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IGParametersEstim<-function(x,pm=0,...) {
par <- KogonParametersEstim(x,pm)
alpha <- par[1];beta <- par[2];gam <- par[3]
if (alpha==2) alpha <- alpha-eps
if (alpha==0) alpha <- eps
if (beta==-1) beta <- -1+eps
if (beta==1) beta <- 1-eps
if (gam==0) gam <- eps
c(alpha,beta,gam,par[4])
}
McCullochParametersEstim<-function(x){
tr <- tryCatch(.qStableFit(x, doplot=FALSE),
error=function(e)e)
err <- inherits(tr, "error")
if (!err) {
ans <- tr
alpha <- ifelse(is.na(ans@fit$estimate[1]),0.5,ans@fit$estimate[1])
beta <- ifelse(is.na(ans@fit$estimate[2]),0,ans@fit$estimate[2])
gamma <- ifelse(is.na(ans@fit$estimate[3]),1,ans@fit$estimate[3])
delta <- ifelse(is.na(ans@fit$estimate[4]),0,ans@fit$estimate[4])
}
else{
alpha <- 0.5
beta <- 0
gamma <- 1;delta <- 0
}
c(alpha,beta,gamma,delta)
}
KogonParametersEstim<-function(x,pm=0){
t <- seq(from=0.1,to=1,length.out=10)
Par <- McCullochParametersEstim(x)
alpha <- Par[1];beta <- Par[2]
gamma <- Par[3];delta <- Par[4]
## Shift data to fit the regression requirement
if (pm==0) x <- x+beta*gamma*tan(pi2*alpha)
s <- (x-delta)/gamma
PhiHat <- .ecf(t,s)
alpha <- EstimateAlpha(PhiHat,t)
beta <- EstimateBeta(s,t,alpha)
c(alpha=alpha,beta=beta,gamma,delta)
}
EstimateAlpha <- function(PhiHat,t){
Y1 <- log(-log(Mod(PhiHat)))
X1 <- log(Mod(t))
reg1 <- lm(Y1~X1)
alpha <- as.numeric((reg1[[1]])[2])
alpha=max(alpha,0)
alpha=min(alpha,2)
alpha
}
EstimateBeta <- function(s,t,alpha){
Y2 <- .get.arctan(s,t)
X2 <- (abs(t)**alpha)*(t/abs(t))*tan(pi2*alpha)
reg2 <- lm(Y2~X2)
beta <- as.numeric((reg2[[1]])[2])
beta=min(beta,1);beta=max(beta,-1)
beta
}
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