dFB | R Documentation |
Density function, distribution function, quantile function, and random generation for the (augmented) flexible beta distribution.
dFB(x, mu, phi, p, w, q0 = NULL, q1 = NULL, log = FALSE)
qFB(prob, mu, phi, p, w, q0 = NULL, q1 = NULL, log.prob = FALSE)
pFB(q, mu, phi, p, w, q0 = NULL, q1 = NULL, log.prob = FALSE)
rFB(n, mu, phi, p, w, q0 = NULL, q1 = NULL)
x , q |
a vector of quantiles. |
mu |
the mean parameter. It must lie in (0, 1). |
phi |
the precision parameter. It must be a real positive value. |
p |
the mixing weight. It must lie in (0, 1). |
w |
the normalized distance among component means. It must lie in (0, 1). |
q0 |
the probability of augmentation in zero. It must lie in (0, 1). In case of no augmentation, it is |
q1 |
the probability of augmentation in one. It must lie in (0, 1). In case of no augmentation, it is |
log |
logical; if TRUE, densities are returned on log-scale. |
prob |
a vector of probabilities. |
log.prob |
logical; if TRUE, probabilities |
n |
the number of values to generate. If |
The FB distribution is a special mixture of two beta distributions with probability density function
f_{FB}(x;\mu,\phi,p,w)=p f_B(x;\lambda_1,\phi)+(1-p)f_B(x;\lambda_2,\phi),
for 0<x<1
, where f_B(x;\cdot,\cdot)
is the beta density with a mean-precision parameterization.
Moreover, 0<\mu=p\lambda_1+(1-p)\lambda_2<1
is the overall mean, \phi>0
is a precision parameter,
0<p<1
is the mixing weight, 0<w<1
is the normalized distance between component means, and
\lambda_1=\mu+(1-p)w
and \lambda_2=\mu-pw
are the means of the first and second component of the mixture, respectively.
The augmented FB distribution has density
q_0
, if x=0
q_1
, if x=1
(1-q_0-q_1)f_{FB}(x;\mu,\phi,p,w)
, if 0<x<1
where 0<q_0<1
identifies the augmentation in zero, 0<q_1<1
identifies the augmentation in one,
and q_0+q_1<1
.
The function dFB
returns a vector with the same length as x
containing the density values.
The function pFB
returns a vector with the same length as q
containing the values of the distribution function.
The function qFB
returns a vector with the same length as prob
containing the quantiles.
The function rFB
returns a vector of length n
containing the generated random values.
Di Brisco, A. M., Migliorati, S. (2020). A new mixed-effects mixture model for constrained longitudinal data. Statistics in Medicine, 39(2), 129–145. doi:10.1002/sim.8406
Migliorati, S., Di Brisco, A. M., Ongaro, A. (2018). A New Regression Model for Bounded Responses. Bayesian Analysis, 13(3), 845–872. doi:10.1214/17-BA1079
dFB(x = c(.5,.7,.8), mu = .3, phi = 20, p = .5, w = .5)
dFB(x = c(.5,.7,.8), mu = .3, phi = 20, p = .5, w = .5, q0 = .2)
dFB(x = c(.5,.7,.8), mu = .3, phi = 20, p = .5, w = .5, q0 = .2, q1 = .1)
qFB(prob = c(.5,.7,.8), mu = .3, phi = 20, p = .5, w = .5)
qFB(prob = c(.5,.7,.8), mu = .3, phi = 20, p = .5, w = .5, q0 = .2)
qFB(prob = c(.5,.7,.8), mu = .3, phi = 20, p = .5, w = .5, q0 = .2, q1 = .1)
pFB(q = c(.5,.7,.8), mu = .3, phi = 20, p = .5, w = .5)
pFB(q = c(.5,.7,.8), mu = .3, phi = 20, p = .5, w = .5, q0 = .2)
pFB(q = c(.5,.7,.8), mu = .3, phi = 20, p = .5, w = .5, q0 = .2, q1 = .1)
rFB(n = 100, mu = .5, phi = 30,p = .3, w = .6)
rFB(n = 100, mu = .5, phi = 30,p = .3, w = .6, q0 = .2, q1 = .1)
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