R/BurrX.R

In reliaR: Package for some probability distributions.

## ****************************************************************************
## Probability density function(pdf) of Burr X (Generalized Rayleigh)distribution
dburrX <- 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(2*(log(lambda)+log(x)))
    pdf <- exp(log(2)+log(alpha) + 2*log(lambda)+log(x) -u 
               +(alpha -1.0)* log(1.0 - exp(-u)))       
    if (log)  
        pdf <- log(pdf)
    return(pdf)   
}
## ****************************************************************************
## Cummulative distribution function(cdf) of Burr X distribution
pburrX <- 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(2*(log(lambda)+log(q)))
    cdf <- ((1.0 - exp(-u)) ^ alpha)   
    if(!lower.tail)
        cdf <- 1.0 - cdf
    if(log.p)
        cdf <- log(cdf)
    return(cdf)   
}
## ****************************************************************************
## Quantile function of Burr X distribution
qburrX <- 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/alpha)))) ^ 0.5)    
    if (!lower.tail) 
        qtl<- (1.0/lambda) * ((-log(1.0 - ((1.0 -p)^(1.0/alpha)))) ^ 0.5)    
    if (log.p) 
        qtl<- log(qtl)    
    return(qtl)   
}
## ****************************************************************************
## Random variate generation from Burr X distribution
rburrX<-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")
    return((1.0/lambda) * ((-log(1.0 - (runif(n)^(1.0/alpha)))) ^ 0.5))
}
## **************************************************************************** 
## Reliability function of Burr X distribution
sburrX <- 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(2 * (log(lambda) + log(x)))     
    return(1.0 - ((1.0 - exp(-u))^ alpha))   
}
## ****************************************************************************
## Hazard function of Burr X distribution
hburrX <- 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( 2 * (log(lambda) + log(x)))
    num <- exp(log(2)+log(alpha) + 2*log(lambda)+log(x) - u +(alpha -1.0)* log(1.0 - exp(-u)))    
    den <-  1.0 - ((1.0 - exp(-u))^ alpha)        
    return(num/den)   
} 
## ****************************************************************************
## Hazard rate average function of Burr X distribution
hra.burrX <-function(x, alpha, lambda)
{
    r <- sburrX(x, alpha, lambda)
    fra <- ((-1) * log(r)) / x
    return(fra)
}
## *************************************************************************
# Conditional Hazard rate function of Burr X distribution
crf.burrX <-function(x, t=0, alpha, lambda)
{
    t <- t
    x <- x
    nume <- hburrX(x+t, alpha, lambda)
    deno <- hburrX(x, alpha, lambda)
    return(nume/deno)
}
## ****************************************************************************
## Kolmogorov-Smirnov test (One-sample)for Burr X distribution
ks.burrX <- function(x, alpha.est, lambda.est,
                   alternative = c("less", "two.sided", "greater"), plot = FALSE, ...)
{
    alpha <- alpha.est
    lambda <- lambda.est
    res <- ks.test(x, pburrX, 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 <- pburrX(t, alpha, lambda)
        lines(t, y, lwd = 2, col = 2)
    }
    return(res)
}
## ****************************************************************************
## Quantile-Quantile(QQ) plot for Burr X distribution
qq.burrX <- 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 <- qburrX(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 <- qburrX(0.25, alpha, lambda)
        y2 <- qburrX(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 Burr X distribution
pp.burrX <- function(x, alpha.est, lambda.est, main = ' ', line = FALSE, ...)
{
    xlab <- 'Empirical distribution function'
    ylab <- 'Theoretical distribution function'
    alpha <- alpha.est
    lambda <- lambda.est
    F <- pburrX(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)  and
## Bayesian information criterion (BIC) for Burr X distribution
abic.burrX <- function(x, alpha.est, lambda.est)
{ 
    alpha <- alpha.est
    lambda <- lambda.est
    n <- length(x)
    p <- 2
    f <- dburrX(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))
}
## **************************************************************************