Nothing
## **************************************************************************
## Probability density function(pdf) of Marshall-Olkin Extended Exponential(MOEE) distribution
dmoee <- 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 <- exp(log(lambda) + log(x))
pdf <- exp(log(alpha) + log(lambda) - u - 2 * log(1.0 - (1.0-alpha) * exp(-u)))
if (log)
pdf <- log(pdf)
return(pdf)
}
## **************************************************************************
## Cummulative distribution function(cdf) of Marshall-Olkin Extended Exponential(MOEE) distribution
pmoee <- 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 <- exp(log(lambda) + log(q))
cdf <- exp(log(1.0 - exp(-u)) - log(1.0 - (1.0-alpha) * exp(-u)))
if (!lower.tail)
cdf <- 1.0 - cdf
if (log.p)
cdf <- log(cdf)
return(cdf)
}
## **************************************************************************
## Quantile function of Marshall-Olkin Extended Exponential(MOEE) distribution
qmoee <- 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")
qtl <- (1.0/lambda) * log(1.0 + (alpha * p / (1.0 - p)))
if (!lower.tail)
qtl <- (1.0 / lambda) * log(1.0 + (alpha * (1 - p) / p))
if (log.p)
qtl <- log(qtl)
return(qtl)
}
## **************************************************************************
## Random variate generation from Marshall-Olkin Extended Exponential(MOEE) distribution
rmoee <- 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 / lambda) * log((alpha / runif(n))+ (1.0 - alpha)))
}
## **************************************************************************
## Reliability function of Marshall-Olkin Extended Exponential(MOEE) distribution
smoee <- 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 <- exp(log(lambda) + log(x))
cdf <- exp(log(1.0 - exp(-u)) - log(1.0 - (1.0-alpha) * exp(-u)))
return(1.0 - cdf)
}
## **************************************************************************
## Hazard function of Marshall-Olkin Extended Exponential(MOEE) distribution
hmoee <- 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 <- exp(log(lambda) + log(x))
num <- exp(log(alpha) + log(lambda) -u - 2 * log(1.0 - (1.0-alpha) * exp(-u)))
den <- 1.0 - exp(log(1.0 - exp(-u)) - log(1.0 - (1.0-alpha) * exp(-u)))
return(num/den)
}
## **************************************************************************
## Hazard rate average function of Marshall-Olkin Extended Exponential(MOEE) distribution
hra.moee <- function(x, alpha, lambda)
{
return(-pmoee(x, alpha, lambda, lower.tail = FALSE, log.p = TRUE) / x)
}
## **************************************************************************
## Conditional Hazard rate function of Marshall-Olkin Extended Exponential(MOEE) distribution
crf.moee <- function(x, t=0, alpha, lambda)
{
t <- t
x <- x
nume <- hmoee(x+t, alpha, lambda)
deno <- hmoee(x, alpha, lambda)
return(nume/deno)
}
## **************************************************************************
## Kolmogorov-Smirnov test (One-sample)for Marshall-Olkin Extended Exponential(MOEE) distribution
ks.moee <- function(x, alpha.est, lambda.est,
alternative = c("less","two.sided", "greater"), plot = FALSE, ...)
{
alpha <- alpha.est
lambda <- lambda.est
res <- ks.test(x, pmoee, 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 <- pmoee(t, alpha, lambda)
lines(t, y, lwd = 2, col = 2)
}
return(res)
}
## **************************************************************************
## Quantile-Quantile(QQ) plot for Marshall-Olkin Extended Exponential(MOEE) distribution
qq.moee <- 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
Finv <- qmoee(P, alpha, lambda)
quantiles <- sort(x)
limx <- range(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] # first quartile Q1
x2 <- quant[4] # third quartile Q3
y1 <- qmoee(0.25, alpha, lambda)
y2 <- qmoee(0.75, alpha, lambda)
m <- ((y2-y1) / (x2-x1))
inter <- y1 - (m*x1)
abline(inter, m, col = 4, lwd = 2)
}
invisible(list(x = quantiles, y = Finv))
}
## **************************************************************************
## Probability-Probability(PP) plot for Marshall-Olkin Extended Exponential(MOEE) distribution
pp.moee <- function(x, alpha.est, lambda.est, main = ' ', line = FALSE, ...)
{
xlab <- 'Empirical distribution function'
ylab <- 'Theoretical distribution function'
alpha <- alpha.est
lambda <- lambda.est
F <- pmoee(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 Marshall-Olkin Extended Exponential(MOEE) distribution
abic.moee <- function(x, alpha.est, lambda.est) {
alpha <- alpha.est
lambda <- lambda.est
n <- length(x)
p <- 2
f <- dmoee(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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