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In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] or (0, 1) in terms of two positive parameters, denoted by alpha (α) and beta (β), that appear as exponents of the variable and its complement to 1, respectively, and control the shape of the distribution.
The gamma distribution is the maximum entropy probability distribution (both with respect to a uniform base measure and a base measure) for a random variable X for which E[X] = kθ = α/β is fixed and greater than zero, and E[ln X] = ψ(k) + ln θ = ψ(α) − ln β is fixed (ψ is the digamma function). [1]
The Bernoulli distribution, which takes value 1 with probability p and value 0 with probability q = 1 − p. The Rademacher distribution, which takes value 1 with probability 1/2 and value −1 with probability 1/2. The binomial distribution, which describes the number of successes in a series of independent Yes/No experiments all with the same ...
Beta regression is a form of regression which is used when the response variable, , takes values within and can be assumed to follow a beta distribution. [1] It is generalisable to variables which takes values in the arbitrary open interval through transformations. [1] Beta regression was developed in the early 2000s by two sets of ...
Continuous uniform. In probability theory and statistics, the continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions. Such a distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. [1]
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);
PERT distribution. In probability and statistics, the PERT distributions are a family of continuous probability distributions defined by the minimum (a), most likely (b) and maximum (c) values that a variable can take. It is a transformation of the four-parameter beta distribution with an additional assumption that its expected value is.
Beta prime distribution. In probability theory and statistics, the beta prime distribution (also known as inverted beta distribution or beta distribution of the second kind[1]) is an absolutely continuous probability distribution. If has a beta distribution, then the odds has a beta prime distribution.