Jerndistribusjon

Jerndistribusjon, also known as the Irwin-Hall distribution, is a probability distribution that arises from the sum of a fixed number of independent, identically distributed random variables, each with a uniform distribution over the interval [0, 1]. It is named after John W. Irwin and Paul Hall, who studied its properties in the 1930s.

The Irwin-Hall distribution is defined as the distribution of the sum of n independent random variables, each uniformly distributed over [0, 1]. The probability density function (PDF) of the Irwin-Hall distribution for n variables is given by a piecewise function, which is non-zero only over the interval [0, n]. The PDF is symmetric around the midpoint n/2, and its shape depends on the value of n.

The Irwin-Hall distribution has several interesting properties. For example, it can be used to approximate the normal distribution when n is large, due to the central limit theorem. It also has applications in statistics, particularly in the study of order statistics and the distribution of sample means.

In addition to its theoretical significance, the Irwin-Hall distribution has practical applications in various fields, such as physics, engineering, and computer science. For instance, it can be used to model the distribution of the sum of independent random variables in systems where the individual variables are uniformly distributed, such as in certain types of noise or error models.