On the Variation-Diminishing Property

1998 ◽  
Vol 33 (1-2) ◽  
pp. 96-105 ◽  
Author(s):  
Ioan Gavrea ◽  
Heinz H. Gonska ◽  
Daniela P. Kacsó
Keyword(s):  
Variation Diminishing ◽  
Variation Diminishing Property

A generalization of the variation diminishing property

1995 ◽  
Vol 3 (4) ◽  
pp. 375-394 ◽  
Author(s):  
J. M. Carnicer ◽  
T. N. T. Goodman ◽  
J. M. Peña
Keyword(s):  
Variation Diminishing ◽  
Variation Diminishing Property

Crossing Properties of Mixture Distributions

1989 ◽  
Vol 3 (3) ◽  
pp. 355-366 ◽  
Author(s):  
Philip J. Boland ◽  
Frank Proschan ◽  
Y. L. Tong
Keyword(s):  
Mixture Distributions ◽  
Variation Diminishing ◽  
Gamma Distributions ◽  
Totally Positive ◽  
Variation Diminishing Property ◽  
Positive Functions ◽  
Family Of Distributions

Mixture distributions are a frequently used tool in modelling random phenomena. We consider mixtures of densities from a one-parameter exponenvial family of distributions. Using the tools of totally positive functions and the variation-diminishing property of such, we study the effect of sign-crossing properties of two mixing densities μ1 and μ2 on the resulting mixture distributions f1 and f2. The results enable us to make stochastic and variability cornparisons for binomial-beta, mixed Weibull, and mixed gamma distributions.

A refinement of the variation diminishing property of Bézier curves

2010 ◽  
Vol 27 (2) ◽  
pp. 202-211 ◽  
Author(s):  
Rachid Ait-Haddou ◽  
Taishin Nomura ◽  
Luc Biard
Keyword(s):  
Bezier Curves ◽  
Bézier Curves ◽  
Variation Diminishing ◽  
Variation Diminishing Property

Interpolatory and variation-diminishing properties of generalized B-splines

1984 ◽  
Vol 96 (3-4) ◽  
pp. 249-259 ◽  
Author(s):  
T. N. T. Goodman ◽  
S. L. Lee
Keyword(s):  
Complex Polynomial ◽  
Polynomial Splines ◽  
Decomposition Property ◽  
B Splines ◽  
Variation Diminishing ◽  
Variation Diminishing Property ◽  
Finite Set ◽  
Class Of Functions

SynopsisWe consider classes of functions satisfying certain simple criteria of sign and smoothness and a decomposition property. It is known that these properties are possessed by Chebysheffian B-splines and it is shown here that they are also possessed by certain trigonometric B-splines. For such a class of functions, we derive a variation-diminishing property and analyse interpolation both on a finite set of nodes and on an infinite, periodically spaced set of nodes. The results are also applied to interpolation by complex polynomial splines on the circle.

Global smoothness preservation and the variation-diminishing property

1999 ◽  
Vol 1999 (2) ◽  
pp. 126510 ◽  
Author(s):  
Claudia Cottin ◽  
Ioan Gavrea ◽  
Heinz H Gonska ◽  
Daniela P Kacsó ◽  
Ding-Xuan Zhou
Keyword(s):  
Global Smoothness Preservation ◽  
Variation Diminishing ◽  
Variation Diminishing Property ◽  
Global Smoothness
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