Cumulative Distribution Function given mean, std dev, skew and kurtosis? Is there a function that calculates the cumulative distribution function (CDF) of a Gaussian distribution given the mean, std dev, skew, and kurtosis?  Does anyone know of one written in a c-like language (c, c++, java, c#)?
Thanks
 A: If the given CDF is Gaussian, then it has no skewness nor excess kurtosis by definition.
In general, programming functions do not take statistical moments of the distribution in as inputs in order to construct the CDF, since an infinitely many different distribution families could share the exact same moments. For example, a t-distribution or beta distribution CDF, if parameterized right, could have the exact same $\mu, \sigma, \xi, \kappa$ as a Gaussian CDF.
The CDF is usually constructed by sorting the empirical data by rank and some additional normalization step applied to the frequencies of samples/outcomes/indices.
This is more of something to consider regarding the connection between moments and your distribution family of interest, in terms of the specificity of your question. What are you more interested in: the Gaussian distribution, or targeted values for moments (i.e. non-normality), when modeling CDFs?
Besides, I thought skewness and kurtosis were not visible in the CDF, only the PDF. maybe someone can correct me on that
