R/pepan.R

In epandist: Statistical Functions for the Censored and Uncensored Epanechnikov Distribution

#' Cumulative distribution function (cdf) for an uncensored epanechnikov distribution
#'
#' The inverse of this function is \code{qepan}.
#'
#' @param x point on x-axis.
#' @param mu mean of distribution.
#' @param r half the range of the distribution, ie the distance from the mean to the smallest/largest value supported by the distribution. \code{r=5^.5} corresponds to a standard deviation of 1.
#' @return probability of value below \code{x} given \code{mu} and \code{r}.
#' @keywords distribution
#' @examples
#' #Probability of a value below -1.96:
#' pepan(x=-1.96,mu=0,r=5^.5)
#'
#' #Cumulative distribution function of epanechnikov distribution:
#' curve(pepan(x),col='blue',xlim=c(-2.5,2.5),yaxs='i',xaxs='i',
#' main='Cumulative distribution function',ylab='Probability')
#'
#' #Cumulative distribution function of standard normal distribution:
#' curve(pnorm(x),col='green',add=TRUE)
#'
#' #Legend
#' legend(x=-2.5,y=1,legend=c('Epanechnikov cdf','Normal cdf'),lty=c(1,1),col=c('blue','green'))


pepan <- function(x = 0, mu = 0, r = 5^0.5) {
    # Cumulative distribution function
    if (any(r <= 0)) {
        stop("Range must be strictly positive")
    }
    
    alpha <- (x - mu)/r
    
    ifelse(abs(alpha) <= 1, 1/4 * (-alpha^3 + 3 * alpha + 2), ifelse(alpha < -1, 0, 1))
    
}