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 language | English |
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Pages (from-to) | 444–461 |
Number of pages | 18 |
Journal | Lithuanian Mathematical Journal |
Volume | 52 |
Issue number | 4 |
DOIs | |
Publication status | Published - Oct 2012 |
Keywords
- Difference quotient
- Poincaré series
- Poisson-gamma laws
- Reciprocity
- Refined saddlepoint approximations
- Stable laws
- Stokes phenomenon
- Wright function
- Zolotarev duality