T2distribuutio

The T2distribuutio, also known as the bivariate t-distribution or two-dimensional Student's t-distribution, is a probability distribution used in statistics to model the joint distribution of two continuous random variables that exhibit heavy tails. It is a generalization of the univariate Student's t-distribution to two dimensions. The T2distribuutio is characterized by its degrees of freedom and a correlation parameter that describes the dependence between the two variables.

This distribution is particularly useful when dealing with data that shows more variability than a bivariate normal distribution would suggest, a phenomenon known as heavy tails or leptokurtosis. It finds applications in areas such as finance, where it can model the joint returns of assets that experience extreme movements, and in spatial statistics, where it can describe the joint distribution of locations or measurements. The shape of the T2distribuutio is similar to that of a bivariate normal distribution, but with more probability mass concentrated in the tails, meaning extreme values are more likely.

The T2distribuutio is defined by its probability density function, which involves the Gamma function and depends on the degrees of freedom parameter. The correlation parameter, typically denoted by rho, ranges from -1 to 1 and influences the shape and orientation of the distribution's contours. Higher degrees of freedom lead to a shape that more closely resembles a bivariate normal distribution, while lower degrees of freedom result in heavier tails and a more peaked center. Estimation of the parameters for a T2distribuutio often involves methods like maximum likelihood estimation.