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

#### Documented in abic.lfrcrf.lfrhra.lfrks.lfrplfrpp.lfrqlfrqq.lfrrlfr

```## ***************************************************************************
## Probability density function(pdf) of LFR Distribution
dlfr <- 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 <- - ((alpha * x) + (beta * x * x) / 2)
pdf <- (alpha + (beta * x)) * exp(u)
if (log)
pdf<- log(pdf)
return(pdf)
}
## ***************************************************************************
## Cummulative distribution function(cdf) of LFR Distribution
plfr <- 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 <- - ((alpha * q) + (beta * q * q) / 2)
cdf <- 1.0 - exp(u)
if(!lower.tail)
cdf <- 1.0 - cdf
if(log.p)
cdf <- log(cdf)
return(cdf)
}
## ***************************************************************************
## Quantile function of Linear Failure Rate (LFR) Distribution
qlfr <- 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 <- (1.0/beta)*(-alpha+((alpha^2.0)-(2.0*beta)*log(1.0-p))^0.5)
if (!lower.tail)
qtl<-(1.0/beta)*(-alpha+((alpha^2.0)-(2.0*beta)*log(1.0-(1.0-p)))^0.5)
if (log.p)
qtl<- log(qtl)
return(qtl)
}
## ***************************************************************************
## Random variate generation from LFR Distribution
rlfr <- 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((1.0/beta) * (- alpha + ((alpha ^ 2.0) - (2.0 * beta)
* log(1.0 - runif(n))) ^ 0.5))
}
## ***************************************************************************
## Reliability function of Linear Failure Rate (LFR) Distribution
slfr <- 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 <- - ((alpha * x) + (beta * x * x) / 2)
relia <-  exp(u)
return(relia)
}
## ***************************************************************************
## Hazard function of Linear Failure Rate (LFR) Distribution
hlfr <- 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(alpha + (beta * x))
}
## ***************************************************************************
## Hazard rate average function of LFR Distribution
hra.lfr <- function(x, alpha, beta)
{
r <- slfr(x, alpha, beta)
fra <- ((-1) * log(r)) / x
return(fra)
}
## ***************************************************************************
## Conditional Hazard rate function of Linear Failure Rate (LFR) Distribution
crf.lfr <- function(x, t=0, alpha, beta)
{
t <- t
x <- x
nume <- hlfr(x+t, alpha, beta)
deno <- hlfr(x, alpha, beta)
return(nume/deno)
}

## ***************************************************************************
## Kolmogorov-Smirnov test (One-sample) for LFR Distribution
ks.lfr <- function(x, alpha.est, beta.est,
alternative = c("less", "two.sided", "greater"), plot = FALSE, ...)
{
alpha <- alpha.est
beta <- beta.est
res<-ks.test(x,plfr, 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 <- plfr(t, alpha, beta)
lines(t, y, lwd = 2, col = 2)
}
return(res)
}
## ***************************************************************************
## Quantile-Quantile(QQ) plot for LFR Distribution
qq.lfr <- 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 <- qlfr(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 <- qlfr(0.25, alpha, beta)
y2 <- qlfr(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 LFR Distribution
pp.lfr <- function(x, alpha.est, beta.est, main=' ', line = FALSE, ...)
{
xlab<-'Empirical distribution function'
ylab<-'Theoretical distribution function'
alpha <- alpha.est
beta <- beta.est
F <- plfr(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 LFR Distribution
abic.lfr <- function(x, alpha.est, beta.est)
{
alpha <- alpha.est
beta <- beta.est
n <- length(x)
p <- 2
f <- dlfr(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.