poweRlaw (version 0.60.0)

bootstrap: Estimating the lower bound (xmin)

Description

When fitting heavy tailed distributions, sometimes it is necessary to estimate the lower threshold, xmin. The lower bound is estimated by calculating the minimising the Kolmogorov-Smirnoff statistic (as described in Clauset, Shalizi, Newman (2009)). [object Object],[object Object],[object Object],[object Object]

Usage

bootstrap(m, xmins = NULL, pars = NULL, xmax = 1e+05, no_of_sims = 100,
  threads = 1, seed = NULL, distance = "ks")
bootstrap_p(m, xmins = NULL, pars = NULL, xmax = 1e+05,
  no_of_sims = 100, threads = 1, seed = NULL, distance = "ks")
get_distance_statistic(m, xmax = 1e+05, distance = "ks")
estimate_xmin(m, xmins = NULL, pars = NULL, xmax = 1e+05,
  distance = "ks")

Details

When estimating xmin for discrete distributions, the search space when comparing the data-cdf (empirical cdf) and the distribution_cdf runs from xmin to max(x) where x is the data set. This can often be computationally brutal. In particular, when bootstrapping we generate random numbers from the power law distribution, which has a long tail.

To speed up computations for discrete distributions it is sensible to put an upper bound, i.e. xmax and/or explicitly give values of where to search, i.e. xmin.

Occassionally bootstrapping can generate strange situations. For example, all values in the simulated data set are less then xmin. In this case, the estimated distance measure will be Inf and the parameter values, NA.

There are other possible distance measures that can be calculated. The default is the Kolomogorov Smirnoff statistic (KS). This is equation 3.9 in the CSN paper. The other measure currently available is reweight, which is equation 3.11.

Examples

###################################################
# Load the data set and create distribution object#
###################################################
x = 1:10
m = displ$new(x)

###################################################
# Estimate xmin and pars                          #
###################################################
est = estimate_xmin(m)
m$setXmin(est)

###################################################
# Bootstrap examples                              #    
###################################################
bootstrap(m, no_of_sims=1, threads=1)
bootstrap_p(m, no_of_sims=1, threads=1)