poweRlaw (version 0.20.3)

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 = 1e+05, pars = NULL, no_of_sims = 100, threads = 1)
bootstrap_p(m, xmins = 1e+05, pars = NULL, no_of_sims = 100,
  threads = 1)
get_KS_statistic(m)
estimate_xmin(m, xmins = 1e+05, pars = NULL)

Details

When estimating xmin for discrete distributions, the search space when comparing the data-cdf (empirical cdf) and the distribution_cdf runs from 1 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 or explicitly give values of where to search. If a single value is used in xmins, this will be used as the maximum search space value. If length(xmins) > 1, this will explicitly define the search space.

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)