×

Skewness, kurtosis and Newton’s inequality. (English) Zbl 1355.60028

Summary: 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.

MSC:

60E15 Inequalities; stochastic orderings
26C10 Real polynomials: location of zeros

Software:

Stata
PDF BibTeX XML Cite
Full Text: DOI arXiv Euclid

References:

[1] J. Dalen, Algebraic bounds on standardized sample moments , Stat. Prob. Lett. 5 (1987), 329-331. · Zbl 0659.62028
[2] I. Newton, Arithmetica universalis : sive de compositione et resolutione arithmetica liber , 1707.
[3] J.C. Nicholas, Speaking stata : The limits of sample skewness and kurtosis , The Stata Journal 10 (2010), 482-495.
[4] K. Pearson, Mathematical contributions to the theory of evolution , XIX; Second supplement to a memoir on skew variation , Philos. Trans. Roy. Soc. Lond. 216 (1916), 432. · JFM 46.1495.08
[5] P.A. Samuelson, How deviant can you be? , J. Amer. Stat. Assoc. 63 (1968), 1522-1525.
[6] R. Sharma, R. Bhandari and M. Gupta, Inequalities related to the Cauchy-Schwarz inequality , Sankhya 74 (2012), 101-111. · Zbl 1284.47010
[7] R. Sharma, R. Bhandari and A. Thakur, Some bounds for integrals with refinements of the Gruss inequality , Indian J. Pure Appl. Math. 42 (2011), 187-202. · Zbl 1307.26038
[8] J.E. Wilkins, A note on skewness and kurtosis , Ann. Math. Stat. 15 (1944), 333-335. · Zbl 0063.08254
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.