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Sharp inequalities between skewness and kurtosis for unimodal distributions. (English) Zbl 0820.60009
Let $X$ be a random variable with zero mean and unit variance and define $\gamma\sb 1 = E(X\sp 3)$, $\gamma\sb 2 = E(X\sp 4) - 3$. The main result is an upper bound for $\gamma\sb 2$ in terms of $\gamma\sb 1$ in the case that $X$ has a unimodal distribution with support $[a,b]$, where $a + b \geq 0$. The bound is sharp.
Reviewer: M.Quine (Sydney)

60E15Inequalities in probability theory; stochastic orderings
Full Text: DOI
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