PsiMomentFit Distribution

PsiMomentFit (mean,stdev,skew,kurtosis,...)

PsiMomentFit is a distribution from the the Johnson system fitted to the entered statistical moments.  The resultant distribution is either a JohnsonSU, JohnsonSB, lognormal, or normal distribution.   The standard deviation (stdev) must be positive.  The kurtosis value must be > 1.

Examples:  

•     PsiMomentFit(10, 20, 4, 41) returns a distribution from the Johnson family with mean 10, standard deviation 20, skewness 4 and kurtosis 41.  
•     PsiMomentFit(A1, A2, A3, A4) returns a distribution from the Johnson family using parameters from cells A1:A4.

Parameters
mean
standard deviation  > 0
skewness
kurtosis > 1

Range of Function Values
(-∞,∞)

Probability Density Function and Cumulative Distribution Function
See distribution functions for the specific Johnson system distribution:  PsiJohnsonSU, PsiJohnsonSB, PsiLogNormal and PsiNormal.

Mean
µ

Variance
σ²

Skewness
s

Kurtosis
k

Mode
No closed form