R/def_disexp.R

In poweRlaw: Analysis of Heavy Tailed Distributions

#############################################################
#Reference Class definition
#############################################################
#' @rdname displ
#' @aliases disexp-class disexp
#' @exportClass disexp
#' @export disexp
disexp =
  setRefClass("disexp",
              contains = "discrete_distribution",
              fields = list(
                dat = function(x) {
                  if (!missing(x) && !is.null(x)) {
                    check_discrete_data(x)
                    x = sort(x)
                    tab = table(x)
                    values = as.numeric(names(tab))
                    freq = as.vector(tab)

                    internal[["cum_n"]] <<- rev(cumsum(rev(freq)))
                    internal[["freq"]] <<- freq
                    internal[["values"]] <<- values
                    internal[["dat"]] <<- x
                    xmin <<- min(values)
                  } else {
                    internal[["dat"]]
                  }
                },
                xmin = function(x) {
                  if (!missing(x) && !is.null(x)) {
                    if ("estimate_xmin" %in% class(x)) {
                      pars <<- x$pars
                      x = x$xmin
                    }
                    internal[["xmin"]] <<- x
                    if (length(internal[["values"]])) {
                      selection = min(which(internal[["values"]] >= x))
                      internal[["n"]] <<- internal[["cum_n"]][selection]
                    }

                  } else {
                    internal[["xmin"]]
                  }
                },
                pars = function(x) {
                  if (!missing(x) && !is.null(x)) {
                    if ("estimate_pars" %in% class(x)) x = x$pars
                    internal[["pars"]] <<- x
                  } else internal[["pars"]]
                }
              ))

#############################################################
#Initialisation
#############################################################
disexp$methods(
  list(
    initialize = function(dat) {
      no_pars <<- 1
      ##Use the internal attribute for copying
      if (!missing(dat)) {
        check_discrete_data(dat)
        x = sort(dat)
        tab = table(x)
        values = as.numeric(names(tab))
        freq = as.vector(tab)

        internal[["cum_n"]] <<- rev(cumsum(rev(freq)))
        internal[["freq"]] <<- freq
        internal[["values"]] <<- values
        internal[["dat"]] <<- x
        xmin <<- min(values)
      }
    }
  )
)

#############################################################
#PDF method
#############################################################
#' @rdname dist_pdf-methods
#' @aliases dist_pdf,disexp-method
setMethod("dist_pdf",
          signature = signature(m = "disexp"),
          definition = function(m, q = NULL, log = FALSE) {
            xmin = m$getXmin()
            pars = m$getPars()
            if (is.null(q)) q = m$dat

            l1 = pexp(q - 0.5, pars, lower.tail = FALSE, log.p = TRUE)
            l2 = pexp(q + 0.5, pars, lower.tail = FALSE, log.p = TRUE)

            pdf = l1 + log(1 - exp(l2 - l1)) -
              pexp(xmin - 0.5, pars, lower.tail = FALSE, log.p = TRUE)
            if (!log) {
              pdf = exp(pdf)
              pdf[q < xmin] = 0
            } else {
              pdf[q < xmin] = -Inf
            }
            pdf
          }
)
#############################################################
#CDF method
#############################################################
#' @rdname dist_cdf-methods
#' @aliases dist_cdf,disexp-method
setMethod("dist_cdf",
          signature = signature(m = "disexp"),
          definition = function(m, q = NULL, lower_tail = TRUE) {
            xmin = m$getXmin()
            pars = m$getPars()
            if (is.null(pars)) stop("Model parameters not set.")
            if (is.null(q)) q = m$dat

            p = pexp(q + 0.5, pars, lower.tail = lower_tail)
            if (lower_tail) {
              C = pexp(xmin - 0.5, pars, lower.tail = FALSE)
              cdf = (p / C - 1 / C + 1)
            } else {
              C = 1 - pexp(xmin + 0.5, pars)
              cdf = p / C
            }
            cdf[q < xmin] = 0
            cdf
          }
)

#' @rdname dist_cdf-methods
#' @aliases dist_all_cdf,disexp-method
setMethod("dist_all_cdf",
          signature = signature(m = "disexp"),
          definition = function(m, lower_tail = TRUE, xmax = 1e5) {
            xmin = m$getXmin()
            xmax = min(max(m$dat), xmax)
            dist_cdf(m, q = xmin:xmax, lower_tail = lower_tail)
          }
)

#############################################################
#ll method
#############################################################
#' @rdname dist_ll-methods
#' @aliases dist_ll,disexp-method
setMethod("dist_ll",
          signature = signature(m = "disexp"),
          definition = function(m) {
            xmin = m$getXmin()
            d = m$getDat()
            dis_exp_tail_ll(d[d >= xmin], m$getPars(), xmin)
          }
)
########################################################
#Log-likelihood
########################################################
dis_exp_tail_ll = function(x, pars, xmin) {
  n = length(x)
  joint_prob = colSums(sapply(pars, function(i)
    log(pexp(x - 0.5, i, lower.tail = FALSE) -
          pexp(x + 0.5, i, lower.tail = FALSE))))
  prob_over = sapply(pars, function(i)
    pexp(xmin - 0.5, i, lower.tail = FALSE, log.p = TRUE))

  return(joint_prob - n * prob_over)
}

########################################################
#Rand number generator
########################################################
#' @rdname dist_rand-methods
#' @aliases dist_rand,disexp-method
setMethod("dist_rand",
          signature = signature(m = "disexp"),
          definition = function(m, n = "numeric") {
            ## Rearrange the usual formula for generating
            ## exp random numbers: -log(u)/lambda > xmin - 0.5
            u = runif(n, 0, exp(-m$pars * (m$xmin - 0.5)))
            round(-log(u) / m$pars)
          }
)

#############################################################
#MLE method
#############################################################
disexp$methods(
  mle = function(set = TRUE, initialise = NULL) {
    x = dat
    x = x[x > (xmin - 0.5)]
    if (is.null(initialise))
      theta_0 = mean(1 / x)
    else
      theta_0 = initialise
    # Chop off values below
    negloglike = function(par) {
      r = -dis_exp_tail_ll(x, par, xmin)
      if (!is.finite(r)) r = 1e12
      r
    }
    mle = suppressWarnings(optim(par = theta_0, fn = negloglike,
                                 method = "L-BFGS-B", lower = 0))
    if (set)
      pars <<- mle$par
    class(mle) = "estimate_pars"
    names(mle)[1L] = "pars"
    mle
  }
)