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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.
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 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).
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.
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 beta-binomial distribution is the binomial distribution in which the probability of success at each of n trials is not fixed but randomly drawn from a beta distribution. It is frequently used in Bayesian statistics , empirical Bayes methods and classical statistics to capture overdispersion in binomial type distributed data.
The beta negative binomial distribution contains the beta geometric distribution as a special case when either = or =. It can therefore approximate the geometric distribution arbitrarily well. It also approximates the negative binomial distribution arbitrary well for large α {\displaystyle \alpha } .
The term was introduced by R. H. Whittaker [1] together with the terms alpha diversity (α-diversity) and beta diversity (β-diversity). Whittaker's idea was that the total species diversity in a landscape (γ) is determined by two different things, the mean species diversity in sites at a more local scale (α) and the differentiation among ...