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
PY - 2012/10
Y1 - 2012/10
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
U2 - 10.1007/s10986-012-9186-0
DO - 10.1007/s10986-012-9186-0
M3 - Article
VL - 52
SP - 444
EP - 461
JO - Lithuanian Mathematical Journal
JF - Lithuanian Mathematical Journal
SN - 0363-1672
IS - 4
ER -