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

#### Documented in abic.expo.logisticcrf.expo.logistichra.expo.logisticks.expo.logisticpp.expo.logisticqq.expo.logisticrexpo.logistic

```## ***************************************************************************
## Probability density function(pdf) of exponentiated Logistic distribution
dexpo.logistic <- 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 <- -(x / beta)
pdf <- exp(log(alpha) - log(beta) - (alpha + 1.0)* log(1.0 + exp(u)) + u)
if (log)
pdf <- log(pdf)
return(pdf)
}
## ***************************************************************************
## Cummulative distribution function(cdf) of exponentiated Logistic distribution
pexpo.logistic <- 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(-q / beta)
cdf <- (1 + u) ^ - alpha
if (!lower.tail)
cdf <- 1.0 - cdf
if (log.p)
cdf <- log(cdf)
return(cdf)
}
## ***************************************************************************
## Quantile function of exponentiated Logistic distribution
qexpo.logistic <- function (p, alpha, beta, lower.tail = TRUE, log.p = FALSE)
{
if((!is.numeric(alpha)) || (!is.numeric(beta)) || (!is.numeric(p)))
stop("non-numeric argument to mathematical function")
if((min(alpha) <= 0) || (min(beta) <= 0) || (p <= 0) || (p > 1))
stop("Invalid arguments")
qtl<- - beta * log(p^(-1.0/alpha) - 1.0)
if (!lower.tail)
qtl<- - beta * log((1.0-p)^(-1.0/alpha) - 1.0)
if (log.p)
qtl<- log(qtl)
return(qtl)
}
## ***************************************************************************
## Random variate generation from exponentiated Logistic distribution
rexpo.logistic <- 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")
return(- beta * log(runif(n)^(-1.0/alpha) - 1.0))
}
## ****************************************************************************
## Reliability function of exponentiated Logistic distribution
sexpo.logistic <- 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(-x / beta)
return(1.0 - ((1 + u) ^ - alpha))
}
## ****************************************************************************
## Hazard function of exponentiated Logistic distribution
hexpo.logistic <- 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(-x / beta)
num <- (alpha / beta) * u * ((1.0 + u)^ -(alpha + 1.0))
deno <- 1.0 - ((1 + u) ^ - alpha)
return(num/deno)
}
## ****************************************************************************
## Hazard rate average function of exponentiated Logistic distribution
hra.expo.logistic <- function(x, alpha, beta)
{
r <- sexpo.logistic(x, alpha, beta)
fra <- - log(r) / x
return(fra)
}
## ***************************************************************************
## Conditional Hazard rate function of exponentiated Logistic distribution
crf.expo.logistic <- function(x, t=0, alpha, beta)
{
t <- t
x <- x
nume <- hexpo.logistic(x+t, alpha, beta)
deno <- hexpo.logistic(x, alpha, beta)
return(nume/deno)
}
## ****************************************************************************
## Kolmogorov-Smirnov test (One-sample)for exponentiated Logistic distribution
ks.expo.logistic <- function(x, alpha.est, beta.est,
alternative = c("less","two.sided","greater"), plot = FALSE, ...)
{
alpha <- alpha.est
beta <- beta.est
res<-ks.test(x, pexpo.logistic, 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 <- pexpo.logistic(t, alpha, beta)
lines(t, y, lwd = 2, col = 2)
}
return(res)
}
## ****************************************************************************
## Quantile-Quantile(QQ) plot for exponentiated Logistic distribution
qq.expo.logistic <- 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 <- qexpo.logistic(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 <- qexpo.logistic(0.25, alpha, beta)
y2 <- qexpo.logistic(0.75, alpha, beta)
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 exponentiated Logistic distribution
pp.expo.logistic <- function(x, alpha.est, beta.est, main=' ', line = FALSE, ...)
{
xlab <- 'Empirical distribution function'
ylab <- 'Theoretical distribution function'
alpha <- alpha.est
beta <- beta.est
F <- pexpo.logistic(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 exponentiated Logistic distribution
abic.expo.logistic <- function(x, alpha.est, beta.est)
{
alpha <- alpha.est
beta <- beta.est
n <- length(x)
p <- 2
f <- dexpo.logistic(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.