cNORM (version 3.3.1)

betaCoefficients: Compute Parameters of a Beta Binomial Distribution

Description

This function calculates the \(\alpha\) (a) and \(\beta\) (b) parameters of a beta binomial distribution, along with the mean (m), variance (var) based on the input vector `x` and the maximum number `n`.

Usage

betaCoefficients(x, n = NULL)

Value

A numeric vector containing the calculated parameters in the following order: alpha (a), beta (b), mean (m), standard deviation (sd), and the maximum number (n).

Arguments

x

A numeric vector of non-negative integers representing observed counts.

n

The maximum number or the maximum possible value of `x`. If not specified, uses max(x) instead.

Details

The beta-binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of trials, where the probability of success varies from trial to trial. This variability in success probability is modeled by a beta distribution. Such a calculation is particularly relevant in scenarios where there is heterogeneity in success probabilities across trials, which is common in real-world situations, as for example the number of correct solutions in a psychometric test, where the test has a fixed number of items.

Examples

x <- c(1, 2, 3, 4, 5)
n <- 5

betaCoefficients(x, n) # or, to set n to max(x)
betaCoefficients(x)