curve.density: Draw density plots

In FlexReg: Regression Models for Bounded Continuous and Discrete Responses

Draw density plots

Description

The function draws a curve corresponding to the probability density/mass function of the specified distribution (beta, flexible beta, variance-inflated beta, binomial, beta-binomial, or flexible beta-binomial). For beta, flexible beta, and variance-inflated beta, it also allows to include the representation of the probability of augmentation in zero and/or one values.

Usage

curve.density(
  type = NULL,
  size = NULL,
  mu = NULL,
  theta = NULL,
  phi = NULL,
  p = NULL,
  w = NULL,
  k = NULL,
  q0 = NULL,
  q1 = NULL,
  ...
)

Arguments

type	a character specifying the distribution type to be plotted ("Beta", "FB", "VIB", "Bin", "BetaBin", or "FBB").
size	the total number of trials (to be specified only if type is "Bin", "BetaBin", or "FBB").
mu	the mean parameter of the distribution. It must lie in (0, 1).
theta	the overdispersion parameter (to be specified only if type is "BetaBin" or "FBB"). It must lie in (0, 1).
phi	the precision parameter (if type is "BetaBin" or "FBB", it represents an alternative way to specify the theta parameter). It must be a real positive value.
p	the mixing weight (to be specified only if type is "FB", "VIB", or "FBB"). It must lie in (0, 1).
w	the normalized distance among component means of the FB and FBB distributions (to be specified only if type = "FB", or type = "FBB"). It must lie in (0, 1).
k	the extent of the variance inflation (to be specified only if type = "VIB"). It must lie in (0, 1).
q0	the probability of augmentation in zero (to be specified only if type is "Beta", "FB", or "VIB"). It must lie in (0, 1). In case of no augmentation, it is NULL (default).
q1	the probability of augmentation in one (to be specified only if type is "Beta", "FB", or "VIB"). It must lie in (0, 1). In case of no augmentation, it is NULL (default).
...	additional arguments of stat_function.

References

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

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

Di Brisco, A. M., Migliorati, S., Ongaro, A. (2020). Robustness against outliers: A new variance inflated regression model for proportions. Statistical Modelling, 20(3), 274–309. doi:10.1177/1471082X18821213

Ferrari, S.L.P., and Cribari-Neto, F. (2004). Beta Regression for Modeling Rates and Proportions. Journal of Applied Statistics, 31(7), 799–815. doi:10.1080/0266476042000214501

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

Examples

curve.density("Beta", mu=.5, phi=20)
curve.density("Beta", mu=.5, phi=20, q1 = .3)
curve.density("FB", mu=.5, phi=20, p=.4, w=.8)
curve.density("FB", mu=.5, phi=20, p=.4, w=.8, q0= .1)
curve.density("VIB", mu=.5, phi=20, p=.9, k=.8, col=3)
curve.density("VIB", mu=.5, phi=20, p=.9, k=.8, col=3, q0=.1, q1=.3)

curve.density("Bin", size=10, mu=.7)
curve.density("BetaBin", size=10, mu=.7, phi=10)
curve.density("FBB", size=10, mu=.7, phi=10, p=.2,w=.7)

FlexReg documentation built on Sept. 29, 2023, 9:06 a.m.