Improvement of Ostrowski integral type inequalities with application

The aim of this paper is to establish new inequalities which are more generalized than the inequalities of Dragomir, Wang and Cerone. The current article also obtains bounds for the deviation of a function from a combination of integral means over the end intervals covering the entire interval. A variety of earlier results are recaptured as special cases of the inequalities obtained. Some new perturbed results and application for cumulative distribution function are also discussed.

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On New Generalized Ostrowski Type Integral Inequalities

Abstract and Applied Analysis ◽

10.1155/2014/275806 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8

Author(s):

A. Qayyum ◽

M. Shoaib ◽

A. E. Matouk ◽

M. A. Latif

Keyword(s):

Distribution Function ◽

Cumulative Distribution Function ◽

Current Paper ◽

Cumulative Distribution ◽

Second Derivative ◽

Ostrowski Inequality ◽

Integral Means ◽

Entire Interval ◽

Type Integral ◽

New Inequalities

The Ostrowski inequality expresses bounds on the deviation of a function from its integral mean. The aim of this paper is to establish some new inequalities similar to the Ostrowski's inequality. The current paper obtains bounds for the deviation of a function from a combination of integral means over the end intervals covering the entire interval in terms of the norms of the second derivative of the function. Some new perturbed results are obtained. Application for cumulative distribution function is also discussed.

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Exact distributions of order statistics from ln,p-symmetric sample distributions

Dependence Modeling ◽

10.1515/demo-2017-0013 ◽

2017 ◽

Vol 5 (1) ◽

pp. 221-245 ◽

Cited By ~ 1

Author(s):

K. Müller ◽

W.-D. Richter

Keyword(s):

Distribution Function ◽

Finite Number ◽

Order Statistics ◽

Cumulative Distribution Function ◽

Cumulative Distribution ◽

Symmetric Distributions ◽

Sample Distribution ◽

Special Cases ◽

Exact Distributions ◽

Gaussian Sample

Abstract We derive the exact distributions of order statistics from a finite number of, in general, dependent random variables following a joint ln,p-symmetric distribution. To this end,we first review the special cases of order statistics fromspherical aswell as from p-generalized Gaussian sample distributions from the literature. To study the case of general ln,p-dependence, we use both single-out and cone decompositions of the events in the sample space that correspond to the cumulative distribution function of the kth order statistic if they are measured by the ln,p-symmetric probability measure.We show that in each case distributions of the order statistics from ln,p-symmetric sample distribution can be represented as mixtures of skewed ln−ν,p-symmetric distributions, ν ∈ {1, . . . , n − 1}.

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Gradient based empirical cumulative distribution function approximation for robust aerodynamic design

Aerospace Science and Technology ◽

10.1016/j.ast.2021.106630 ◽

2021 ◽

pp. 106630

Author(s):

Elisa Morales ◽

Andrea Bornaccioni ◽

Domenico Quagliarella ◽

Renato Tognaccini

Keyword(s):

Distribution Function ◽

Function Approximation ◽

Cumulative Distribution Function ◽

Cumulative Distribution ◽

Aerodynamic Design ◽

Empirical Cumulative Distribution Function ◽

Gradient Based

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Determinants of the Strategic Mortgage Default Cumulative Distribution Function

Journal of Real Estate Literature ◽

10.1080/10835547.2016.12090420 ◽

2016 ◽

Vol 24 (1) ◽

pp. 183-199

Author(s):

Michael J. Seiler

Keyword(s):

Distribution Function ◽

Cumulative Distribution Function ◽

Cumulative Distribution ◽

Mortgage Default

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DISSONANCE — A MEASURE OF VARIABILITY FOR ORDINAL RANDOM VARIABLES

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488501000594 ◽

2001 ◽

Vol 09 (01) ◽

pp. 39-53 ◽

Cited By ~ 2

Author(s):

RONALD R. YAGER

Keyword(s):

Distribution Function ◽

Cumulative Distribution Function ◽

Probability Distributions ◽

Random Variables ◽

Cumulative Distribution ◽

General Properties

We look at the issue of obtaining a variance like measure associated with probability distributions over ordinal sets. We call these dissonance measures. We specify some general properties desired in these dissonance measures. The centrality of the cumulative distribution function in formulating the concept of dissonance is pointed out. We introduce some specific examples of measures of dissonance.

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