# R/cdfemu.R In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

```"cdfemu" <-
function(x, para, paracheck=TRUE, yacoubsintegral=TRUE) {
if(paracheck == TRUE) {
if(! are.paremu.valid(para)) return()
}

ETA.SMALL <- 1E-3
SMALL <- 1E-10
ONEminusSMALL <- 1 - SMALL
LARGE <- sqrt(.Machine\$double.xmax)

names(para\$para) <- NULL
E <- para\$para[1]
M <- para\$para[2]
b <- sqrt( 2*M / (1-E^2) )
Ymuleft <- sqrt(pi)*2^(3/2 - M)*(1 - E^2)^M
Ymuleft <- Ymuleft / (gamma(M) * E^(M-1/2))

if(E >= 1 - ETA.SMALL) {
#warning("Eta is near unity, going to use integration of the pdf")
yacoubsintegral <- FALSE
}
if(E <= ETA.SMALL) {
#warning("Eta is near zero, going to use integration of the pdf")
yacoubsintegral <- FALSE
}
"Ymu" <- function(x=NULL, y=NULL) {
if(y < 0) return(NA)
"afunc" <- function(t) {
B <- vector(mode="numeric", length=length(t))
for(i in 1:length(B)) {
toI <- t[i]^2*x
b <- NULL
try(b <- besselI(toI, nu=M-1/2, expon.scaled=TRUE)/exp(-toI),
silent=TRUE)
if(is.null(b) | is.nan(b) | ! is.finite(b)) b <- LARGE
B[i] <- b
}
B[! is.finite(B)] <- LARGE
z <- exp(-t^2)*t^(2*M) * B
z[! is.finite(z)] <- LARGE
return( z )
}
int1 <- NULL
try( int1 <- integrate(afunc, lower=y, upper=Inf), silent=TRUE )
if(is.null(int1)) return(NA)
val <- int1\$value
if(val == 0) return(0)
return(Ymuleft * int1\$value)
}

f <- sapply(1:length(x), function(i) {
xi <- x[i]
if(xi == 0) return(0)
if(is.na(xi) || xi < 0) return(NA) # return zero?
if(yacoubsintegral) {
Y <- Ymu(x=E, y=b*xi)
if(is.na(Y)) {# | Y <= SMALL) {
return(ONEminusSMALL)
} else {
return(1 - Y)
}
} else {
int1 <- NULL
try( int1 <- integrate(pdfemu, 0, xi, para=para, paracheck=FALSE) )
if(is.null(int1)) return(NA)
val <- int1\$value
ifelse(val >= ONEminusSMALL, return(ONEminusSMALL),
return(val))  } })
names(f) <- NULL
return(f)
}
```

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lmomco documentation built on Sept. 21, 2018, 6:40 p.m.