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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.
In ecology, alpha diversity (α-diversity) is the mean species diversity in a site at a local scale. The term was introduced by R. H. Whittaker [ 1 ] [ 2 ] together with the terms beta diversity (β-diversity) and gamma diversity (γ-diversity).
Knowledge of type I errors and type II errors is applied widely in fields of in medical science, biometrics and computer science. Minimising these errors is an object of study within statistical theory, though complete elimination of either is impossible when relevant outcomes are not determined by known, observable, causal processes.
Gamma diversity and alpha diversity can be calculated directly from species inventory data. [2] [13] The simplest of Whittaker's original definitions of beta diversity is β = γ/α Here gamma diversity is the total species diversity of a landscape and alpha diversity is the mean species diversity per site.
In Bayesian statistics, the gamma distribution is widely used as a conjugate prior. It is the conjugate prior for the precision (i.e. inverse of the variance) of a normal distribution. It is also the conjugate prior for the exponential distribution.
It is a multivariate generalization of the beta distribution, [1] hence its alternative name of multivariate beta distribution (MBD). [2] Dirichlet distributions are commonly used as prior distributions in Bayesian statistics , and in fact, the Dirichlet distribution is the conjugate prior of the categorical distribution and multinomial ...
Alpha is also a function of the number of items, so shorter scales will often have lower reliability estimates yet still be preferable in many situations because they are lower burden. An alternative way of thinking about internal consistency is that it is the extent to which all of the items of a test measure the same latent variable. The ...
Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities.