Nothing
#___________________________________________________________________________________________________________________
dKIWARING=
function (x, mu = 1, sigma = 1, nu = 0.3, kinf=0 ,log = 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(nu <= 0) | any(nu >= 1))
stop(paste("nu must be between 0 and 1 ", "\n", ""))
if (any(x < 0))
stop(paste("x must be >=0", "\n", ""))
ly <- max(length(x), length(mu), length(sigma), length(nu))
x <- rep(x, length = ly)
sigma <- rep(sigma, length = ly)
mu <- rep(mu, length = ly)
nu <- rep(nu, length = ly)
inf<- rep(kinf, length = ly)
fy <- dWARING(x, mu = mu, sigma = sigma, log = T)
logfy <- rep(inf, length(x))
logfy <- ifelse((x == inf), log(nu + (1 - nu) * exp(fy)), (log(1 -
nu) + fy))
if (log == FALSE)
fy2 <- exp(logfy)
else fy2 <- logfy
fy2
}
#___________________________________________________________________________________________________________________
pKIWARING=
function (q, mu = 1, sigma = 1, nu = 0.3, 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(nu <= 0) | any(nu >= 1))
stop(paste("nu must be between 0 and 1 ", "\n", ""))
if (any(q < 0))
stop(paste("y must be >=0", "\n", ""))
ly <- max(length(q), length(mu), length(sigma), length(nu))
q <- rep(q, length = ly)
sigma <- rep(sigma, length = ly)
mu <- rep(mu, length = ly)
nu <- rep(nu, length = ly)
inf<- rep(kinf, length = ly)
cdf <- pWARING(q, mu = mu, sigma = sigma)
cdf <- ifelse((q< inf), (1 - nu) * cdf, nu + (1 - nu) * cdf)
if (lower.tail == TRUE)
cdf <- cdf
else cdf <- 1 - cdf
if (log.p == FALSE)
cdf <- cdf
else cdf <- log(cdf)
cdf
}
#___________________________________________________________________________________________________________________
qKIWARING=
function (p, mu = 1, sigma = 1, nu = 0.3, 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(nu <= 0) | any(nu >= 1))
stop(paste("nu must be between 0 and 1 ", "\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), length(nu))
p <- rep(p, length = ly)
sigma <- rep(sigma, length = ly)
mu <- rep(mu, length = ly)
nu <- rep(nu, length = ly)
inf<- rep(kinf, length = ly)
pnew <-ifelse(p>pKIWARING(max(inf-1,0), mu=mu, sigma=sigma, nu=nu, kinf=inf),
(p - nu)/(1 - nu)-(1e-07), p /(1 - nu)-(1e-07))
pnew <-ifelse( inf==0,(p - nu)/(1 - nu)-(1e-07), pnew)
pnew <- ifelse((pnew > 0), pnew, 0)
q <- qWARING(pnew, mu = mu, sigma = sigma)
q
}
#___________________________________________________________________________________________________________________
rKIWARING=
function (n, mu = 1, sigma = 1, nu = 0.3, kinf=0)
{
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(nu <= 0) | any(nu >= 1))
stop(paste("nu 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=c()
for(i in 1:n){
if(p[i]<nu){r[i]=kinf}
else{r[i] = rWARING(1, mu = mu, sigma = sigma)}
}
r
}
#___________________________________________________________________________________________________________________
KIWARING=
function (mu.link = "log", sigma.link = "log", nu.link = "logit", kinf="K")
{
mstats <- checklink("mu.link", "kIWARING", substitute(mu.link),
c("inverse", "log", "identity"))
dstats <- checklink("sigma.link", "kIWARING", substitute(sigma.link),
c("inverse", "log", "identity"))
vstats <- checklink("nu.link", "kIWARING", substitute(nu.link),
c("logit", "probit", "cloglog", "log", "own"))
structure(list(family = c(paste("inf",kinf,"WARING", sep = ""),paste(kinf,"-inflated waring", sep = "") ),
parameters = list(mu = TRUE, sigma = TRUE, nu = TRUE),
nopar = 3, type = "Discrete", mu.link = as.character(substitute(mu.link)),
sigma.link = as.character(substitute(sigma.link)), nu.link = as.character(substitute(nu.link)),
mu.linkfun = mstats$linkfun, sigma.linkfun = dstats$linkfun,
nu.linkfun = vstats$linkfun, mu.linkinv = mstats$linkinv,
sigma.linkinv = dstats$linkinv, nu.linkinv = vstats$linkinv,
mu.dr = mstats$mu.eta, sigma.dr = dstats$mu.eta, nu.dr = vstats$mu.eta,
dldm = function(y, mu, sigma, nu) {
dldm0 <- (1 - nu) * ((nu + (1 - nu) * dWARING(kinf, mu,
sigma))^(-1)) * dWARING(kinf, mu, sigma) * WARING()$dldm(kinf,
mu, sigma)
dldm <- ifelse(y == kinf, dldm0, WARING()$dldm(y, mu, sigma))
dldm
}, d2ldm2 = function(y, mu, sigma, nu) {
dldm0 <- (1 - nu) * ((nu + (1 - nu) * dWARING(kinf, mu,
sigma))^(-1)) * dWARING(kinf, mu, sigma) * WARING()$dldm(kinf,
mu, sigma)
dldm <- ifelse(y == kinf, dldm0, WARING()$dldm(y, mu, sigma))
d2ldm2 <- -dldm * dldm
d2ldm2 <- ifelse(d2ldm2 < -1e-15, d2ldm2, -1e-15)
d2ldm2
}, dldd = function(y, mu, sigma, nu) {
dldd0 <- (1 - nu) * ((nu + (1 - nu) * dWARING(kinf, mu,
sigma))^(-1)) * dWARING(kinf, mu, sigma) * WARING()$dldd(kinf,
mu, sigma)
dldd <- ifelse(y == kinf, dldd0, WARING()$dldd(y, mu, sigma))
dldd
}, d2ldd2 = function(y, mu, sigma, nu) {
dldd0 <- (1 - nu) * ((nu + (1 - nu) * dWARING(kinf, mu,
sigma))^(-1)) * dWARING(kinf, mu, sigma) * WARING()$dldd(kinf,
mu, sigma)
dldd <- ifelse(y == kinf, dldd0, WARING()$dldd(y, mu, sigma))
d2ldd2 <- -dldd^2
d2ldd2 <- ifelse(d2ldd2 < -1e-15, d2ldd2, -1e-15)
d2ldd2
}, dldv = function(y, mu, sigma, nu) {
dldv0 <- ((nu + (1 - nu) * dWARING(kinf, mu, sigma))^(-1)) *
(1 - dWARING(kinf, mu, sigma))
dldv <- ifelse(y == kinf, dldv0, -1/(1 - nu))
dldv
}, d2ldv2 = function(y, mu, sigma, nu) {
dldv0 <- ((nu + (1 - nu) * dWARING(kinf, mu, sigma))^(-1)) *
(1 - dWARING(kinf, mu, sigma))
dldv <- ifelse(y == kinf, dldv0, -1/(1 - nu))
d2ldv2 <- -dldv^2
d2ldv2 <- ifelse(d2ldv2 < -1e-15, d2ldv2, -1e-15)
d2ldv2
}, d2ldmdd = function(y, mu, sigma, nu) {
dldm0 <- (1 - nu) * ((nu + (1 - nu) * dWARING(kinf, mu,
sigma))^(-1)) * dWARING(kinf, mu, sigma) * WARING()$dldm(kinf,
mu, sigma)
dldm <- ifelse(y == kinf, dldm0, WARING()$dldm(y, mu, sigma))
dldd0 <- (1 - nu) * ((nu + (1 - nu) * dWARING(kinf, mu,
sigma))^(-1)) * dWARING(kinf, mu, sigma) * WARING()$dldd(kinf,
mu, sigma)
dldd <- ifelse(y == kinf, dldd0, WARING()$dldd(y, mu, sigma))
d2ldm2 <- -dldm * dldd
d2ldm2
}, d2ldmdv = function(y, mu, sigma, nu) {
dldm0 <- (1 - nu) * ((nu + (1 - nu) * dWARING(kinf, mu,
sigma))^(-1)) * dWARING(kinf, mu, sigma) * WARING()$dldm(kinf,
mu, sigma)
dldm <- ifelse(y == kinf, dldm0, WARING()$dldm(y, mu, sigma))
dldv0 <- ((nu + (1 - nu) * dWARING(kinf, mu, sigma))^(-1)) *
(1 - dWARING(kinf, mu, sigma))
dldv <- ifelse(y == kinf, dldv0, -1/(1 - nu))
d2ldmdv <- -dldm * dldv
d2ldmdv
}, d2ldddv = function(y, mu, sigma, nu) {
dldd0 <- (1 - nu) * ((nu + (1 - nu) * dWARING(kinf, mu,
sigma))^(-1)) * dWARING(kinf, mu, sigma) * WARING()$dldd(kinf,
mu, sigma)
dldd <- ifelse(y == kinf, dldd0, WARING()$dldd(y, mu, sigma))
dldv0 <- ((nu + (1 - nu) * dWARING(kinf, mu, sigma))^(-1)) *
(1 - dWARING(kinf, mu, sigma))
dldv <- ifelse(y == kinf, dldv0, -1/(1 - nu))
d2ldddv <- -dldd * dldv
d2ldddv
}, G.dev.incr = function(y, mu, sigma, nu, kinf, ...) -2 *
dKIWARING(y, mu = mu, sigma = sigma, nu = nu, kinf=kinf, log = TRUE),
rqres = expression(rqres(pfun = "pKIWARING", type = "Discrete",
ymin = 0, y = y, mu = mu, sigma = sigma, nu = nu)),
mu.initial = expression(mu <- rep(mean(y), length(y))),
sigma.initial = expression(sigma <- rep(1, length(y))), nu.initial = expression(nu <- rep(((sum(y ==
kinf)/length(y)) + 0.01)/2, length(y))), mu.valid = function(mu) all(mu >
0), sigma.valid = function(sigma) all(sigma > 0),
nu.valid = function(nu) all(nu > 0 & nu < 1), y.valid = function(y) all(y >=0)),
class = c("gamlss.family", "family"))
}
#___________________________________________________________________________________________________________________
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