Let x be a random variable with a density function f(x) with a mean of zero and a variance of 1. Let z be a normally distributed random variable and let zα be the value of z at the αth percentile. Let - -percent qunatile of the standard normal density function, β1 be the skewness of this distribution, and let β2 be its kurtosis. As an illustration of this last definition when α = 0.975, zα = 1.96
where xα is the corresponding value for f(x), that is the value of x at its αth percentile.
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