Nothing
#---------------------------#
#---- YULE DISTRIBUTION ----#
#---------------------------#
dYU1<-function (x, mu = 2, log = FALSE)
{
if (any(mu < 0))
stop(paste("mu must be > 0)", "\n", ""))
if (any(x < 0))
stop(paste("x must be >=0", "\n", ""))
lx <- max(length(x), length(mu))
x <- rep(x, length = lx)
mu <- rep(mu, length = lx)
logfx <- log(mu) + lbeta( mu+1, x+1)
if (log==FALSE) logfx<-exp(logfx)
logfx
}
#Cumulative density function
pYU1<-function (q, mu = 2, lower.tail = TRUE, log.p = FALSE)
{
if (any(mu < 0))
stop(paste("mu must be > 0", "\n", ""))
if (any(q < 0))
stop(paste("q must be >=0", "\n", ""))
ly <- max(length(q), length(mu))
q <- rep(q, length = ly)
mu<- rep(mu, length = ly)
s1<- seq(0, max(q))
cdf<- cumsum(dYU1(s1, mu=mu))
s2<-match(q,s1, nomatch=0)
cdf<- cdf[s2]
if (log.p == TRUE) cdf<-log(cdf)
cdf
}
#Quantile function
qYU1<-function (p, mu = 2, lower.tail = TRUE, log.p = FALSE, max.value = 10000)
{
if (any(p < 0) | any(p > 1.0001))
stop(paste("p must be in [0,1]", "\n", ""))
if (any(mu < 0))
stop(paste("mu must be > 0)", "\n", ""))
if (lower.tail) p <- p
else p <- 1 - p
ly <- max(length(p), length(mu))
p <- rep(p, length = ly)
QQQ <- rep(0, length = ly)
mu <- rep(mu, length = ly)
for (i in seq(along = p)) {
cumpro <- 0
if (p[i] + 1e-09 >= 1)
QQQ[i] <- Inf
else {
for (j in seq(from = 0, to = max.value)) {
cumpro <- pYU1(j, mu= mu[i])
QQQ[i] <- j
if (p[i] <= cumpro)
break
}
}
}
QQQ
}
#Random Generating Function
rYU1<- function(n, mu=2)
{
if (any(mu < 0))
stop(paste("mu must be > 0)", "\n", ""))
if (any(n <= 0))
stop(paste("n must be a positive integer", "\n", ""))
n <- ceiling(n)
p <- runif(n)
r <- qYU1(p, mu=mu)
r
}
#Distribution function
YU1<-function (mu.link = "log")
{
mstats <- checklink(which.link="mu.link",
which.dist="Yule", link=substitute(mu.link),
link.List="log")
#One of these for each parameter to specify which link to use.
structure(list(family = c("YU1", "Yule"),
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){
dldm <- digamma(mu+1) - digamma(mu+y+2) + (1/mu)
dldm
},
d2ldm2 = function(y, mu){
dldm <- digamma(mu+1) - digamma(mu+y+2) + (1/mu)
d2ldm2 <- -dldm*dldm
d2ldm2
},
G.dev.incr = function(y, mu, ...)
-2 * dYU1(y, mu = mu, log = TRUE),
rqres = expression(rqres(pfun = "pYU1", type = "Discrete",
ymin = 0, y = y, mu = mu)),
mu.initial = expression({
if (any(y < 0)) stop(paste("Negative values in the response not allowed for",
"the Yule family"))
mu <- (y + mean(y))/2}),
mu.valid = function(mu) all(mu > 0) ,
y.valid = function(y) all(y >=0)),
class = c("gamlss.family", "family"))
}
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