R/ExpPower.R

In reliaR: Package for some probability distributions.

## ***************************************************************************
## Probability density function(pdf) of Exponential Power (EP)  distribution
dexp.power <- 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)^alpha)
    pdf <- alpha*(lambda^alpha)* (x^(alpha-1.0))*u*exp(1.0-u)
    if(log)
        pdf <- log(pdf)
    return(pdf)
}
## ***************************************************************************
## Cummulative distribution function(cdf) of Exponential Power (EP)  distribution
pexp.power <- 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)^alpha)
     cdf <- 1.0 - exp(1.0-u)    
     if(!lower.tail)
        cdf <- 1.0 - cdf
    if(log.p)
        cdf <- log(cdf)
    return(cdf)   
}
## ***************************************************************************
## Quantile function of Exponential Power (EP) distribution
qexp.power <- 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 - log(1.0-p))) ^ (1.0/alpha))    
      if(!lower.tail)  
      qtl<- (1.0/lambda) * ((log(1.0 - log(p))) ^ (1.0/alpha))     
    if(log.p)
        qtl <- log(qtl)
    return(qtl)  
}
## ***************************************************************************
## Random variate generation from Exponential Power (EP)  distribution
rexp.power <- 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 - log(1.0-runif(n))))) ^ (1.0/alpha))
}
## ***************************************************************************
## Reliability function of Exponential Power (EP)  distribution
sexp.power <- 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)^alpha)  
    return(exp(1.0-u))   
}
## ***************************************************************************
## Hazard function of Exponential Power (EP) distribution
hexp.power <- 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)^alpha)
      return(alpha*(lambda^alpha)* (x^(alpha-1.0))* u )  
} 
## ***************************************************************************
## Hazard rate average function of Exponential Power (EP) distribution
hra.exp.power <- function(x, alpha, lambda)
{
  r<-sexp.power(x, alpha, lambda)
  return(((-1) * log(r)) / x)
}
## ***************************************************************************
## Conditional Hazard rate function of Exponential Power (EP) distribution
crf.exp.power <- function(x, t=0, alpha, lambda)
{
    t <- t
    x <- x
    nume <- hexp.power(x+t, alpha, lambda)
    deno <- hexp.power(x, alpha, lambda)
    return(nume/deno)
}
## ***************************************************************************
## Kolmogorov-Smirnov test (One-sample) for Exponential Power (EP) distribution
ks.exp.power<- function(x, alpha.est, lambda.est, 
    alternative = c("less", "two.sided", "greater"), plot = FALSE, ...)
{
    alpha <- alpha.est
    lambda <- lambda.est
    res<- ks.test(x,pexp.power, 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 <- pexp.power(t, alpha, lambda)
        lines(t, y, lwd = 2, col = 2)
    }
    return(res)
}
## ***************************************************************************
## Quantile-Quantile(QQ) plot for Exponential Power (EP) distribution
qq.exp.power <- 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 <- qexp.power(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 <- qexp.power(0.25, alpha, lambda)
        y2 <- qexp.power(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 Exponential Power (EP)  distribution
pp.exp.power<-function(x, alpha.est, lambda.est, main=' ', line = FALSE, ...)
{
    xlab <- 'Empirical distribution function'
    ylab <- 'Theoretical distribution function'
    alpha <- alpha.est
    lambda <- lambda.est
    F<-pexp.power(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 Exponential Power distribution
abic.exp.power <-function(x, alpha.est, lambda.est)
{ 
    alpha <- alpha.est
    lambda <- lambda.est
    n <- length(x)
    p <- 2
    f <- dexp.power(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))
}
## ***************************************************************************