polynomials. MSC: primary 60E07, 60E10, 60F10, 62E10, 62E20; secondary 33C10, 33C15, 33E20, 41A60
Original languageEnglish
Pages (from-to)444–461
Number of pages18
JournalLithuanian Mathematical Journal
Volume52
Issue number4
DOIs
Publication statusPublished - Oct 2012

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Wright Function
Saddlepoint
Polynomial
Series
Arbitrary
Coefficient
Term
Approximation
Family

Cite this

Vinogradov, Vladimir ; Paris, Richard B. ; Yanushkevichiene, Olga. / New properties and representations for members of the power-variance family.I. In: Lithuanian Mathematical Journal. 2012 ; Vol. 52, No. 4. pp. 444–461.
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New properties and representations for members of the power-variance family.I. / Vinogradov, Vladimir; Paris, Richard B.; Yanushkevichiene, Olga.

In: Lithuanian Mathematical Journal, Vol. 52, No. 4, 10.2012, p. 444–461.

Research output: Contribution to journalArticle

TY - JOUR

T1 - New properties and representations for members of the power-variance family.I

AU - Vinogradov, Vladimir

AU - Paris, Richard B.

AU - Yanushkevichiene, Olga

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N2 - We derive new Wright-function representations for the densities of the generating measures of most representatives of the power-variance family of distributions. For all members of this family, we construct new saddlepoint-type approximations having an arbitrary fixed number of refining terms. To this end, we derive new, “exponentially small,” Poincaré series for a subclass of the Wright functions whose coefficients are expressed in terms of the Zolotarev polynomials. MSC: primary 60E07, 60E10, 60F10, 62E10, 62E20; secondary 33C10, 33C15, 33E20, 41A60

AB - We derive new Wright-function representations for the densities of the generating measures of most representatives of the power-variance family of distributions. For all members of this family, we construct new saddlepoint-type approximations having an arbitrary fixed number of refining terms. To this end, we derive new, “exponentially small,” Poincaré series for a subclass of the Wright functions whose coefficients are expressed in terms of the Zolotarev polynomials. MSC: primary 60E07, 60E10, 60F10, 62E10, 62E20; secondary 33C10, 33C15, 33E20, 41A60

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DO - 10.1007/s10986-012-9186-0

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EP - 461

JO - Lithuanian Mathematical Journal

JF - Lithuanian Mathematical Journal

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