R/ksgof.R

In Dogoftest: Distributed Online Goodness-of-Fit Tests for Distributed Datasets

#' Perform the Lilliefors (Kolmogorov-Smirnov) Goodness-of-Fit Test for Normality
#'
#' @param x A numeric vector containing the sample data.
#'
#' @return
#' \item{statistic}{The value of the Lilliefors (Kolmogorov-Smirnov) test statistic.}
#' \item{p.value}{The p-value for the test.}
#' \item{method}{A character string describing the test.}
#'
#' @export
#' @importFrom stats pnorm sd
#' @examples
#' # Example usage:
#' set.seed(123)
#' x <- rnorm(100)  # Generate a sample from a normal distribution
#' result <- ksgof(x)
#' print(result)
#'
#' # Example with non-normal data:
#' y <- rexp(100)  # Generate a sample from an exponential distribution
#' result <- ksgof(y)
#' print(result)

ksgof <- function(x) {
  n <- length(x)
  mean.x <- mean(x)
  sd.x <- sd(x)
  p <- pnorm((x - mean.x) / sd.x)
  Dplus <- max(seq(1:n)/n - p)
  Dminus <- max(p - (seq(1:n) - 1)/n)
  K <- max(Dplus, Dminus)
  if (n <= 100) {
    Kd <- K
    nd <- n
  } else {
    Kd <- K * ((n/100)^0.49)
    nd <- 100
  }
  pvalue <- exp(-7.01256 * Kd^2 * (nd + 2.78019) + 2.99587 *
                  Kd * sqrt(nd + 2.78019) - 0.122119 +
                  0.974598/sqrt(nd) + 1.67997/nd)
  if (pvalue > 0.1) {
    KK <- (sqrt(n) - 0.01 + 0.85/sqrt(n)) * K
    if (KK <= 0.302) {
      pvalue <- 1
    } else if (KK <= 0.5) {
      pvalue <- 2.76773 - 19.828315 * KK + 80.709644 *
        KK^2 - 138.55152 * KK^3 + 81.218052 * KK^4
    } else if (KK <= 0.9) {
      pvalue <- -4.901232 + 40.662806 * KK - 97.490286 *
        KK^2 + 94.029866 * KK^3 - 32.355711 * KK^4
    } else if (KK <= 1.31) {
      pvalue <- 6.198765 - 19.558097 * KK + 23.186922 *
        KK^2 - 12.234627 * KK^3 + 2.423045 * KK^4
    } else {
      pvalue <- 0
    }
  }
  htest <- list(statistic = c(D = K), p.value = pvalue, method = "Lilliefors (Kolmogorov-Smirnov) normality test")
  return(htest)
}