dFBB | R Documentation |
The function computes the probability mass function of the flexible beta-binomial distribution.
dFBB(x, size, mu, theta = NULL, phi = NULL, p, w)
x |
a vector of quantiles. |
size |
the total number of trials. |
mu |
the mean parameter. It must lie in (0, 1). |
theta |
the overdispersion paramete. It must lie in (0, 1). |
phi |
the precision parameter. It is an alternative way to specify the |
p |
the mixing weight. It must lie in (0, 1). |
w |
the normalized distance among clusters. It must lie in (0, 1). |
The FBB distribution is a special mixture of two beta-binomial distributions
p BB(x;λ_1,φ)+(1-p)BB(x;λ_2,φ)
for x \in \lbrace 0, 1, …, n \rbrace where BB(x;\cdot,\cdot) is the beta-binomial distribution with a mean-precision parameterization. Moreover, φ=(1-θ)/θ, 0<p<1 is the mixing weight, φ>0 is a precision parameter, λ_1=μ+(1-p)w and λ_2=μ-pw are the component means of the first and second component of the mixture, 0<μ=pλ_1+(1-p)λ_2<1 is the overall mean, and 0<w<1 is the normalized distance between clusters.
A vector with the same length as x
.
Ascari, R., Migliorati, S. (2021). A new regression model for overdispersed binomial data accounting for outliers and an excess of zeros. Statistics in Medicine, 40(17), 3895–3914. doi:10.1002/sim.9005
dFBB(x = c(5,7,8), size=10, mu = .3, phi = 20, p = .5, w = .5)
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