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

#### Documented in abic.gp.weibullcrf.gp.weibullhra.gp.weibullks.gp.weibullpp.gp.weibullqq.gp.weibullrgp.weibull

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