R/norm_HD.R

In bayespm: Bayesian Statistical Process Monitoring

# HPRD - Normal likelihood ; Mean unknown
norm_HD <- function( cover = NULL, mu = NULL, sdv = NULL, plot = FALSE, xlab = "x",
                     ylab = "Density" ){



  # 'cover' (i) missing (ii) non-numeric (iii) out of the range (0,1)
  if ( is.null(cover) ) {
    stop("'cover' has not been defined")
  } else {
    if ( length(unlist(cover))>1 ) { message("More than one value for 'cover', the first one will only be used")
      if ( !is.numeric(cover[1]) | cover<=0 | cover>=1 ) { stop("Invalid 'cover' value") } else { cover <- cover[1] }
    } else { if ( !is.numeric(cover) | cover<=0 | cover>=1 ) { stop("Invalid 'cover' value") } }
  }

  # mu input (i) more than one value for parameters (ii) non-numeric input
  if ( is.null(mu) ) {
    stop("'mu' has not been defined")
  } else {
    if ( length(unlist(mu))>1 ) { message("More than one value for 'mu', the first one will only be used")
      if ( !is.numeric(mu) ) { stop("Invalid 'mu' value") } else { mu <- mu[1] }
    } else { if ( !is.numeric(mu)  ) { stop("Invalid 'mu' value") } }
  }

  # Likelihood sd input (i) more than one value for parameters (ii) non-numeric input (iii) non-positive
  if ( is.null(sdv) ) {
    stop("'sdv' has not been defined")
  } else {
    if ( length(unlist(sdv))>1 ) { message("More than one value for 'sdv', the first one will only be used")
      if ( !is.numeric(sdv) | sdv<=0 ) { stop("Invalid 'sdv' value") } else { sdv <- sdv[1] }
    } else { if ( !is.numeric(sdv) | sdv<=0 ) { stop("Invalid 'sdv' value") } }
  }


  # Calculation of the HD region
  far <- 1-cover
  ed <- c( qnorm( far/2, mu, sdv ), qnorm( 1-far/2, mu, sdv ) )

  if (plot==T) {

    # Graphical parameters for the range and the plotted region
    range <- ed[2] - ed[1]
    xi <- seq( ed[1] - 0.15*range, ed[2] + 0.15*range, length.out = 1e4 )
    yi <- dnorm( xi, mean = mu, sd = sdv )

    # Graphical parameters for the main of the plot
    percov <- 100*cover
    ed1 <- round( ed[1], 2 )
    ed2 <- round( ed[2], 2 )

    plot( xi, yi, xlim = c( 0.978*min(xi), 1.025*max(xi) ), ylim = c( 0, 1.05*max(yi) ), type = "l",
          xlab = xlab, ylab = ylab, main = bquote("Normal: "~.(percov)*"% HD = ["*.(ed1)*", "~ .(ed2)*"]" ), axes = F,  lwd = 2)

    # Green vertical segments on the bounds of the HD region
    segments( ed[1], 0, ed[1], dnorm( ed[1], mean = mu, sd = sdv), lwd = 3, col = "green" )
    segments( ed[2], 0, ed[2], dnorm( ed[2], mean = mu, sd = sdv), lwd = 3, col = "green" )

    axis(1) ; axis(2)

    # Adding the light green area in the graph
    xi2 <- seq( ed[1], ed[2], length.out = 1e4 )
    polygon( c(xi2, rev(xi2)), c( dnorm(xi2, mean = mu, sd = sdv), rep( 0, 1e4 ) ), col = rgb(0, 1, 0, 0.3), border = NA )

  }

  # The data frame of the output
  RES <- data.frame( lower.bound = ed[1], upper.bound = ed[2], coverage = cover )

  return(RES)
}