The ZABI()
function defines the zero adjusted binomial distribution, a two parameter distribution,
for a gamlss.family
object to be used
in GAMLSS fitting using the function gamlss()
.
The functions dZABI
, pZABI
, qZABI
and rZABI
define the density, distribution function, quantile function and random
generation for the zero adjusted binomial, ZABI()
, distribution.
The ZIBI()
function defines the zero inflated binomial distribution, a two parameter distribution,
for a gamlss.family
object to be used
in GAMLSS fitting using the function gamlss()
.
The functions dZIBI
, pZIBI
, qZIBI
and rZIBI
define the density, distribution function, quantile function and random
generation for the zero inflated binomial, ZIBI()
, distribution.
ZABI(mu.link = "logit", sigma.link = "logit")
dZABI(x, bd = 1, mu = 0.5, sigma = 0.1, log = FALSE)
pZABI(q, bd = 1, mu = 0.5, sigma = 0.1, lower.tail = TRUE, log.p = FALSE)
qZABI(p, bd = 1, mu = 0.5, sigma = 0.1, lower.tail = TRUE, log.p = FALSE)
rZABI(n, bd = 1, mu = 0.5, sigma = 0.1) ZIBI(mu.link = "logit", sigma.link = "logit")
dZIBI(x, bd = 1, mu = 0.5, sigma = 0.1, log = FALSE)
pZIBI(q, bd = 1, mu = 0.5, sigma = 0.1, lower.tail = TRUE, log.p = FALSE)
qZIBI(p, bd = 1, mu = 0.5, sigma = 0.1, lower.tail = TRUE, log.p = FALSE)
rZIBI(n, bd = 1, mu = 0.5, sigma = 0.1)
Defines the mu.link
, with "logit" link as the default for the mu
parameter.
Other links are "probit" and "cloglog"'(complementary log-log)
Defines the sigma.link
, with "logit" link as the default for the mu
parameter.
Other links are "probit" and "cloglog"'(complementary log-log)
vector of (non-negative integer) quantiles
vector of positive probabilities
vector of positive probabilities
vector of binomial denominators
vector of probabilities
vector of quantiles
number of random values to return
logical; if TRUE, probabilities p are given as log(p)
logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
The functions ZABI
and ZIBI
return a gamlss.family
object which
can be used to fit a binomial distribution in the gamlss()
function.
For the definition of the distributions see Rigby and Stasinopoulos (2010) below.
Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.
Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).
Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.
Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or see http://www.gamlss.org/)
ZABI()
curve(dZABI(x, mu = .5, bd=10), from=0, to=10, n=10+1, type="h")
tN <- table(Ni <- rZABI(1000, mu=.2, sigma=.3, bd=10))
r <- barplot(tN, col='lightblue')
ZIBI()
curve(dZIBI(x, mu = .5, bd=10), from=0, to=10, n=10+1, type="h")
tN <- table(Ni <- rZIBI(1000, mu=.2, sigma=.3, bd=10))
r <- barplot(tN, col='lightblue')
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