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Earth's atmosphere-ocean system is distinguished by its variability over a wide range of time scales. The non-linear interactions between these time scales are complex and are further complicated by the large number of subsystems and modes in the atmosphere-ocean system. Here, we explore a stochastic model developed by Sardeshmukh and Sura which uses correlated additive and multiplicative (CAM) noise and relies on a state-dependent (multiplicative) noise forcing to represent the multi-scale interactions between weather and climate. An important problem in climate variability is the statistical representation of extreme weather and climate events. While a description of the tails of a probability density function (pdf) is essential for modeling extreme events, an understanding of the full pdf is required to capture the full dynamics of the atmosphere-ocean system. On daily scales, the statistics of the large-scale atmospheric circulation are non-Gaussian. A one-dimensional pdf produced by the CAM noise model, or stochastically generated skewed (SGS) distribution, attempts to probabilistically represent the non-Gaussian statistics of atmospheric climate anomalies. This study evaluates the ability of the SGS distribution to represent the non-Gaussian statistics of several atmospheric variables using NOAA-CIRES-DOE Twentieth Century Reanalysis Project version 2c (20CRv2c) dataset. A method of moments SGS parameter estimation technique described Sardeshmukh et al (2015) is implemented in a Julia software package and applied to global gridded time series of reanalysis data. Goodness-of-fit tests show the SGS distribution performs well in regions of near-zero and positive kurtosis, but produces statistically implausible with time series with negative sample kurtosis. However, the SGS distribution is found to outperform the standard normal (Gaussian) distribution at nearly all gridded locations, even where the SGS fit is poor. The SGS distributions of two 67 year 20CRv2c periods are also compared, where few significant changes in the shape of the SGS distribution are found.