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Negative of a Distribution
The negative of a distribution is the distribution of -X (negative of the values) when X varies according to the distribution. For example, if the value X follows the lognormal distribution, then -X follows the negative lognormal distribution. For symmetrical distributions like the normal distribution, the negative of the distribution is the same as the original distribution.
The moments of -X are:
Average of (-X) = - (Average of X)
Standard Deviation of (-X) = Standard Deviation of X
Skewness of (-X) = - (Skewness of X)
Kurtosis of (-X) = Kurtosis of X
The average and skewness change sign while the standard deviation and kurtosis are not affected.