A distribution with negative skew can have its mean greater than or less than the median, and likewise for positive skew A configuration of skew lines is a set of lines in which all pairs are skew [2] a general relationship of mean and median under differently skewed unimodal distribution
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In the older notion of nonparametric skew, defined as where is the mean, is the median, and is.
Nonparametric skew in statistics and probability theory, the nonparametric skew is a statistic occasionally used with random variables that take real values
[1][2] it is a measure of the skewness of a random variable's distribution —that is, the distribution's tendency to lean to one side or the other of the mean. If this difference is positive, the distribution is skewed to the right and if negative, then it is skewed to the left. In statistics, the concept of the shape of a probability distribution arises in questions of finding an appropriate distribution to use to model the statistical properties of a population, given a sample from that population A similar effect can be achieved by taking the square root of the data
To fit a symmetrical distribution to data obeying a negatively skewed distribution (i.e Skewed to the left, with mean < mode, and with a right hand tail this is shorter than the left hand tail) one could use the squared values of the data to accomplish the fit. That is, its density is asymptotically proportional to for some positive. Since , the probability left of the mode, and therefore right of the mode as well, can equal any value in (0,1) depending on the value of
Thus the skewed generalized t distribution can be highly skewed as well as symmetric
If , then the distribution is negatively skewed If , then the distribution is positively skewed.
