R/def_dislnorm.R

In poweRlaw: Analysis of Heavy Tailed Distributions

#############################################################
#Reference Class definition
#############################################################
#' @rdname displ
#' @aliases dislnorm-class dislnorm
#' @exportClass dislnorm
#' @export dislnorm
dislnorm =
  setRefClass("dislnorm",
              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
#############################################################

dislnorm$methods(
  list(
    initialize = function(dat) {
      no_pars <<- 2
      ##Use the internal attribute for copying
      if (!missing(dat)) {
        check_discrete_data(dat)
        x = sort(dat)
        tab = table(x)
        values = as.numeric(names(tab))
        freq = as.vector(tab)
        internal[["cum_n"]] <<- rev(cumsum(rev(freq)))
        internal[["freq"]] <<- freq
        internal[["values"]] <<- values
        internal[["dat"]] <<- x
        xmin <<- min(values)
      }
    }
  )
)
#############################################################
#PDF method
#############################################################
#' @rdname dist_pdf-methods
#' @aliases dist_pdf,dislnorm-method
setMethod("dist_pdf",
          signature = signature(m = "dislnorm"),
          definition = function(m, q = NULL, log = FALSE) {
            xmin = m$getXmin(); pars = m$getPars()
            if (is.null(q)) q = m$dat

            l1 = plnorm(q - 0.5, pars[1], pars[2], lower.tail = FALSE, log.p = TRUE)
            l2 = plnorm(q + 0.5, pars[1], pars[2], lower.tail = FALSE, log.p = TRUE)

            pdf = l1 + log(1 - exp(l2 - l1)) -
              plnorm(xmin - 0.5, pars[1], pars[2], 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,dislnorm-method
setMethod("dist_cdf",
          signature = signature(m = "dislnorm"),
          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

            ## lower_tail == TRUE numerical unstable
            ## Not sure how best to fix it
            if (lower_tail) {
              p = plnorm(q + 0.5, pars[1], pars[2], lower.tail = lower_tail)
              C = plnorm(xmin - 0.5, pars[1], pars[2], lower.tail = FALSE)
              cdf = (p / C - 1 / C + 1)
            } else {
              log_p = plnorm(q + 0.5, pars[1], pars[2], lower.tail = FALSE, log.p = TRUE)
              log_C = plnorm(xmin + 0.5, pars[1], pars[2], lower.tail = FALSE, log.p = TRUE)
              cdf = exp(log_p - log_C)
            }
            cdf[q < xmin] = 0
            cdf
          }
)

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

#############################################################
#ll method
#############################################################
#' @rdname dist_ll-methods
#' @aliases dist_ll,dislnorm-method
setMethod("dist_ll",
          signature = signature(m = "dislnorm"),
          definition = function(m) {
            xmin = m$getXmin()

            dv =  m$internal[["values"]]
            cut_off = (dv >= xmin)
            dv = dv[cut_off]
            df = m$internal[["freq"]][cut_off]
            dis_lnorm_tail_ll(dv, df, m$getPars(), xmin)
          }
)
########################################################
#Log-likelihood
########################################################
dis_lnorm_tail_ll = function(xv, xf, pars, xmin) {
  if (is.vector(pars)) pars = t(as.matrix(pars))
  n = sum(xf)
  p = function(par) {
    m_log = par[1]; sd_log = par[2]
    plnorm(xv - 0.5, m_log, sd_log, lower.tail = FALSE) -
      plnorm(xv + 0.5, m_log, sd_log, lower.tail = FALSE)
  }
  if (length(xv) == 1L) {
    joint_prob = sum(xf * log(apply(pars, 1, p)))
  } else {
    joint_prob = colSums(xf * log(apply(pars, 1, p)))
  }
  prob_over = apply(pars, 1, function(i)
    plnorm(xmin - 0.5, i[1], i[2],
           lower.tail = FALSE, log.p = TRUE))

  return(joint_prob - n * prob_over)
}

########################################################
#Rand number generator
########################################################
#' @rdname dist_rand-methods
#' @aliases dist_rand,dislnorm-method
setMethod("dist_rand",
          signature = signature(m = "dislnorm"),
          definition = function(m, n = "numeric") {
            xmin = m$getXmin(); pars = m$getPars()
            lower = xmin - 0.5
            rns = numeric(n)
            i = 0; N = 0
            ## n-0.5 to avoid floating point sillyness.
            while (i < (n - 0.5)) {
              ## Since we reject RNs less than lower=xmin - 0.5 we should simulate >> n rns
              ## If we simulate N Rns (below), we will keep n-i (or reject N-(n-i))
              N = ceiling((n - i) / plnorm(lower, pars[1L], pars[2L], lower.tail = FALSE))

              ## Simple rejection sampler
              x = rlnorm(N, pars[1L], pars[2L])
              x = x[x >= lower]
              if (length(x)) {
                x = x[1:min(length(x), n - i)]
                rns[(i + 1L):(i + length(x))] = x
                i = i + length(x)
              }
            }
            ##Round at end (more efficient)
            round(rns)
          }
)

#############################################################
#MLE method
#############################################################
dislnorm$methods(
  mle = function(set = TRUE, initialise = NULL) {
    xv = internal[["values"]]
    cut_off = (xv > xmin - 0.5)
    xv = xv[cut_off]
    xf = internal[["freq"]][cut_off]

    if (is.null(initialise)) {
      n = sum(xf) # XXX: cum_sum?
      x_log = log(xv)
      expect2 = sum(x_log^2 * xf) / n
      x_log_mean = sum(x_log * xf) / n
      x_log_sd = sqrt((expect2 - x_log_mean^2))
      theta_0 = c(x_log_mean, x_log_sd)
    } else {
      theta_0 = initialise
    }
    # Chop off values below
    negloglike = function(par) {
      r = -dis_lnorm_tail_ll(xv, xf, par, xmin)
      if (!is.finite(r)) r = 1e12
      r
    }

    mle = suppressWarnings(optim(par = theta_0,
                                 fn = negloglike,
                                 method = "L-BFGS-B",
                                 lower = c(-Inf, .Machine$double.eps)))
    if (set)
      pars <<- mle$par
    class(mle) = "estimate_pars"
    names(mle)[1L] = "pars"
    mle
  }
)