exGaussianverdeling

The exGaussian distribution is a probability distribution that combines properties of both the Gaussian (normal) distribution and the exponential distribution. It is often used to model data that exhibits both a symmetric, bell-shaped distribution around a central value and a long tail on one side, typically to the right. This makes it particularly useful in fields such as finance, where it can describe the distribution of stock returns or other financial variables.

The exGaussian distribution is defined by two parameters: the mean (μ) of the Gaussian component and the rate (λ) of the exponential component. The probability density function (PDF) of the exGaussian distribution is given by the convolution of a Gaussian PDF with an exponential PDF. This convolution results in a function that is not symmetric and has a longer tail on the right side.

One of the key features of the exGaussian distribution is its ability to capture the skewness often observed in real-world data. This skewness arises from the exponential component, which introduces an asymmetry that is not present in the Gaussian distribution. The exGaussian distribution is particularly useful in scenarios where the data is positively skewed, meaning that the tail on the right side of the distribution is longer than the tail on the left side.

In practice, the exGaussian distribution can be fitted to data using maximum likelihood estimation or other statistical methods. Once fitted, it can be used to model the distribution of the data, make predictions, and perform hypothesis testing. The exGaussian distribution is a versatile tool in statistical modeling, providing a more accurate representation of data that deviates from the symmetric Gaussian distribution.