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

#### Documented in abic.flex.weibullcrf.flex.weibullhra.flex.weibullks.flex.weibullpp.flex.weibullqflex.weibullqq.flex.weibullrflex.weibull

## ****************************************************************************
## Probability density function(pdf) of Flexible Weibull distribution
dflex.weibull <- function (x, alpha, beta, log = FALSE)
{
if((!is.numeric(alpha)) || (!is.numeric(beta)) || (!is.numeric(x)))
stop("non-numeric argument to mathematical function")
if((min(alpha) <= 0) || (min(beta) <= 0) || (x <= 0))
stop("Invalid arguments")
u <- exp((alpha * x) - (beta / x))
pdf <-(alpha + beta /(x * x)) * u * exp(-u)
if (log)
pdf<- log(pdf)
return(pdf)
}
## ****************************************************************************
## Cummulative distribution function(cdf) of flexible Weibull distribution
pflex.weibull <- function (q, alpha, beta, lower.tail = TRUE, log.p = FALSE)
{
if((!is.numeric(alpha)) || (!is.numeric(beta)) || (!is.numeric(q)))
stop("non-numeric argument to mathematical function")
if((min(alpha) <= 0) || (min(beta) <= 0) || (q <= 0))
stop("Invalid arguments")
u <- exp((alpha * q) - (beta / q))
cdf <- 1.0 - exp(-u)
if (!lower.tail)
cdf<- 1.0 - cdf
if (log.p)
cdf<- log(cdf)
return(cdf)
}
## ****************************************************************************
## Quantile function of flexible Weibull distribution
qflex.weibull <- function(p, alpha, beta, lower.tail = TRUE, log.p = FALSE)
{
if(!is.numeric(alpha) || !is.numeric(beta))
{stop("non-numeric argument to mathematical function")}
if (min(alpha) <=0 || min(beta) <=0 || p <= 0.0)
stop("Invalid arguments")
tmp <- log(-log(1.0 - p))
if (!lower.tail)
tmp <- log(-log(p))
qtl <- (1.0/(2 * alpha))* (tmp + (tmp^2.0 + (4.0 * alpha * beta))^0.5)
if (log.p)
qtl <- log(qtl)
return(qtl)
}
## ****************************************************************************
## Random variate generation from flexible Weibull distribution
rflex.weibull <- function(n, alpha, beta)
{
if((!is.numeric(alpha)) || (!is.numeric(beta)) || (!is.numeric(n)))
stop("non-numeric argument to mathematical function")
if((min(alpha) <= 0) || (min(beta) <= 0) || (n <= 0))
stop("Invalid arguments")
u <- runif(n)
tmp <- log(-log(1 - u))
return((1.0/(2 * alpha)) * (tmp + (tmp^2.0 + (4.0 * alpha * beta)) ^0.5))
}
## ****************************************************************************
## Reliability function of Burr distribution
sflex.weibull <- function (x, alpha, beta)
{
if((!is.numeric(alpha)) || (!is.numeric(beta)) || (!is.numeric(x)))
stop("non-numeric argument to mathematical function")
if((min(alpha) <= 0) || (min(beta) <= 0) || (x <= 0))
stop("Invalid arguments")
return(exp(-exp((alpha * x) - (beta / x))))
}
## ****************************************************************************
## Hazard function of flexible Weibull distribution
hflex.weibull <- function (x, alpha, beta)
{
if((!is.numeric(alpha)) || (!is.numeric(beta)) || (!is.numeric(x)))
stop("non-numeric argument to mathematical function")
if((min(alpha) <= 0) || (min(beta) <= 0) || (x <= 0))
stop("Invalid arguments")
u <- exp((alpha * x) - (beta / x))
return((alpha + (beta/(x * x))) * u )
}
## ****************************************************************************
## Hazard rate average function of flexible Weibull distribution
hra.flex.weibull <- function(x, alpha, beta)
{
r <- sflex.weibull(x, alpha, beta)
fra <-((-1) * log(r)) / x
return(fra)
}
## ****************************************************************************
## Conditional Hazard rate function of flexible Weibull distribution
crf.flex.weibull <- function(x, t=0, alpha, beta)
{
t <- t
x <- x
nume <- hflex.weibull(x+t, alpha, beta)
deno <- hflex.weibull(x, alpha, beta)
return(nume/deno)
}
## ****************************************************************************
## Kolmogorov-Smirnov test (One-sample)for flexible Weibull distribution
ks.flex.weibull <- function(x, alpha.est, beta.est,
alternative = c("less", "two.sided", "greater"), plot = FALSE, ...)
{
alpha <- alpha.est
beta <- beta.est
res <- ks.test(x, pflex.weibull, alpha, beta, 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 <- pflex.weibull(t, alpha, beta)
lines(t, y, lwd = 2, col = 2)
}
return(res)
}
## ****************************************************************************
## Quantile-Quantile(QQ) plot for flexible Weibull distribution
qq.flex.weibull <- function(x, alpha.est, beta.est, main=' ', line.qt = FALSE, ...)
{
xlab <- 'Empirical quantiles'
ylab <- 'Theoretical quantiles'
alpha <- alpha.est
beta <- beta.est
n <- length(x)
k <- seq(1, n, by = 1)
P <- (k - 0.5)/n
limx <- c(min(x), max(x))
Finv <- qflex.weibull(P, alpha, beta)
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 <- qflex.weibull(0.25, alpha, beta)
y2 <- qflex.weibull(0.75, alpha, beta)
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 flexible Weibull distribution
pp.flex.weibull <- function(x, alpha.est, beta.est, main=' ', line = FALSE, ...)
{
xlab <- 'Empirical distribution function'
ylab <- 'Theoretical distribution function'
alpha <- alpha.est
beta <- beta.est
F <- pflex.weibull(x,alpha, beta)
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 flexible Weibull distribution
abic.flex.weibull <- function(x, alpha.est, beta.est)
{
alpha <- alpha.est
beta <- beta.est
n <- length(x)
p <- 2
f <- dflex.weibull(x, alpha, beta)
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.