R/Gompertz.R

In reliaR: Package for some probability distributions.

## **************************************************************************
## Probability density function(pdf) of Gompertz Distribution
dgompertz <- 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(theta) <= 0) || (x <= 0))    
        stop("Invalid arguments")
    u <- x * alpha
    pdf <- theta * exp(u) * exp((theta / alpha) * (1.0 - exp(u)))
    if (log) 
        pdf <- log(pdf)
    return(pdf)   
}
## ***************************************************************************
## Cummulative distribution function(cdf) of Gompertz Distribution
pgompertz <- 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(theta) <= 0) || (q <= 0))    
        stop("Invalid arguments")
    u <- q * alpha
    cdf <- 1.0 - exp((theta / alpha) * (1.0 - exp(u)))                   
    if (!lower.tail) 
        cdf <- 1.0 - cdf 
    if (log.p) 
        cdf <- log(cdf)    
    return(cdf)   
}
## ***************************************************************************
## Quantile function of Gompertz Distribution
qgompertz <- 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(theta) <= 0) || (p <= 0) || (p > 1))
        stop("Invalid arguments")
    qtl <- (1.0/alpha) * log(1.0 - (alpha/theta) * log(1.0 - p))      
    if (!lower.tail) 
        qtl<- (1.0/alpha) * log(1.0 - (alpha/theta) * log(p))      
    if (log.p) 
        qtl<- log(qtl)    
    return(qtl)   
}
## ***************************************************************************
## Random variate generation from Gompertz Distribution
rgompertz <- function(n, alpha, theta)
{
    if((!is.numeric(alpha)) || (!is.numeric(theta)) || (!is.numeric(n)))
        stop("non-numeric argument to mathematical function")
    if((min(theta) <= 0) || (n <= 0))    
        stop("Invalid arguments")
    return((1.0/alpha) * log(1.0 - (alpha/theta) * log(1.0 - runif(n))))  
}
## *************************************************************************** 
## Reliability function of Gompertz Distribution
sgompertz <- function (x, alpha, theta)
{
    if((!is.numeric(alpha)) || (!is.numeric(theta)) || (!is.numeric(x)))
        stop("non-numeric argument to mathematical function")
    if((min(theta) <= 0) || (x <= 0))    
        stop("Invalid arguments")
    u <- x * alpha                
    return(exp((theta /alpha) * (1.0 - exp(u))))   
}
## ***************************************************************************
## Hazard function of Gompertz Distribution
hgompertz <- function (x, alpha, theta)
{
    if((!is.numeric(alpha)) || (!is.numeric(theta)) || (!is.numeric(x)))
        stop("non-numeric argument to mathematical function")
    if((min(theta) <= 0) || (x <= 0))    
        stop("Invalid arguments")                 
    return(theta * exp(x * alpha))   
} 
## ***************************************************************************
## Hazard rate average function of Gompertz Distribution
hra.gompertz <- function(x, alpha, theta)
{
    r <- sgompertz(x, alpha, theta)
    fra <-((-1) * log(r)) / x
    return(fra)
}
## ***************************************************************************
## Conditional Hazard rate function of Gompertz Distribution
crf.gompertz <- function(x, t=0, alpha, theta)
{
    t <- t
    x <- x
    nume <- hgompertz(x+t, alpha, theta)
    deno <- hgompertz(x, alpha, theta)
    return(nume/deno)
  }
## ***************************************************************************
## Kolmogorov-Smirnov test (One-sample)for Gompertz Distribution
ks.gompertz <- function(x, alpha.est, theta.est, 
                alternative = c("less","two.sided","greater"), plot = FALSE, ...)
{
    alpha <- alpha.est
    theta <- theta.est
    main <- 'Empirical and Theoretical distribution functions'
    res <- ks.test(x, pgompertz, 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 <- pgompertz(t, alpha, theta)
        lines(t, y, lwd = 2, col = 2)
    }
    return(res)
} 
## ***************************************************************************
## Quantile-Quantile(QQ) plot for Gompertz Distribution
qq.gompertz <- 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 <- qgompertz(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 <- qgompertz(0.25, alpha, theta)
        y2 <- qgompertz(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 Gompertz Distribution
pp.gompertz <- function(x, alpha.est, theta.est, main=' ', line = FALSE, ...)
{
    xlab <- 'Empirical distribution function'
    ylab <- 'Theoretical distribution function'
    alpha <- alpha.est
    theta <- theta.est
    F <- pgompertz(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 Gompertz Distribution
abic.gompertz <- function(x, alpha.est, theta.est)
{ 
    alpha <- alpha.est
    theta <- theta.est
    n <- length(x)
    p <- 2
    f <- dgompertz(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))
  }  
## ***********************************************************************