Nothing
#___________________________________________________________________________________________________________________
dKIYULE=
function (x, mu = 1, sigma = 0.1, kinf=0, log = FALSE)
{
if (any(mu <= 0))
stop(paste("mu must be greater than 0", "\n", ""))
if (any(sigma <= 0) | any(sigma >= 1))
stop(paste("sigma must be between 0 and 1", "\n", ""))
if (any(x < 0))
stop(paste("x must be 0 or greater than 0", "\n", ""))
ly <- max(length(x), length(mu))
x <- rep(x, length = ly)
sigma <- rep(sigma, length = ly)
mu <- rep(mu, length = ly)
inf<- rep(kinf, length = ly)
fy <- dYULE(x, mu = mu, log=T)
logfy <- rep(kinf, ly)
logfy <- ifelse((x == inf), log(sigma + (1 - sigma) * exp(fy)), (log(1 -
sigma) + fy))
if (log == FALSE)
fy <- exp(logfy)
else fy <- logfy
fy
}
#___________________________________________________________________________________________________________________
pKIYULE=
function (q, mu = 1, sigma = 0.1, kinf=0, lower.tail = TRUE, log.p = FALSE)
{
if (any(mu <= 0))
stop(paste("mu must be greater than 0", "\n", ""))
if (any(sigma <= 0) | any(sigma >= 1))
stop(paste("sigma must be between 0 and 1", "\n", ""))
if (any(q < 0))
stop(paste("y must be 0 or greater than 0", "\n", ""))
ly <- max(length(q), length(mu), length(sigma))
q <- ifelse((q< 100), q, 100)
q <- rep(q, length = ly)
mu <- rep(mu, length = ly)
sigma <- rep(sigma, length = ly)
inf<- rep(kinf, length = ly)
cdf <- rep(kinf, ly)
cdf <- pYULE(q, mu = mu, lower.tail = TRUE, log.p = FALSE)
cdf <- ifelse((q< inf), (1 - sigma) * cdf, sigma + (1 - sigma) * cdf)
if (lower.tail == TRUE)
cdf <- cdf
else cdf <- 1 - cdf
if (log.p == FALSE)
cdf <- cdf
else cdf <- log(cdf)
cdf
}
#___________________________________________________________________________________________________________________
qKIYULE=
function (p, mu = 1, sigma = 0.1, kinf=0, lower.tail = TRUE, log.p = FALSE)
{
if (any(mu <= 0))
stop(paste("mu must be greater than 0", "\n", ""))
if (any(sigma <= 0))
stop(paste("sigma must be greater than 0", "\n", ""))
if (any(p <= 0) | any(p >= 1))
stop(paste("p must be between 0 and 1", "\n", ""))
if (log.p == TRUE)
p <- exp(p)
else p <- p
if (lower.tail == TRUE)
p <- p
else p <- 1 - p
ly <- max(length(p), length(mu), length(sigma))
p <- rep(p, length = ly)
sigma <- rep(sigma, length = ly)
mu <- rep(mu, length = ly)
inf<- rep(kinf, length = ly)
pnew <-ifelse(p>pKIYULE(max(inf-1,0), mu=mu, sigma=sigma, kinf=inf),
(p - sigma)/(1 - sigma)-(1e-07), p /(1 - sigma)-(1e-07))
pnew <-ifelse( inf==0,(p - sigma)/(1 - sigma)-(1e-07), pnew)
pnew <- ifelse((pnew > 0), pnew, 0)
q <- qYULE(pnew, mu = mu)
q
}
#___________________________________________________________________________________________________________________
rKIYULE=
function (n, mu = 1, sigma = 0.1, kinf=0)
{
if (any(mu <= 0))
stop(paste("mu must greated than 0", "\n", ""))
if (any(sigma <= 0))
stop(paste("sigma must greated than 0", "\n", ""))
if (any(n <= 0))
stop(paste("n must be a positive integer", "\n", ""))
n <- ceiling(n)
p <- runif(n)
r=c()
for(i in 1:n){
if(p[i]<sigma){r[i]=kinf}
else{r[i] = rYULE(1, mu = mu)}
}
r
}
#___________________________________________________________________________________________________________________
KIYULE=
function (mu.link = "log", sigma.link = "logit", kinf="K")
{
mstats <- checklink(which.link = "mu.link", which.dist = "KIYULE",
link = substitute(mu.link), link.List = "log")
dstats <- checklink("sigma.link", "KIYULE", substitute(sigma.link),
c("logit", "probit", "cloglog", "cauchit", "log", "own"))
structure(list(family = c(paste("inf",kinf,"YULE", sep = ""), paste(kinf,"-inflated Yule", sep = "") ),
parameters = list(mu = TRUE, sigma = TRUE), nopar = 2,
type = "Discrete", mu.link = as.character(substitute(mu.link)),
sigma.link = as.character(substitute(sigma.link)), mu.linkfun = mstats$linkfun,
sigma.linkfun = dstats$linkfun, mu.linkinv = mstats$linkinv,
sigma.linkinv = dstats$linkinv, mu.dr = mstats$mu.eta,
sigma.dr = dstats$mu.eta, dldm = function(y, mu, sigma) {
dldm0 <- (1 - sigma) * ((sigma + (1 - sigma) * dYULE(kinf, mu))
^(-1)) * dYULE(kinf, mu) * YULE()$dldm(kinf, mu)
dldm <- ifelse(y == kinf, dldm0, YULE()$dldm(y, mu))
dldm
}, d2ldm2 = function(y, mu, sigma) {
dldm0 <- (1 - sigma) * ((sigma + (1 - sigma) * dYULE(kinf, mu))
^(-1)) * dYULE(kinf, mu) * YULE()$dldm(kinf, mu)
dldm <- ifelse(y == kinf, dldm0, YULE()$dldm(y, mu))
d2ldm2 <- -dldm * dldm
d2ldm2 <- ifelse(d2ldm2 < -1e-15, d2ldm2, -1e-15)
d2ldm2
}, dldd = function(y, mu, sigma) {
dldd0 <- ((sigma + (1 - sigma) * dYULE(kinf, mu))^(-1)) *
(1 - dYULE(kinf, mu))
dldd <- ifelse(y == kinf, dldd0, -1/(1 - sigma))
dldd
}, d2ldd2 = function(y, mu, sigma) {
dldd0 <- ((sigma + (1 - sigma) * dYULE(kinf, mu))^(-1)) *
(1 - dYULE(kinf, mu))
dldd <- ifelse(y == kinf, dldd0, -1/(1 - sigma))
d2ldd2 <- -dldd * dldd
d2ldd2 <- ifelse(d2ldd2 < -1e-15, d2ldd2, -1e-15)
d2ldd2
}, d2ldmdd = function(y, mu, sigma) {
dldm0 <- (1 - sigma) * ((sigma + (1 - sigma) * dYULE(kinf, mu))
^(-1)) * dYULE(kinf, mu) * YULE()$dldm(kinf, mu)
dldm <- ifelse(y == kinf, dldm0, YULE()$dldm(y, mu))
dldd0 <- ((sigma + (1 - sigma) * dYULE(kinf, mu))^(-1)) *
(1 - dYULE(kinf, mu))
dldd <- ifelse(y == kinf, dldd0, -1/(1 - sigma))
d2ldmdd <- -dldm * dldd
d2ldmdd
}, G.dev.incr = function(y, mu, sigma, kinf, ...) -2 * dKIYULE(y,
mu, sigma, kinf=kinf, log = TRUE), rqres = expression(rqres(pfun = "pKIYULE",
type = "Discrete", ymin = 0, y = y, mu = mu, sigma = sigma, kinf=kinf)),
mu.initial = expression(mu <- rep(mean(y),length(y))),
sigma.initial = expression(sigma <- rep(0.5,length(y))), mu.valid = function(mu) all(mu > 0),
sigma.valid = function(sigma) all(sigma > 0 & sigma <1),
y.valid = function(y) all(y >= 0)),
class = c("gamlss.family","family"))
}
#___________________________________________________________________________________________________________________
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