Some analytical properties of γ-convex functions on the real line

1996 ◽  
Vol 91 (3) ◽  
pp. 671-694 ◽  
Author(s):  
H. X. Phú ◽  
N. N. Hai
Keyword(s):  
Real Line ◽  
Convex Functions ◽  
The Real ◽  
Analytical Properties

Uniform conditional variability ordering of probability distributions

1985 ◽  
Vol 22 (03) ◽  
pp. 619-633 ◽  
Author(s):  
Ward Whitt
Keyword(s):  
Probability Distribution ◽  
Real Line ◽  
Convex Functions ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Queueing Network ◽  
Network Models ◽  
Scalar Multiplication ◽  
Closed Queueing Network ◽  
The Real

Variability orderings indicate that one probability distribution is more spread out or dispersed than another. Here variability orderings are considered that are preserved under conditioning on a common subset. One density f on the real line is said to be less than or equal to another, g, in uniform conditional variability order (UCVO) if the ratio f(x)/g(x) is unimodal with the model yielding a supremum, but f and g are not stochastically ordered. Since the unimodality is preserved under scalar multiplication, the associated conditional densities are ordered either by UCVO or by ordinary stochastic order. If f and g have equal means, then UCVO implies the standard variability ordering determined by the expectation of all convex functions. The UCVO property often can be easily checked by seeing if f(x)/g(x) is log-concave. This is illustrated in a comparison of open and closed queueing network models.

Uniform conditional variability ordering of probability distributions

1985 ◽  
Vol 22 (3) ◽  
pp. 619-633 ◽  
Author(s):  
Ward Whitt
Keyword(s):  
Probability Distribution ◽  
Real Line ◽  
Convex Functions ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Queueing Network ◽  
Network Models ◽  
Scalar Multiplication ◽  
Closed Queueing Network ◽  
The Real

Variability orderings indicate that one probability distribution is more spread out or dispersed than another. Here variability orderings are considered that are preserved under conditioning on a common subset. One density f on the real line is said to be less than or equal to another, g, in uniform conditional variability order (UCVO) if the ratio f(x)/g(x) is unimodal with the model yielding a supremum, but f and g are not stochastically ordered. Since the unimodality is preserved under scalar multiplication, the associated conditional densities are ordered either by UCVO or by ordinary stochastic order. If f and g have equal means, then UCVO implies the standard variability ordering determined by the expectation of all convex functions. The UCVO property often can be easily checked by seeing if f(x)/g(x) is log-concave. This is illustrated in a comparison of open and closed queueing network models.

The properties of Bessel-type fractional derivatives and integrals

2016 ◽  
pp. 3973-3982
Author(s):  
V. R. Lakshmi Gorty
Keyword(s):  
Fractional Order ◽  
Real Line ◽  
Computer Algebra System ◽  
Fractional Derivatives ◽  
Graphical Representation ◽  
Fractional Integrals ◽  
The Real ◽  
Fractional Derivatives And Integrals ◽  
Half Axis ◽  
Derivatives Of

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b.

AN OSCILLATION FUNCTION ON THE REAL LINE

2000 ◽  
Vol 26 (1) ◽  
pp. 237
Author(s):  
Duszyński
Keyword(s):  
Real Line ◽  
The Real

DERIVATION BASES ON THE REAL LINE (I)

1982 ◽  
Vol 8 (1) ◽  
pp. 67 ◽  
Author(s):  
Thomson
Keyword(s):  
Real Line ◽  
The Real
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