ZOIP (version 0.1)

dZOIP: ZOIP Distribution

Description

The dZOIP function defines the probability density function of the ZOIP distribution.

Usage

dZOIP(x, mu = 0.5, sigma = 0.1, p0 = 0.08333333, p1 = 0.08333333,
  family = "R-S", log = FALSE)

Arguments

x

quantiles vector.

mu

vector of location parameters.

sigma

vector of scale parameters.

p0

parameter of proportion of zeros.

p1

Parameter of proportion of ones.

family

choice of the parameterization or distribution, family = 'R-S' parameterization beta distribution Rigby and Stasinopoulos, 'F-C' distribution Beta parametrization Ferrari and Cribari-Neto, 'Original' Beta distribution classic parameterization, 'Simplex' simplex distribution.

log

logical; if TRUE, the probabilities of p will be given as log (p).

Details

x has ZOIP distribution with shape parameters "\(\mu\)", scale "\(\sigma\)", proportion of zeros "\(p0\)" and proportion of ones "\( p1\) ", has density: \(p0\) if \(x = 0\), \(p1\) if \(x = 1\), \((1-p0-p1) f (x; \mu, \sigma)\) yes \(0 <x <1\).

where \(p0 \ge 0\) represents the probability that \(x = 0, p1 \ge 0\) represents the probability that \(x = 1, 0 \le p0 + p1 \le 1\) and \(f (x; \mu, \sigma)\) represents some of the functions of probability density for proportional data, such as the beta distribution with its different parameterizations and the simplex distribution.

When family =' R-S 'uses the beta distribution with beta parameterization Rigby and Stasinopoulos (2005) which has a beta distribution function. \(\mu\) is the parameter of mean and shape, plus \(\sigma\) is the dispersion parameter of the distribution. family =' F-C 'distribution Beta parametrization Ferrari and Cribari-Neto (2004), where \(\sigma = \phi\), \(\phi\) is a precision parameter. family =' Original 'beta distribution original parametrization where \(\mu = a\), a parameter of form 1; \(\sigma = b\), b parameter of form 2. family =' Simplex 'simplex distribution. proposed by Barndorff-Nielsen and J<U+00F8>rgensen (1991)

Examples

# NOT RUN {
library(ZOIP)
dZOIP(x=0.5, mu = 0.2, sigma = 0.5, p0 = 0.2, p1 =0.2,family='R-S',log = FALSE)
dZOIP(x=0.5, mu = 0.2, sigma = 3, p0 = 0.2, p1 = 0.2,family='F-C',log = FALSE)
dZOIP(x=0.5, mu = 0.6, sigma = 2.4, p0 = 0.2, p1 = 0.2,family='Original',log = FALSE)
dZOIP(x=0.5, mu = 0.2, sigma = 3, p0 = 0, p1 = 0,family='Simplex',log = FALSE)
dZOIP(x=0.5, mu = 0.2, sigma = 0.5, p0 = 0.2, p1 =0,family='R-S',log = FALSE)
dZOIP(x=0.5, mu = 0.2, sigma = 0.5, p0 = 0, p1 =0.2,family='R-S',log = FALSE)
dZOIP(x=0.5, mu = 0.2, sigma = 0.5, p0 = 0, p1 =0,family='R-S',log = FALSE)
# }