# Skewness, kurtosis and Newton's inequality

@article{Sharma2013SkewnessKA, title={Skewness, kurtosis and Newton's inequality}, author={R. Sharma and R. Bhandari}, journal={arXiv: Statistics Theory}, year={2013} }

We show that an inequality related to Newton's inequality provides one more relation between skewness and kurtosis. This also gives simple and alternative proofs of the bounds for skewness and kurtosis.

#### 14 Citations

Means, moments and Newton's inequalities

- Mathematics
- Rocky Mountain Journal of Mathematics
- 2019

It is shown that Newton's inequalities and the related Maclaurin's inequalities provide several refinements of the fundamental Arithmetic mean - Geometric mean - Harmonic mean inequality in terms of… Expand

Complementary upper bounds for fourth central moment with extensions and applications

- Mathematics
- 2015

We prove some inequalities involving fourth central moment of a random variable that takes values in a given finite interval. Both discrete and continuous cases are considered. Bounds for the spread… Expand

Bounds on Spreads of Matrices Related to Fourth Central Moment

- Mathematics
- 2018

We prove some inequalities involving fourth central moment of a random variable that takes values in a given finite interval. Both discrete and continuous cases are considered. Bounds for the spread… Expand

Standard Curves for Empirical Likelihood Ratio Tests of Means

- Mathematics
- 2021

We present simulated standard curves for the calibration of empirical likelihood ratio (ELR) tests of means. With the help of these curves, the nominal significance level of the ELR test can be… Expand

Deterministic Feature Decoupling by Surfing Invariance Manifolds

- Computer Science, Mathematics
- ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
- 2020

A formalism is introduced that justifies and extends a heuristic method for algebraically decoupling deterministic features that recently proved useful for improving feature-based classifi-cation, based on defining transformations inside manifolds by following trajectories along the features’ gradients. Expand

The link between carbon emissions, renewable energy consumption, and economic growth: a heterogeneous panel evidence from West Africa

- Economics, Medicine
- Environmental Science and Pollution Research
- 2020

This study examined the nexus between carbon emissions, renewable energy consumption, and the economic growth of West African countries for the period 1990 to 2018. To be able to uncover reliable and… Expand

Econometric Data Analysis Affecting Performance of Supply Chain Systems in the Petroleum Industries in Kenya

- Business
- 2015

The purpose of this paper was to do econometric data analysis on performance of supply chain systems in the petroleum industries in Kenya. Specifically, the objectives of the study were to establish… Expand

Nested Normalizations for Decoupling Global Features

- Computer Science
- 2018 25th IEEE International Conference on Image Processing (ICIP)
- 2018

This work proposes a sequential method for modifying arbitrary features independently of each other, and derives a decoupling method based on hierarchical normalization that yields new features with gradients mutually orthogonal everywhere in the signal space. Expand

Features ranking for the classification of epileptic seizure from temporal EEG

- Computer Science
- 2016 International Conference on Circuits, Controls, Communications and Computing (I4C)
- 2016

This study makes use of twelve different features to select suitable quantitative features for classification and detection of epileptic seizure from temporal EEG and observed that the variance, maximum, wavelet log energy entropy, rms and band power features were increasing parameters for epileptic EEG, on the other hand, the minimum and wavelet Shannon entropy and zero crossing features were decreasing parameters for normal EEG. Expand

Determinant Affecting Performance of Supply Chain Systems in the Petroleum Industries in Kenya

- Business
- 2015

The purpose of this paper was to analyze the effect of crude oil price as a determinant on performance of supply chain systems in the petroleum industries in Kenya. Supply chain is a dynamic process… Expand

#### References

SHOWING 1-8 OF 8 REFERENCES

Inequalities related to the Cauchy-Schwarz inequality

- Mathematics
- 2012

We obtain an inequality complementary to the Cauchy-Schwarz inequality in Hilbert space. The inequalities involving first three powers of a self-adjoint operator are derived. The inequalities include… Expand

Algebraic bounds on standardized sample moments

- Mathematics
- 1987

Best possible bounds are given for standardized sample (or finite population) moments and absolute moments of arbitrary order, generalizing those given by Cramer (1945) and Kirby (1974) on sample… Expand

Some bounds for integrals with refinements of the Grüss inequality

- Mathematics
- 2011

Some integral bounds are obtained which provide refinements and extensions of the Grüss type inequalities. We also get an alternative formulation of the Grüss inequality.

Speaking Stata: The Limits of Sample Skewness and Kurtosis

- Mathematics
- 2010

Sample skewness and kurtosis are limited by functions of sample size. The limits, or approximations to them, have repeatedly been rediscovered over the last several decades, but nevertheless seem to… Expand

Mathematical contributions to the theory of evolution.—X. Supplement to a memoir on skew variation

- Mathematics
- Proceedings of the Royal Society of London
- 1901

In the second memoir of this series a system of curves suitable for describing skew distributions of frequency was deduced from the solutions of the differential equation 1/y dy/dx = b0 + b1x/a0 +… Expand

How Deviant Can You Be

- Mathematics
- 1968

Abstract For a finite universe of N items, it is proved no one can lie more than standard deviations away from the mean. This is an improvement over the result given by Tchebycheff's inequality: and… Expand

Inequalities related to the CauchySchwarz inequality, Sankhya

- 2012