FitJohnsonFromMoments( [IN] Mean, [IN] StandardDeviation, [IN] Skewness,

This function estimates the type (JohnsonType) of the best-fitting Johnson system (curve), and the parameters (Gamma, Delta, Lambda, Xi) for that curve from the first four moments of a distribution (mean, standard deviation, skewness, kurtosis). If the function fails, the error object will have a description of what went wrong (e.g., if function couldn't be fitted given the moments).

The parameter estimates (JohnsonType, Gamma, Delta, Lambda, Xi) can be directly submitted to the iJohnson, vJohnson, and Johnson functions. This is computationally more efficient than using the iJohnsonFromMoments, vJohnsonFromMoments, and JohnsonFromMoments functions, which take the moments themselves (Mean, StandardDeviation, Skewness, Kurtosis) as arguments, and require to compute (fit) the Johnson curves every time when the function is called.

JohnsonType values and its interpretation:

SL curve. Type 1 or SL

SU curve. Type 2 or SU

SB curve. Type 3 or SB

Normal curve. Type 4 or Normal

See also, Johnson Distribution and Johnson From Moments Distribution.