Fordelinger

Fordelinger is the Norwegian term for distributions in probability theory and statistics. It describes how the probability is allocated among the possible values of a random variable. Distributions can be discrete, with probabilities assigned to individual outcomes, or continuous, described by probability density functions.

A discrete distribution is specified by a probability mass function, which gives the probability of each outcome. A continuous distribution is described by a probability density function, from which probabilities are derived as areas under the curve, and by a cumulative distribution function, which gives the probability that a variable is at most a given value.

Distributions have parameters that determine their shape, center and spread, such as mean and variance (moments). Common examples include the normal, uniform, Bernoulli, binomial, Poisson, exponential, gamma, and beta distributions. The normal distribution is continuous with a bell-shaped density; the binomial distribution models the number of successes in a fixed number of independent trials; the Poisson distribution models rare events over a fixed interval.

In data analysis, empirical distributions can be summarized by histograms or empirical distribution functions, while theoretical distributions are fitted to data using methods such as maximum likelihood or the method of moments. Goodness-of-fit tests assess how well a chosen distribution describes observed data. Distributions underpin probabilistic modelling, statistical inference, simulations, and risk assessment across science, engineering, and finance.