chikvadratsfordeling

Chikvadratsfordeling, often referred to as the chi-squared distribution (χ²) in English, is a continuous probability distribution. It is a special case of the gamma distribution. The chi-squared distribution arises in statistics, particularly in hypothesis testing and confidence interval construction, most notably in the chi-squared test.

The distribution is defined for a non-negative random variable. It is characterized by a single parameter, known as the degrees of freedom, denoted by k. The degrees of freedom determine the shape of the distribution. As the degrees of freedom increase, the distribution becomes more symmetric and bell-shaped, approaching a normal distribution for large values of k.

The chi-squared distribution is frequently used when analyzing categorical data. For instance, it is employed in the chi-squared test of independence to determine if there is a statistically significant association between two categorical variables. It is also used in goodness-of-fit tests to assess how well an observed frequency distribution matches an expected distribution. Another key application is in constructing confidence intervals for the variance of a normally distributed population. The probability density function of the chi-squared distribution involves the gamma function.