R/def_displ.R

In poweRlaw: Analysis of Heavy Tailed Distributions

#############################################################
#Reference Class definition
#############################################################
#' Heavy-tailed distributions
#'
#' The \pkg{poweRlaw} package supports a number of distributions:
#' \describe{
#' \item{displ}{Discrete power-law}
#' \item{dislnorm}{Discrete log-normal}
#' \item{dispois}{Discrete Poisson}
#' \item{disexp}{Discrete Exponential}
#' \item{conpl}{Continuous power-law}
#' \item{conlnorm}{Continuous log-normal}
#' \item{conexp}{Continuous exponential}}
#' Each object inherits the \code{discrete_distribution} or the \code{ctn_distribution} class.
#'
#' @section Fields:
#'
#' Each distribution object has four fields. However, the object
#' is typically created by passing
#' data, to the \code{dat} field. Each field has standard
#' setters and getters. See examples below
#' \describe{
#' \item{dat}{The data set.}
#' \item{xmin}{The lower threshold, xmin. Typically set after initialisation.
#' For the continuous  power-law, xmin >= 0 for the discrete
#' distributions, xmin >0}
#' \item{pars}{A parameter vector. Typically set after initialisation.
#' Note the lognormal distribution has two parameters.}
#' \item{internal}{A list. This list differs between objects and shouldn't be altered.}}
#' @param ... The object is typically created by passing
#' data using the \code{dat} field.
#' Each field has standard setters and getters.
#'
#' @section Copying objects:
#' Distribution objects are reference classes. This means that when we copy
#' objects, we need to use the \code{copy} method, i.e. \code{obj$copy()}.
#' See the examples below for further details.
#'
#' @return a reference object
#' @rdname displ
#' @aliases displ-class displ
#' @docType class
#' @aliases conpl
#' @importFrom pracma zeta
#' @exportClass displ
#' @export displ
#' @examples
#' ##############################################################
#' #Load data and create distribution object                    #
#' ##############################################################
#' data(moby)
#' m = displ$new(moby)
#'
#' ##############################################################
#' #Xmin is initially the smallest x value                      #
#' ##############################################################
#' m$getXmin()
#' m$getPars()
#'
#' ##############################################################
#' #Set Xmin and parameter                                      #
#' ##############################################################
#' m$setXmin(2)
#' m$setPars(2)
#'
#'
#' ##############################################################
#' #Plot the data and fitted distribution                       #
#' ##############################################################
#' plot(m)
#' lines(m)
#' ##############################################################
#' #Copying                                                     #
#' ##############################################################
#' ## Shallow copy
#' m_cpy = m
#' m_cpy$setXmin(5)
#' m$getXmin()
#' ## Instead
#' m_cpy = m$copy()
displ =
  setRefClass("displ",
              contains = "discrete_distribution",
              fields = list(
                dat = function(x) {
                  if (!missing(x) && !is.null(x)) {
                    check_discrete_data(x)
                    x = sort(x)
                    tab = table(x)
                    values = as.numeric(names(tab))
                    freq = as.vector(tab)
                    internal[["freq"]] <<- freq
                    internal[["values"]] <<- values
                    internal[["cum_slx"]] <<-
                      rev(cumsum(log(rev(values)) * rev(freq)))
                    internal[["cum_n"]] <<- rev(cumsum(rev(freq)))
                    internal[["dat"]] <<- x
                    xmin <<- min(values)
                  } else internal[["dat"]]
                },
                xmin = function(x) {
                  if (!missing(x) && !is.null(x)) {
                    if ("estimate_xmin" %in% class(x)) {
                      pars <<- x$pars
                      x = x$xmin
                    }
                    internal[["xmin"]] <<- x
                    internal[["v"]] <<- 1:(x - 1) # Not sure why I need this???
                    ##Check for empty data or xmin = NA (happens when data is all equal)
                    if (length(internal[["values"]]) && !is.na(x)) {
                      selection = min(which(internal[["values"]] >= x))
                      internal[["slx"]] <<- internal[["cum_slx"]][selection]
                      internal[["n"]] <<- internal[["cum_n"]][selection]
                    }
                  } else  internal[["xmin"]]
                },
                pars = function(x) {
                  if (!missing(x) && !is.null(x)) {
                    if ("estimate_pars" %in% class(x)) x = x$pars
                    internal[["pars"]] <<- x
                    internal[["constant"]] <<- zeta(x)
                  } else internal[["pars"]]
                }
              ))

#############################################################
#Initialisation
#############################################################
displ$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[["freq"]] <<- freq
        internal[["values"]] <<- values
        internal[["cum_slx"]] <<-
          rev(cumsum(log(rev(values)) * rev(freq)))
        internal[["cum_n"]] <<- rev(cumsum(rev(freq)))
        internal[["dat"]] <<- x
        xmin <<- min(values)
      }
    }
  )
)

#############################################################
#PDF method
#############################################################
#' @rdname dist_pdf-methods
#' @aliases dist_pdf,displ-method
setMethod("dist_pdf",
          signature = signature(m = "displ"),
          definition = function(m, q = NULL, log = FALSE) {
            xmin = m$getXmin(); pars = m$getPars()
            if (is.null(q)) q = m$dat
            q = q[q >= m$xmin]
            pdf = dpldis(q[q >= m$xmin], m$xmin, m$pars, TRUE)
            if (!log) pdf = exp(pdf)
            pdf
          }
)
#############################################################
#CDF method
#############################################################
#' @rdname dist_cdf-methods
#' @aliases dist_cdf,displ-method
setMethod("dist_cdf",
          signature = signature(m = "displ"),
          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
            ppldis(q, xmin, pars, lower_tail)
          }
)

#' @rdname dist_cdf-methods
#' @aliases dist_all_cdf,displ-method
setMethod("dist_all_cdf",
          signature = signature(m = "displ"),
          definition = function(m, lower_tail = TRUE, xmax = 1e5) {

            xmin = m$getXmin(); pars = m$getPars()
            if (is.null(pars)) stop("Model parameters not set.")

            inter = m$internal
            xmax = max(m$dat[m$dat <= xmax])
            v = ifelse(xmin == 1, 0, sum((1:(xmin - 1))^-pars))
            cumsum((((xmin:xmax) ^ -pars)) / (inter[["constant"]] - v))
          }
)

#############################################################
#ll method
#############################################################
#' @rdname dist_ll-methods
#' @aliases dist_ll,displ-method
setMethod("dist_ll",
          signature = signature(m = "displ"),
          definition = function(m) {
            inter = m$internal
            con = inter[["constant"]]
            if (m$xmin > 2)
              con = con -
              colSums(vapply(m$pars,
                             function(i) inter[["v"]] ^ (-i), double(m$xmin - 1)))
            else if (m$xmin > 1)
              con = con - 1

            log_con = log(con)
            ll = -inter[["n"]] * log_con - inter[["slx"]] * m$pars
            ll[is.nan(log_con)] = -Inf
            ll
          }
)
########################################################
#Log-likelihood
########################################################
dis_pl_ll = function(x, pars, xmin) {
  n = length(x)
  joint_prob = colSums(sapply(pars,
                              function(i) dpldis(x, xmin, i, log = TRUE)))
  #   ##Normalise due to xmax
  prob_over = 0
  return(joint_prob - n * prob_over)
}

########################################################
#Rand number generator
########################################################
#' @rdname dist_rand-methods
#' @aliases dist_rand,displ-method
setMethod("dist_rand",
          signature = signature(m = "displ"),
          definition = function(m, n = "numeric") {
            rpldis(n, m$xmin, m$pars)
          }
)

#############################################################
#MLE method
#############################################################
displ$methods(
  mle = function(set = TRUE, initialise = NULL) {
    n = internal[["n"]]

    if (is.null(initialise)) {
      slx = internal[["slx"]]
      theta_0 = 1 + n * sum(slx - log(xmin - 1 / 2) * n) ^ (-1)
    } else {
      theta_0 = initialise
    }

    x = dat[dat > (xmin - 0.5)]
    negloglike = function(par) {
      r = -dis_pl_ll(x, par, xmin)
      if (!is.finite(r)) r = 1e12
      r
    }

    mle = suppressWarnings(optim(par = theta_0, fn = negloglike,
                                 method = "L-BFGS-B", lower = 1))

    if (set)  pars <<- mle$par
    class(mle) = "estimate_pars"
    names(mle)[1L] = "pars"
    mle
  }
)