R/LogisExp.R In reliaR: Package for some probability distributions.

Documented in abic.logis.expcrf.logis.expdlogis.exphlogis.exphra.logis.expks.logis.expplogis.exppp.logis.expqlogis.expqq.logis.exprlogis.expslogis.exp

```## *************************************************************************
## Probability density function(pdf) of Logistic-Exponential distribution
dlogis.exp <- 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(lambda * x)
num <- lambda * alpha * u * ((u - 1.0)^(alpha -1.0))
deno <- (1.0 + (u - 1.0) ^ alpha) ^ 2.0
pdf <- num/deno
if(log)
pdf <- log(pdf)
return(pdf)
}
## *************************************************************************
## Cummulative distribution function(cdf) of Logistic-Exponential distribution
plogis.exp <- 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(lambda * q)
tmp <- 1.0 + ((u - 1.0) ^ alpha)
cdf <- 1.0 - (1.0/tmp)
if(!lower.tail)
cdf <- 1.0 - cdf
if(log.p)
cdf <- log(cdf)
return(cdf)
}
## *************************************************************************
## Quantile function of Logistic-Exponential distribution
qlogis.exp <- 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 +((p/(1.0-p)) ^ (1.0/alpha)))
if (!lower.tail)
qtl <- (1.0/lambda) * log(1.0 +(((1.0-p)/p) ^ (1.0/alpha)))
if (log.p)
qtl <- log(qtl)
return(qtl)
}
## *************************************************************************
## Random variate generation from Logistic-Exponential distribution
rlogis.exp<-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((1.0/lambda) * log(1.0 +((u/(1.0-u)) ^ (1.0/alpha))))
}
## *************************************************************************
## Reliability function of Logistic-Exponential distribution
slogis.exp <- 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(lambda * x)
tmp <-1.0 +((u - 1.0)^alpha)
relia <- 1.0/tmp
return(relia)
}
## *************************************************************************
## Hazard function of Logistic-Exponential distribution
hlogis.exp <- 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(lambda * x)
nume <- lambda * alpha * u * ((u - 1.0)^(alpha -1.0))
deno <- 1.0 + (u - 1.0) ^ alpha
return(nume/deno)
}
## *************************************************************************
## Hazard rate average function of Logistic-Exponential distribution
hra.logis.exp <- function(x, alpha, lambda)
{
r <- slogis.exp(x, alpha, lambda)
fra <- ((-1) * log(r))/x
return(fra)
}
## *************************************************************************
## Conditional Hazard rate function of Logistic-Exponential distribution
crf.logis.exp <-function(x, t=0, alpha, lambda)
{
t <- t
x <- x
nume <- hlogis.exp(x+t, alpha, lambda)
deno <- hlogis.exp(x, alpha, lambda)
return(nume/deno)
}
## *************************************************************************
## Kolmogorov-Smirnov test (One-sample)for Logistic-Exponential distribution
ks.logis.exp <- function(x, alpha.est, lambda.est,
alternative = c("less", "two.sided", "greater"), plot = FALSE, ...)
{
alpha <- alpha.est
lambda <- lambda.est
res <- ks.test(x, plogis.exp, 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 <- plogis.exp(t, alpha, lambda)
lines(t, y, lwd = 2, col = 2)
}
return(res)
}
## *************************************************************************
## Quantile-Quantile(QQ) plot for Logistic-Exponential distribution
qq.logis.exp <- 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
limx <- c(min(x),  max(x))
Finv <- qlogis.exp(P, alpha, lambda)
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 <- qlogis.exp(0.25, alpha, lambda)
y2 <- qlogis.exp(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 Logistic-Exponential distribution
pp.logis.exp <- function(x, alpha.est, lambda.est, main=' ', line = FALSE, ...)
{
xlab <- 'Empirical distribution function'
ylab <- 'Theoretical distribution function'
alpha <- alpha.est
lambda <- lambda.est
F <- plogis.exp(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)
## Bayesian information criterion (BIC)
## for Logistic-Exponential distribution
abic.logis.exp<-function(x, alpha.est, lambda.est)
{
alpha <- alpha.est
lambda <- lambda.est
n <- length(x)
p <- 2
f <- dlogis.exp(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 29, 2017, 12:34 p.m.