Nothing
## *****************************************************************************
## Probability density function(pdf) of Exponentiated Weibull(EW) distribution
dexpo.weibull <- function (x, alpha, theta, log=FALSE)
{
if((!is.numeric(alpha)) || (!is.numeric(theta)) || (!is.numeric(x)))
stop("non-numeric argument to mathematical function")
if((min(alpha) <= 0) || (min(theta) <= 0) || (x <= 0))
stop("Invalid arguments")
u <- exp(alpha * log(x))
pdf <- exp(log(alpha)+log(theta)-log(x)+log(u)-u +(theta -1.0)* log(1.0 - exp(-u)))
if (log)
pdf<- log(pdf)
return(pdf)
}
## *****************************************************************************
## Cummulative distribution function(cdf) of Exponentiated Weibull distribution
pexpo.weibull <- function (q, alpha, theta, lower.tail=TRUE, log.p=FALSE)
{
if((!is.numeric(alpha)) || (!is.numeric(theta)) || (!is.numeric(q)))
stop("non-numeric argument to mathematical function")
if((min(alpha) <= 0) || (min(theta) <= 0) || (q <= 0))
stop("Invalid arguments")
u <- exp(alpha * log(q))
cdf<-exp(theta * log(1.0 - exp(-u)))
if (!lower.tail)
cdf<- 1.0 - cdf
if (log.p)
cdf<- log(cdf)
return(cdf)
}
## *****************************************************************************
## Quantile function of Exponentiated Weibull distribution
qexpo.weibull <- function (p, alpha, theta, lower.tail=TRUE, log.p=FALSE)
{
if((!is.numeric(alpha)) || (!is.numeric(theta)) || (!is.numeric(p)))
stop("non-numeric argument to mathematical function")
if((min(alpha) <= 0) || (min(theta) <= 0) || (p <= 0) || (p > 1))
stop("Invalid arguments")
qtl<- ((- log(1.0 - (p ^ (1.0/theta)))) ^ (1.0/alpha))
if (!lower.tail)
{
qtl<- ((- log(1.0 - ((1.0-p) ^ (1.0/theta)))) ^ (1.0/alpha))
}
if (log.p)
qtl<- log(qtl)
return(qtl)
}
## *****************************************************************************
## Random variate generation from Exponentiated Weibull distribution
rexpo.weibull<-function(n, alpha, theta)
{
if((!is.numeric(alpha)) || (!is.numeric(theta)) || (!is.numeric(n)))
stop("non-numeric argument to mathematical function")
if((min(alpha) <= 0) || (min(theta) <= 0) || (n <= 0))
stop("Invalid arguments")
return(((- log(1.0 - (runif(n) ^ (1.0/theta)))) ^ (1.0/alpha)))
}
## *****************************************************************************
## Reliability function of Exponentiated Weibull distribution
sexpo.weibull <- function (x, alpha, theta)
{
if((!is.numeric(alpha)) || (!is.numeric(theta)) || (!is.numeric(x)))
stop("non-numeric argument to mathematical function")
if((min(alpha) <= 0) || (min(theta) <= 0) || (x <= 0))
stop("Invalid arguments")
u <- exp(alpha * log(x))
return(1.0 - exp(theta * log(1.0 - exp(-u))))
}
## *****************************************************************************
## Hazard function of Exponentiated Weibull distribution
hexpo.weibull <- function (x, alpha, theta)
{
if((!is.numeric(alpha)) || (!is.numeric(theta)) || (!is.numeric(x)))
stop("non-numeric argument to mathematical function")
if((min(alpha) <= 0) || (min(theta) <= 0) || (x <= 0))
stop("Invalid arguments")
u <- exp(alpha * log(x))
num<-exp(log(alpha)+log(theta)-log(x)+log(u)-u +
(theta -1.0)* log(1.0 - exp(-u)))
den <- 1.0 - exp(theta * log(1.0 - exp(-u)))
return(num/den)
}
## *****************************************************************************
## Hazard rate average function of Exponentiated Weibull distribution
hra.expo.weibull <- function(x, alpha, theta)
{
r <- sexpo.weibull(x, alpha, theta)
fra <-((-1) * log(r)) / x
return(fra)
}
## *******************************************************************
## Conditional Hazard rate function of Exponentiated Weibull distribution
crf.expo.weibull <- function(x, t=0, alpha, theta)
{
t <- t
x <- x
nume <- hexpo.weibull(x+t, alpha, theta)
deno <- hexpo.weibull(x, alpha, theta)
return(nume/deno)
}
## *****************************************************************************
## Kolmogorov-Smirnov test (One-sample)for Exponentiated Weibull distribution
ks.expo.weibull <- function(x, alpha.est, theta.est,
alternative = c("less","two.sided","greater"), plot = FALSE, ...)
{
alpha <- alpha.est
theta <- theta.est
res <- ks.test(x, pexpo.weibull, alpha, theta, alternative = alternative)
if(plot){
plot(ecdf(x), do.points = FALSE, main = 'Empirical and Theoretical cdfs',
xlab = 'x', ylab = 'Fn(x)', ...)
mini <- min(x)
maxi <- max(x)
t <- seq(mini, maxi, by = 0.01)
y <- pexpo.weibull(t, alpha, theta)
lines(t, y, lwd = 2, col = 2)
}
return(res)
}
## *****************************************************************************
## Quantile-Quantile(QQ) plot for Exponentiated Weibull distribution
qq.expo.weibull <- function(x, alpha.est, theta.est, main=' ', line.qt=FALSE, ...)
{
xlab <- 'Empirical quantiles'
ylab <- 'Theoretical quantiles'
alpha <- alpha.est
theta <- theta.est
n <- length(x)
k <- seq(1,n,by=1)
P <- (k - 0.5) / n
limx <- c(min(x), max(x))
Finv <- qexpo.weibull(P,alpha, theta)
quantiles <- sort(x)
plot(quantiles, Finv, xlab = xlab, ylab = ylab, xlim = limx,
ylim = limx, main = main, col = 4, lwd = 2, ...)
lines(c(0,limx), c(0,limx), col = 2, lwd = 2)
if(line.qt){
quant <- quantile(x)
x1 <- quant[2]
x2 <- quant[4]
y1 <- qexpo.weibull(0.25, alpha, theta)
y2 <- qexpo.weibull(0.75, alpha, theta)
m <-((y2-y1)/(x2-x1))
inter <- y1 - (m * x1)
abline(inter, m, col = 2, lwd = 2)
}
invisible(list(x = quantiles, y = Finv))
}
## *****************************************************************************
## Probability-Probability(PP) plot for Exponentiated Weibull distribution
pp.expo.weibull <- function(x, alpha.est, theta.est, main=' ', line=FALSE, ...)
{
xlab <- 'Empirical distribution function'
ylab <- 'Theoretical distribution function'
alpha <- alpha.est
theta <- theta.est
F <- pexpo.weibull(x,alpha, theta)
Pemp <- sort(F)
n <- length(x)
k <- seq(1, n, by = 1)
Pteo <-(k - 0.5) / n
plot(Pemp, Pteo, xlab = xlab, ylab = ylab, col = 4,
xlim = c(0, 1), ylim = c(0, 1), main = main, lwd = 2, ...)
if(line)
lines(c(0, 1), c(0, 1), col = 2, lwd = 2)
Cor.Coeff <- cor(Pemp, Pteo)
Determination.Coeff <- (Cor.Coeff^2) * 100
return(list(Cor.Coeff = Cor.Coeff, Determination.Coeff = Determination.Coeff))
}
## *********************************************************************
## Akaike information criterium (AIC) and
## Bayesian information criterion(BIC) for Exponentiated Weibull distribution
abic.expo.weibull <- function(x, alpha.est, theta.est)
{
alpha <- alpha.est
theta <- theta.est
n <- length(x)
p <- 2
f <- dexpo.weibull(x,alpha, theta)
l <- log(f)
LogLik <- sum(l)
AIC <- - 2 * LogLik + 2 * p
BIC <- - 2 * LogLik + p * log(n)
return(list(LogLik = LogLik, AIC = AIC, BIC = BIC))
}
## *************************************************************************
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.