R/BI.R

In Stan125/gamlss.dist: Distributions for Generalized Additive Models for Location Scale and Shape

# RAR+KA+MS Friday, April 5, 2002 at 15:10
# last change Tuesday, December 14, 2004 Saturday, October 8, 2005 
BI <- function (mu.link = "logit") 
{
  mstats <- checklink("mu.link", "Binomial", substitute(mu.link),
                      c("logit", "probit", "cloglog", "cauchit", "log", "own"))# ms 8-10-05
  structure(
    list(family = c("BI", "Binomial"),
         parameters = list(mu=TRUE), 
         nopar = 1,
         type = "Discrete",
         mu.link = as.character(substitute(mu.link)),  
         mu.linkfun = mstats$linkfun, 
         mu.linkinv = mstats$linkinv, 
         mu.dr = mstats$mu.eta,
         dldm = function(y, mu, bd) (y-bd*mu)/(mu*(1-mu)),
         d2ldm2 = function(mu,bd) -(bd/(mu*(1-mu))),
         G.dev.incr  = function(y,mu,bd,...)  -2*dBI(y,bd,mu,log=TRUE),
         rqres = expression(
           rqres(pfun="pBI", type="Discrete", ymin=0, y=y, mu=mu, bd=bd)
         ), #
         mu.initial = expression({mu <- (y + 0.5)/(bd + 1)}),
         mu.valid = function(mu) all(mu > 0) && all(mu < 1),  
         y.valid = function(y)  all(y >= 0),
         mean = function(bd ,mu) bd * mu,
         variance = function(bd, mu) bd * mu * (1 - mu)
    ),
    class = c("gamlss.family","family") )
}
#------------------------------------------------------------------------------------------
dBI<-function(x, bd = 1, mu = 0.5, log = FALSE)
{ 
  if (any(mu < 0) | any(mu > 1))  stop(paste("mu must be between 0 and 1", "\n", "")) 
  if (any(x < 0) )  stop(paste("x must be >=0", "\n", ""))
  if (any(bd < x))  stop(paste("x  must be <=  than the binomial denominator", bd, "\n"))   
  fy <- dbinom(x, size = bd, prob = mu, log = log)
  fy
}
#------------------------------------------------------------------------------------------
pBI <- function(q, bd=1, mu=0.5, lower.tail = TRUE, log.p = FALSE)
{     
  if (any(mu < 0) | any(mu > 1))  stop(paste("mu must be between 0 and 1", "\n", "")) 
  if (any(q < 0) )  stop(paste("q must be >=0", "\n", ""))
  if (any(bd < q))  stop(paste("q  must be <=  than the binomial denominator", bd, "\n"))   
  cdf <- pbinom(q, size = bd, prob = mu, lower.tail=lower.tail, log.p=log.p)
  cdf
}
#------------------------------------------------------------------------------------------
qBI <- function(p, bd = 1, mu = 0.5,  lower.tail = TRUE, log.p = FALSE)
{      
  if (any(mu < 0) | any(mu > 1))  stop(paste("mu must be between 0 and 1", "\n", "")) 
  if (any( p < 0) | any(p >  1))  stop(paste(" p must be between 0 and 1", "\n", ""))    
  q <- qbinom(p, size = bd, prob = mu, lower.tail = lower.tail, log.p = log.p)
  q
}
#------------------------------------------------------------------------------------------
rBI <- function(n, bd = 1, mu = 0.5)
{ 
  if (any(mu < 0) | any(mu > 1))  stop(paste("mu must be between 0 and 1", "\n", "")) 
  if (any(n <= 0))  stop(paste("n must be a positive integer", "\n", ""))  
  n <- ceiling(n)
  p <- runif(n)
  r <- qbinom(p, size = bd, prob = mu)
  r
}
#-------------------------------------------------------------------------------------------