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In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is [ 2 ] [ 3 ] f ( x ) = 1 2 π σ 2 e − ( x − μ ) 2 2 σ 2 . {\displaystyle f(x)={\frac {1}{\sqrt {2\pi \sigma ^{2 ...
The uniform distribution or rectangular distribution on [a,b], where all points in a finite interval are equally likely, is a special case of the four-parameter Beta distribution. The Irwin–Hall distribution is the distribution of the sum of n independent random variables, each of which having the uniform distribution on [0,1].
The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment. [ 1 ] [ 2 ] It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events ( subsets of the sample space).
In number theory, the Erdős–Kac theorem, named after Paul Erdős and Mark Kac, and also known as the fundamental theorem of probabilistic number theory, states that if ω(n) is the number of distinct prime factors of n, then, loosely speaking, the probability distribution of
Total variation distance is half the absolute area between the two curves: Half the shaded area above. In probability theory, the total variation distance is a statistical distance between probability distributions, and is sometimes called the statistical distance, statistical difference or variational distance.
In probability theory and statistics, the Rayleigh distribution is a continuous probability distribution for nonnegative-valued random variables. Up to rescaling, it coincides with the chi distribution with two degrees of freedom. The distribution is named after Lord Rayleigh (/ ˈ r eɪ l i /). [1]
The Wishart distribution arises as the distribution of the sample covariance matrix for a sample from a multivariate normal distribution. It occurs frequently in likelihood-ratio tests in multivariate statistical analysis. It also arises in the spectral theory of random matrices [citation needed] and in multidimensional Bayesian analysis. [5]