# R/MOEW.R In reliaR: Package for some probability distributions.

#### Documented in abic.moewcrf.moewhra.moewks.moewpp.moewqq.moewrmoew

```## ***************************************************************************
## Probability density function(pdf) of Marshall-Olkin Extended Weibull(MOEW) distribution
dmoew <- 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)
num <- alpha * lambda * (x^(alpha-1.0))* exp(u)
deno <- (1.0 - (1.0-lambda)*exp(u))^ 2.0
pdf <- num/deno
if(log)
pdf<- log(pdf)
return(pdf)
}
## ***************************************************************************
## Cummulative distribution function(cdf) of Marshall-Olkin Extended Weibull(MOEW) distribution
pmoew <- 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(u))/(1.0-(1.0-lambda)*exp(u))
if(!lower.tail)
cdf <- 1.0 - cdf
if(log.p)
cdf <- log(cdf)
return(cdf)
}
## ***************************************************************************
## Quantile function of Marshall-Olkin Extended Weibull(MOEW) distribution
qmoew <- 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<- (log(1.0 + ((lambda*p)/(1.0-p))))^(1.0/alpha)
if(!lower.tail)
qtl<- (log(1.0 + ((lambda*(1.0-p))/p)))^(1.0/alpha)
if(log.p)
qtl<- log(qtl)
return(qtl)
}
## ***************************************************************************
## Random variate generation from Marshall-Olkin Extended Weibull(MOEW) distribution
rmoew <- 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")
u <- runif(n)
return(log(1.0 + ((lambda*u)/(1.0-u)))^(1.0/alpha))
}
## ***************************************************************************
## Reliability function of Marshall-Olkin Extended Weibull(MOEW) distribution
smoew <- 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(1.0-(1.0 - exp(u))/(1.0-(1.0-lambda)*exp(u)))
}
## ***************************************************************************
## Hazard function of Marshall-Olkin Extended Weibull(MOEW) distribution
hmoew <- 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(alpha * (x^(alpha-1.0))/(1.0 - (1.0-lambda)*exp(u)))
}
## ***************************************************************************
## Hazard rate average function of Marshall-Olkin Extended Weibull(MOEW) distribution
hra.moew <- function(x, alpha, lambda)
{
r <- smoew(x, alpha, lambda)
fra <-((-1)*log(r))/x
return(fra)
}
## ***************************************************************************
## Conditional Hazard rate function of Marshall-Olkin Extended Weibull(MOEW) distribution
crf.moew <- function(x, t=0, alpha, lambda)
{
t <- t
x <- x
nume<-hmoew(x+t, alpha, lambda)
deno<-hmoew(x, alpha, lambda)
return(nume/deno)
}
## ***************************************************************************
## Kolmogorov-Smirnov test (One-sample)for Marshall-Olkin Extended Weibull(MOEW) distribution
ks.moew <-function(x, alpha.est, lambda.est,
alternative = c("less", "two.sided", "greater"), plot = FALSE, ...)
{
alpha <- alpha.est
lambda <- lambda.est
res <- ks.test(x, pmoew, 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 <- pmoew(t, alpha, lambda)
lines(t, y, lwd = 2, col = 2)
}
return(res)
}
## ***************************************************************************
## Quantile-Quantile(QQ) plot for Marshall-Olkin Extended Weibull(MOEW) distribution
qq.moew <- 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 <-qmoew(P, alpha, lambda)
quantiles <-sort(x)
limx<-c(min(x), max(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 <- qmoew(0.25, alpha, lambda)
y2 <- qmoew(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 Marshall-Olkin Extended Weibull(MOEW) distribution
pp.moew <- function(x, alpha.est, lambda.est, main=' ',line=FALSE, ...)
{
xlab <- 'Empirical distribution function'
ylab <- 'Theoretical distribution function'
alpha <- alpha.est
lambda <- lambda.est
F <- pmoew(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
# Schwartz information criterion (BIC) for Marshall-Olkin Extended Weibull distribution
abic.moew <- function(x, alpha.est,lambda.est){
alpha <- alpha.est
lambda <- lambda.est
n <- length(x)
p <- 2
f <- dmoew(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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reliaR documentation built on May 1, 2019, 9:51 p.m.