  Distributions of strictly positive numbers are common and can be
characterized by standard statistical measures such as mean, standard
deviation, and skewness. We demonstrate that for these distributions the
skewness $D_3$ is bounded from below by a function of the coefficient of
variation (CoV) $\delta$ as $D_3 \ge \delta-1/\delta$. The results are extended
to any distribution that is bounded with minimum value $x_{\rm min}$ and/or
bounded with maximum value $x_{\rm max}$. We build on the results to provide
bounds for kurtosis $D_4$, and conjecture analogous bounds exists for higher
statistical moments.
