The medcouple is a robust measure of skewness yielding values between $-1$ and $1$. For left- and right-skewed data the medcouple is negative and positive respectively. The medcouple is defined as the median of the kernel function
$h(x_i,x_j) = \frac{(x_j - med(x)) - (med(x)-x_i)}{x_j-x_i}$
evaluated over all couples $(x_i,x_j)$ where
$x_i$ is smaller than the median of x and $x_j$ larger than the median of x. When there are multiple observations tied to the median, the kernel is defined separately as the denominator is not defined for these observations. Let $m_1 < ... < m_k$ denote the indices of the observations which are tied to the median. Then $h(x_{m_i},x_{m_j})$ is defined to equal $-1$ if $i + j - 1 < k$, $0$ when $i + j - 1 = k$ and $+1$ if $i + j - 1 > k$. To compute the medcouple an algorithm with time complexity $O(n log(n))$ is applied. For details, see https://en.wikipedia.org/wiki/Medcouple.
For numerical accuracy it is advised, for small data sets, to compute the medcouple on both x and -x. The final value of the medcouple may then be obtained as a linear combination of both calculations. This procedure is warranted by the properties of the medcouple. Indeed the medcouple of the distribution $X$ equals minus the medcouple of the reflected distribution $-X$. Moreover the medcouple is location and scale invariant.
Note that missing values are not allowed.