Nothing
## **************************************************************************
## Probability density function(pdf) of Gumbel distribution
dgumbel <- function(x, mu, sigma, log = FALSE)
{
if((!is.numeric(mu)) || (!is.numeric(sigma)) || (!is.numeric(x)))
stop("non-numeric argument to mathematical function")
if (min(sigma) <= 0.0)
stop("sigma must be positive")
u <- - (x - mu)/sigma
pdf <- (1.0/sigma) * exp(u) * exp( - exp(u))
if (log)
pdf<- log(pdf)
return(pdf)
}
## **************************************************************************
## Cummulative distribution function(cdf) of Gumbel distribution
pgumbel <- function(q, mu, sigma, lower.tail = TRUE, log.p = FALSE)
{
if((!is.numeric(mu)) || (!is.numeric(sigma)) || (!is.numeric(q)))
stop("non-numeric argument to mathematical function")
if (min(sigma) <= 0.0)
stop("sigma must be positive")
u <- - (q - mu)/sigma
cdf<- exp( - exp(u))
if(!lower.tail)
cdf <- 1.0 - cdf
if(log.p)
cdf <- log(cdf)
return(cdf)
}
## **************************************************************************
## Quantile function of Gumbel distribution
qgumbel <- function(p, mu, sigma, lower.tail = TRUE, log.p = FALSE)
{
if((!is.numeric(mu)) || (!is.numeric(sigma)) || (!is.numeric(p)))
stop("non-numeric argument to mathematical function")
if ((min(sigma) <= 0.0) || (p <= 0) || (p > 1.0))
stop("Invalid arguments")
qtl <- mu - sigma * log( - log(p))
if (!lower.tail)
qtl <- mu - sigma * log(- log(1.0 - p))
if (log.p)
qtl <- log(qtl)
return(qtl)
}
## **************************************************************************
## Random variate generation from Gumbel distribution
rgumbel <- function(n, mu, sigma)
{
if((!is.numeric(mu)) ||(!is.numeric(sigma))||(!is.numeric(n)))
stop("non-numeric argument to mathematical function")
if ((min(sigma)<= 0.0) || (n <= 0))
stop("Invalid arguments")
return(mu - sigma * log( - log( runif(n))))
}
## **************************************************************************
## Reliability function of Gumbel distribution
sgumbel <- function(x, mu, sigma)
{
if((!is.numeric(mu)) ||(!is.numeric(sigma))||(!is.numeric(x)))
stop("non-numeric argument to mathematical function")
if (min(sigma) <= 0.0)
stop("sigma must be positive")
u <- - (x - mu)/sigma
return(1.0 - exp( - exp(u)))
}
## **************************************************************************
## Hazard function of Gumbel distribution
hgumbel <- function(x, mu, sigma)
{
if((!is.numeric(mu)) ||(!is.numeric(sigma))||(!is.numeric(x)))
stop("non-numeric argument to mathematical function")
if (min(sigma) <= 0.0)
stop("sigma must be positive")
u <- - (x - mu)/sigma
nume <- (1.0/sigma) * exp(u) * exp( - exp(u))
deno <- 1.0 - exp( - exp(u))
return(nume/deno)
}
## **************************************************************************
## Hazard rate average function of Gumbel distribution
hra.gumbel <- function(x, mu, sigma)
{
r <- sgumbel(x, mu, sigma)
fra <- ((-1)* log(r))/x
return(fra)
}
## **************************************************************************
## Conditional Hazard rate function of Gumbel distribution
crf.gumbel <- function(x, t=0, mu, sigma)
{
t <- t
x <- x
nume <- hgumbel(x+t, mu, sigma)
deno <- hgumbel(x, mu, sigma)
return(nume/deno)
}
## **************************************************************************
## Kolmogorov-Smirnov test (One-sample)for Gumbel distribution
ks.gumbel <- function(x, mu.est, sigma.est,
alternative = c("less", "two.sided", "greater"), plot = FALSE, ...)
{
mu <- mu.est
sigma <- sigma.est
res <- ks.test(x, pgumbel, mu, sigma, 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 <- pgumbel(t, mu, sigma)
lines(t, y, lwd = 2, col = 2)
}
return(res)
}
## **************************************************************************
## Quantile-Quantile(QQ) plot for Gumbel distribution
qq.gumbel <- function(x, mu.est, sigma.est, main=' ', line.qt = FALSE, ...)
{
xlab <- 'Empirical quantiles'
ylab <- 'Theoretical quantiles'
mu <- mu.est
sigma <- sigma.est
n <- length(x)
k <- seq(1, n, by = 1)
P <- (k - 0.5) / n
limx <- c(min(x), max(x))
Finv <- qgumbel(P, mu, sigma)
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 <- qgumbel(0.25, mu, sigma)
y2 <- qgumbel(0.75, mu, sigma)
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 Gumbel distribution
pp.gumbel <- function(x, mu.est, sigma.est, main=' ', line = FALSE, ...)
{
xlab <- 'Empirical distribution function'
ylab <- 'Theoretical distribution function'
mu <- mu.est
sigma <- sigma.est
F <- pgumbel(x, mu, sigma)
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 Gumbel distribution
abic.gumbel <- function(x, mu.est, sigma.est)
{
mu <- mu.est
sigma <- sigma.est
n <- length(x)
p <- 2
f <- dgumbel(x, mu, sigma)
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))
}
## **************************************************************************
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