muotijakauman

Muotijakauma, often translated as shape distribution, is a term used in statistics to describe the qualitative form of a probability distribution. It characterizes how the probability mass or density is arranged along the value axis, independent of the distribution’s location (mean) and scale (variance).

Key characteristics of muotijakauma include symmetry versus skewness, unimodality versus multimodality, and the heaviness of tails (kurtosis). A symmetric distribution around a central point is balanced on either side; skewness indicates a longer tail on one side. Unimodal distributions have a single peak, while multimodal ones have multiple peaks. Tail behavior ranges from light tails (e.g., normal) to heavy tails (e.g., certain power-law families).

Shape is typically assessed with graphical tools such as histograms and kernel density estimates, and with numerical measures such as skewness and excess kurtosis. Quantile-quantile plots help compare sample shape to a reference distribution. In multivariate contexts, shape also relates to the contour of the joint density, with elliptical shapes often associated with normal-like distributions.

Common shapes include the normal distribution (symmetric, bell-shaped), exponential and gamma distributions (right-skewed), the uniform distribution (flat), and the log-normal distribution (right-skewed with a long tail). Multimodal shapes reflect mixtures of differing subpopulations or processes.

Understanding muotijakauma is important for model selection and inference, since the shape influences estimation, hypothesis testing, and predictive performance. The term is Finnish; in English texts it is typically described as the shape of a distribution.