Nothing
## ***************************************************************************
## Probability density function(pdf) of Loglog(Pham) Distribution
dloglog <- function (x, alpha, lambda, log = FALSE)
{
if((!is.numeric(alpha)) || (!is.numeric(lambda)) || (!is.numeric(x)))
stop("non-numeric argument to mathematical function")
if((min(alpha) <= 0) || (min(lambda) <= 0) || (x <= 0))
stop("Invalid arguments")
u <- (x ^alpha)
pdf<-exp(log(alpha) + log(log(lambda))+(alpha-1) *log(x)+log(lambda)* u + 1- lambda^u)
if(log)
pdf <- log(pdf)
return(pdf)
}
## ***************************************************************************
## Cummulative distribution function(cdf) of Loglog Distribution
ploglog <- function (q, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
{
if((!is.numeric(alpha)) || (!is.numeric(lambda)) || (!is.numeric(q)))
stop("non-numeric argument to mathematical function")
if((min(alpha) <= 0) || (min(lambda) <= 0) || (q <= 0))
stop("Invalid arguments")
u <- (q ^alpha)
cdf<- 1.0 - exp(1.0 - (lambda^u))
if(!lower.tail)
cdf <- 1.0 - cdf
if(log.p)
cdf <- log(cdf)
return(cdf)
}
## ***************************************************************************
## Quantile function of Loglog Distribution distribution
qloglog <- function (p, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
{
if((!is.numeric(alpha)) || (!is.numeric(lambda)) || (!is.numeric(p)))
stop("non-numeric argument to mathematical function")
if((min(alpha) <= 0) || (min(lambda) <= 0) || (p <= 0) || (p > 1))
stop("Invalid arguments")
tmp<- log(1.0-p)
qtl<- ((log(1.0 - tmp))/log(lambda))^ (1.0/alpha)
if (!lower.tail)
{
tmp<- log(p)
qtl<- ((log(1.0 - tmp))/log(lambda))^ (1.0/alpha)
}
if (log.p)
qtl<- log(qtl)
return(qtl)
}
## ***************************************************************************
## Random variate generation from Loglog Distribution
rloglog <- function(n, alpha, lambda)
{
if((!is.numeric(alpha)) || (!is.numeric(lambda)) || (!is.numeric(n)))
stop("non-numeric argument to mathematical function")
if((min(alpha) <= 0) || (min(lambda) <= 0) || (n <= 0))
stop("Invalid arguments")
return(-(1.0/lambda) * log(1.0 - (runif(n) ^ (1/alpha))))
}
## ***************************************************************************
## Reliability function of Loglog Distribution
sloglog <- function (x, alpha, lambda)
{
if((!is.numeric(alpha)) || (!is.numeric(lambda)) || (!is.numeric(x)))
stop("non-numeric argument to mathematical function")
if((min(alpha) <= 0) || (min(lambda) <= 0) || (x <= 0))
stop("Invalid arguments")
u <- (x ^alpha)
return(exp(1.0 - (lambda^u)))
}
## ***************************************************************************
## Hazard function of Loglog Distribution
hloglog <- function (x, alpha, lambda)
{
if((!is.numeric(alpha)) || (!is.numeric(lambda)) || (!is.numeric(x)))
stop("non-numeric argument to mathematical function")
if((min(alpha) <= 0) || (min(lambda) <= 0) || (x <= 0))
stop("Invalid arguments")
u <- (x ^alpha)
hazard <- exp(log(alpha)+log(log(lambda))+(alpha-1.0)*log(x)+ u *log(lambda))
return(hazard)
}
## ***************************************************************************
## Hazard rate average function of Loglog Distribution
hra.loglog <- function(x, alpha, lambda)
{
r <- sloglog(x, alpha, lambda)
return(((-1)*log(r))/x)
}
## ***************************************************************************
## Conditional Hazard rate function of Loglog Distribution
crf.loglog <- function(x, t=0, alpha, lambda)
{
t <- t
x <- x
nume <- hloglog(x+t, alpha, lambda)
deno <- hloglog(x, alpha, lambda)
return(nume/deno)
}
## ***************************************************************************
## Kolmogorov-Smirnov test (One-sample) for Loglog Distribution
ks.loglog <-function(x, alpha.est, lambda.est,
alternative=c("less", "two.sided","greater"), plot = FALSE, ...)
{
alpha<-alpha.est
lambda<-lambda.est
res<-ks.test(x, ploglog, alpha, lambda, 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 <- ploglog(t, alpha, lambda)
lines(t, y, lwd = 2, col = 2)
}
return(res)
}
## ***************************************************************************
## Quantile-Quantile(QQ) plot for Loglog Distribution
qq.loglog <- function(x, alpha.est, lambda.est, main=' ', line.qt = FALSE, ...)
{
xlab <- 'Empirical quantiles'
ylab <- 'Theoretical quantiles'
alpha <- alpha.est
lambda <- lambda.est
n <- length(x)
k <- seq(1, n, by = 1)
P <- (k - 0.5) / n
limx <- c(min(x), max(x))
Finv <- qloglog(P, alpha, lambda)
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 <- qloglog(0.25, alpha, lambda)
y2 <- qloglog(0.75, alpha, lambda)
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 Loglog Distribution
pp.loglog <- function(x, alpha.est, lambda.est, main = ' ', line = FALSE, ...)
{
xlab <- 'Empirical distribution function'
ylab <- 'Theoretical distribution function'
alpha <- alpha.est
lambda <- lambda.est
F <- ploglog(x, alpha,lambda)
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 Loglog Distribution
abic.loglog <- function(x, alpha.est, lambda.est)
{
alpha <- alpha.est
lambda <- lambda.est
n <- length(x)
p <- 2
f <- dloglog(x, alpha, lambda)
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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