Approximate Distributions Using Moments in Gram-Charlier Expansion

Consider the following mixture distribution given by:

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You can change this distribution's properties by varying , , , and . This Demonstration plots this distribution and computes its first three central moments. Using these moments and the Gram–Charlier expansion, one can obtain an approximate distribution shown in the same plot in red. Values of the mean, variance, skewness, and kurtosis are given. You can see that the skewness values are negative, which confirms that this distribution has a tail. This Demonstration shows how well the distribution found using the Gram–Charlier expansion approximates the actual distribution.