Moments
The Tukey lambda distribution is symmetric around zero, therefore the expected value of this distribution is equal to zero. The variance exists for λ > −½ and is given by the formula (except when λ = 0)
More generally, the n-th order moment is finite when λ > −1/n and is expressed in terms of the beta function Β(x,y) (except when λ = 0) :
Note that due to symmetry of the density function, all moments of odd orders are equal to zero.
Read more about this topic: Tukey Lambda Distribution
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