Non-Gaussian

Referring to a probability distribution that does not conform to a Gaussian (normal) distribution. In a non-Gaussian distribution, data points are not symmetrically clustered around a central mean and often exhibit skewness (asymmetry) or kurtosis (peakiness or flatness) compared to the bell-shaped curve of a Gaussian distribution. These distributions are common in various natural phenomena and real-world datasets, where the assumption of normality may not hold true, necessitating different statistical methods for analysis and modeling. Such methods account for data that may exhibit extreme values, outliers, or multimodal patterns.

Non-Gaussian meaning with examples

• Financial markets often display non-Gaussian behavior. Price fluctuations, especially during times of crisis, tend to have heavier tails than predicted by a normal distribution, leading to a higher probability of extreme price changes, a phenomenon which traditional models have struggled with. Analyzing such data requires specialized techniques like those from extreme value theory and other alternative frameworks not dependent on Gaussian presumptions.
• In image processing, the distribution of pixel intensities in natural images can be non-Gaussian. This is because edges, textures, and other features of a scene often have different statistical properties than random noise. Gaussian filters can remove noise but blur important details when applied to non-Gaussian data. Using techniques designed for non-Gaussian distributions may be a superior method.
• Measurements of wind speeds in a complex terrain often exhibit a non-Gaussian distribution. Strong gusts and periods of calm can cause significant skewness in the data. This deviation impacts wind energy models and infrastructure. Specialized statistical methods, such as those that model extreme events or time series analysis, are crucial.
• In neuroscience, the firing rates of neurons can sometimes display non-Gaussian patterns. This can reflect complex interaction effects, feedback mechanisms, and nonlinearities in the brain. Understanding these non-Gaussian dynamics helps in developing a more nuanced understanding of cognitive processes and developing models of the brain.