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Figure 1. A simple bimodal distribution, in this case a mixture of two normal distributions with the same variance but different means. The figure shows the probability density function (p.d.f.), which is an equally-weighted average of the bell-shaped p.d.f.s of the two normal distributions.
The Beta distribution on [0,1], a family of two-parameter distributions with one mode, of which the uniform distribution is a special case, and which is useful in estimating success probabilities. The four-parameter Beta distribution, a straight-forward generalization of the Beta distribution to arbitrary bounded intervals [,].
In probability theory and statistics, there are several relationships among probability distributions. These relations can be categorized in the following groups: One distribution is a special case of another with a broader parameter space; Transforms (function of a random variable); Combinations (function of several variables);
The split normal distribution has been used mainly in econometrics and time series. A remarkable area of application is the construction of the fan chart, a representation of the inflation forecast distribution reported by inflation targeting central banks around the globe. [7] [11]
The mode of a sample is the element that occurs most often in the collection. For example, the mode of the sample [1, 3, 6, 6, 6, 6, 7, 7, 12, 12, 17] is 6. Given the list of data [1, 1, 2, 4, 4] its mode is not unique. A dataset, in such a case, is said to be bimodal, while a set with more than two modes may be described as multimodal.
The complex normal family has three parameters: location parameter μ, covariance matrix , and the relation matrix . The standard complex normal is the univariate distribution with μ = 0 {\displaystyle \mu =0} , Γ = 1 {\displaystyle \Gamma =1} , and C = 0 {\displaystyle C=0} .
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] A Rayleigh distribution is often observed when the overall magnitude of a vector in the plane is related to its directional components. One example where the Rayleigh distribution naturally ...
In probability theory and statistics, the gamma distribution is a versatile two-parameter family of continuous probability distributions. [1] The exponential distribution, Erlang distribution, and chi-squared distribution are special cases of the gamma distribution. [2] There are two equivalent parameterizations in common use: