test_dist_cdf.R
In poweRlaw: Analysis of Heavy Tailed Distributions

test_that("Testing dist_cdf function", {

  ##Discrete power-law
  x = c(1, 1, 3)
  mt = displ$new(x); mt$setPars(2)
  expect_equal(dist_cdf(mt),
               c(0.6079, 0.6079, 0.8275),
               tol = 1e-4)

  expect_equal(dist_all_cdf(mt),
               c(0.6079, 0.7599, 0.8275),
               tol = 1e-4)

  expect_equal(dist_cdf(mt, q = 1), 0.6079, tol = 1e-4)

  mt$setXmin(2)
  expect_equal(dist_cdf(mt, 3), 0.5599, tol = 1e-4)
  expect_equal(dist_cdf(mt, c(1, 3)), c(0, 0.5599), tol = 1e-4)

  mt$setXmin(3)
  expect_equal(dist_cdf(mt), c(0, 0, 0.2813), tol = 1e-3)

  ##Discrete log-normal
  x = c(1, 1, 3)
  mt = dislnorm$new(x); mt$setPars(c(1, 1))
  cdf1 = (plnorm(1.5, 1, 1) - plnorm(0.5, 1, 1)) / (1 - plnorm(0.5, 1, 1))
  cdf2 = (plnorm(2.5, 1, 1) - plnorm(0.5, 1, 1)) / (1 - plnorm(0.5, 1, 1))
  cdf3 = (plnorm(3.5, 1, 1) - plnorm(0.5, 1, 1)) / (1 - plnorm(0.5, 1, 1))
  expect_equal(dist_cdf(mt), c(cdf1, cdf1, cdf3), tol = 1e-4)
  expect_equal(dist_all_cdf(mt), c(cdf1, cdf2, cdf3), tol = 1e-4)
  expect_equal(dist_cdf(mt, q = c(1, 3)), c(cdf1, cdf3), tol = 1e-4)

  mt$setXmin(2)
  cdf3 = (plnorm(3.5, 1, 1) - plnorm(1.5, 1, 1)) / (1 - plnorm(1.5, 1, 1))
  expect_equal(dist_cdf(mt), c(0, 0, cdf3), tol = 1e-4)
  expect_equal(dist_cdf(mt, c(1, 3)), c(0, cdf3), tol = 1e-4)

  mt$setXmin(3)
  cdf3 = cdf3 = (plnorm(3.5, 1, 1) - plnorm(2.5, 1, 1)) / (1 - plnorm(2.5, 1, 1))
  expect_equal(dist_cdf(mt), c(0, 0, cdf3), tol = 1e-4)

  ##Discrete Poisson
  x = c(1, 1, 3)
  mt = dispois$new(x); mt$setPars(1)
  cdf1 = dpois(1, 1) / (1 - dpois(0, 1))
  cdf2 = sum(dpois(1:2, 1)) / (1 - dpois(0, 1))
  cdf3 = sum(dpois(1:3, 1)) / (1 - dpois(0, 1))
  expect_equal(dist_cdf(mt), c(cdf1, cdf1, cdf3), tol = 1e-4)
  expect_equal(dist_all_cdf(mt), c(cdf1, cdf2, cdf3), tol = 1e-4)
  expect_equal(dist_cdf(mt, q = c(1, 3)), c(cdf1, cdf3), tol = 1e-4)

  mt$setXmin(2)
  cdf3 = sum(dpois(2:3, 1) / (1 - sum(dpois(0:1, 1))))
  expect_equal(dist_cdf(mt), c(0, 0, cdf3), tol = 1e-4)
  expect_equal(dist_cdf(mt, c(1, 3)), c(0, cdf3), tol = 1e-4)

  mt$setXmin(3)
  cdf3 = sum(dpois(3, 1) / (1 - sum(dpois(0:2, 1))))
  expect_equal(dist_cdf(mt), c(0, 0, cdf3), tol = 1e-4)

  ##Discrete Exp
  x = c(1, 1, 3)
  mt = disexp$new(x); mt$setPars(1)
  cdf1 = (pexp(1.5, 1, 1) - pexp(0.5, 1, 1)) / (1 - pexp(0.5, 1, 1))
  cdf2 = (pexp(2.5, 1, 1) - pexp(0.5, 1, 1)) / (1 - pexp(0.5, 1, 1))
  cdf3 = (pexp(3.5, 1, 1) - pexp(0.5, 1, 1)) / (1 - pexp(0.5, 1, 1))
  expect_equal(dist_cdf(mt), c(cdf1, cdf1, cdf3), tol = 1e-4)
  expect_equal(dist_all_cdf(mt), c(cdf1, cdf2, cdf3), tol = 1e-4)
  expect_equal(dist_cdf(mt, q = c(1, 3)), c(cdf1, cdf3), tol = 1e-4)

  mt$setXmin(2)
  cdf3 = (pexp(3.5, 1, 1) - pexp(1.5, 1, 1)) / (1 - pexp(1.5, 1, 1))
  expect_equal(dist_cdf(mt), c(0, 0, cdf3), tol = 1e-4)
  expect_equal(dist_cdf(mt, c(1, 3)), c(0, cdf3), tol = 1e-4)

  mt$setXmin(3)
  cdf3 = cdf3 = (pexp(3.5, 1, 1) - pexp(2.5, 1, 1)) / (1 - pexp(2.5, 1, 1))
  expect_equal(dist_cdf(mt), c(0, 0, cdf3), tol = 1e-4)



  ################################
  #CTN Distributions
  ################################
  ##Power law
  x = c(2, 2, 4)
  mt = conpl$new(x);
  mt$setXmin(1); mt$setPars(2)
  expect_equal(dist_cdf(mt), c(0.5, 0.5, 0.75), tol = 1e-4)
  expect_equal(dist_all_cdf(mt),
               c(0, 0.5, 2 / 3, 0.75), tol = 1e-4)
  expect_equal(dist_cdf(mt, q = c(2, 4)), c(0.5, 0.75), tol = 1e-4)

  mt$setXmin(2)
  expect_equal(dist_cdf(mt), c(0, 0, 0.5), tol = 1e-4)
  mt$setXmin(3)
  expect_equal(dist_cdf(mt), c(0, 0, 0.25), tol = 1e-4)
  expect_equal(dist_cdf(mt, c(1, 4)), c(0, 0.25), tol = 1e-4)

  ##Log normal
  x = c(2, 2, 4)
  mt = conlnorm$new(x);
  mt$setXmin(1); mt$setPars(c(1, 1))
  cdf2 = (plnorm(2, 1, 1) - plnorm(1, 1, 1)) / (1 - plnorm(1, 1, 1))
  cdf3 = (plnorm(3, 1, 1) - plnorm(1, 1, 1)) / (1 - plnorm(1, 1, 1))
  cdf4 = (plnorm(4, 1, 1) - plnorm(1, 1, 1)) / (1 - plnorm(1, 1, 1))
  expect_equal(dist_cdf(mt), c(cdf2, cdf2, cdf4), tol = 1e-4)
  expect_equal(dist_all_cdf(mt), c(0, cdf2, cdf3, cdf4), tol = 1e-4)
  expect_equal(dist_cdf(mt, q = c(2, 4)), c(cdf2, cdf4), tol = 1e-4)

  cdf4 = (plnorm(4, 1, 1) - plnorm(2, 1, 1)) / (1 - plnorm(2, 1, 1))
  mt$setXmin(2)
  expect_equal(dist_cdf(mt), c(0, 0, cdf4), tol = 1e-4)
  expect_equal(dist_cdf(mt, c(1, 4)), c(0, cdf4), tol = 1e-4)

  mt$setXmin(4)
  expect_equal(dist_cdf(mt), c(0, 0, 0), tol = 1e-8)

  ##Exponential
  x = c(2, 2, 4)
  mt = conexp$new(x);
  mt$setXmin(1); mt$setPars(c(1))
  cdf2 = (pexp(2, 1) - pexp(1, 1)) / (1 - pexp(1, 1))
  cdf3 = (pexp(3, 1) - pexp(1, 1)) / (1 - pexp(1, 1))
  cdf4 = (pexp(4, 1) - pexp(1, 1)) / (1 - pexp(1, 1))
  expect_equal(dist_cdf(mt), c(cdf2, cdf2, cdf4), tol = 1e-4)
  expect_equal(dist_all_cdf(mt), c(0, cdf2, cdf3, cdf4), tol = 1e-4)
  expect_equal(dist_cdf(mt, q = c(2, 4)), c(cdf2, cdf4), tol = 1e-4)

  cdf4 = (pexp(4, 1) - pexp(2, 1)) / (1 - pexp(2, 1))
  mt$setXmin(2)
  expect_equal(dist_cdf(mt), c(0, 0, cdf4), tol = 1e-4)
  expect_equal(dist_cdf(mt, c(0, 4)), c(0, cdf4), tol = 1e-4)

  mt$setXmin(4)
  expect_equal(dist_cdf(mt), c(0, 0, 0), tol = 1e-4)

}
)