OANVASIM: One-adjusted N-Vasicek distribution with mean...

In vasicekreg: Regression Modeling Using Vasicek Distribution

One-adjusted N-Vasicek distribution with mean parameterization

Description

Defines a one-adjusted normal-kernel Vasicek distribution for responses in (0,1]. The parameter \nu is the probability at one. Conditional on an observation in (0,1), the distribution is NVASIM with mean \mu and shape parameter \sigma.

Usage

d1NVASIM(x, mu = 0.5, sigma = 0.5, nu = 0.1, log = FALSE)

p1NVASIM(q, mu = 0.5, sigma = 0.5, nu = 0.1, lower.tail = TRUE, log.p = FALSE)

q1NVASIM(p, mu = 0.5, sigma = 0.5, nu = 0.1, lower.tail = TRUE, log.p = FALSE)

r1NVASIM(n, mu = 0.5, sigma = 0.5, nu = 0.1)

dOANVASIM(x, mu = 0.5, sigma = 0.5, nu = 0.1, log = FALSE)

pOANVASIM(q, mu = 0.5, sigma = 0.5, nu = 0.1, lower.tail = TRUE, log.p = FALSE)

qOANVASIM(p, mu = 0.5, sigma = 0.5, nu = 0.1, lower.tail = TRUE, log.p = FALSE)

rOANVASIM(n, mu = 0.5, sigma = 0.5, nu = 0.1)

OANVASIM(mu.link = "logit", sigma.link = "logit", nu.link = "logit")

Arguments

x	Vector of values in [0,1] at which the density or probability mass is evaluated. The distribution has support (0,1], and the returned value is zero at x=0.
mu	Mean of the continuous Vasicek component, in (0,1).
sigma	Shape parameter of the continuous Vasicek component, in (0,1).
nu	Probability at one, in (0,1).
log	Logical; if TRUE, log probabilities or log densities are returned.
q	Vector of values in [0,1] at which the cumulative distribution function is evaluated.
lower.tail	Logical; if TRUE, probabilities are P(Y\leq y); otherwise, they are P(Y>y).
log.p	Logical; if TRUE, probabilities are supplied or returned on the log scale.
p	Vector of probabilities.
n	Number of observations. If length(n) > 1, its length is taken to be the number required.
mu.link	Link function for \mu.
sigma.link	Link function for \sigma.
nu.link	Link function for \nu.

Details

Let Y_c\sim\mathrm{NVASIM}(\mu,\sigma) and let 0<\nu<1. The BEOI-type one-adjusted distribution is defined by

P(Y=1)=\nu

and

f_Y(y)=(1-\nu)f_{Y_c}(y\mid\mu,\sigma),\quad 0<y<1.

Consequently,

E(Y)=\nu+(1-\nu)\mu

and

\mathrm{Var}(Y)=(1-\nu)\mathrm{Var}(Y_c)+ \nu(1-\nu)(1-\mu)^2.

Thus, \mu=E(Y\mid 0<Y<1) is the mean of the continuous component, whereas \nu+(1-\nu)\mu is the marginal mean.

Value

OANVASIM() returns a gamlss.family object. The functions d1NVASIM(), p1NVASIM(), q1NVASIM(), and r1NVASIM() return probability mass or density values, cumulative probabilities, quantiles, and random observations, respectively. dOANVASIM(), pOANVASIM(), qOANVASIM(), and rOANVASIM() are equivalent names following the GAMLSS family-name convention.

References

Ospina, R. and Ferrari, S. L. P. (2010). Inflated beta distributions. Statistical Papers, 51, 111–126.

Rigby, R. A. and Stasinopoulos, D. M. (2005). Generalized additive models for location, scale and shape. Applied Statistics, 54(3), 507–554.

See Also

NVASIM, ZANVASIM, BEOI

Examples

set.seed(123)
y <- r1NVASIM(1000, mu = 0.60, sigma = 0.30, nu = 0.20)
mean(y == 1)
mean(y)
0.20 + (1 - 0.20) * 0.60

## Not run: 
library(gamlss)
fit <- gamlss(
  y ~ 1,
  sigma.formula = ~ 1,
  nu.formula = ~ 1,
  family = OANVASIM(),
  control = gamlss.control(trace = FALSE)
)

## End(Not run)

vasicekreg documentation built on Aug. 20, 2026, 9:08 a.m.