Lorenz curve — pipgd_lorenz

Returns the Lorenz curve. User provides the cumulative welfare and cumulative weight, as well as the number of points on the lorenz curve required. By default, the best fitting Lorenz parameterization (quadratic or beta) is selected.

Usage

pipgd_lorenz_curve(
  params = NULL,
  welfare = NULL,
  weight = NULL,
  mean = 1,
  times_mean = 1,
  popshare = NULL,
  povline = ifelse(is.null(popshare), mean * times_mean, NA_real_),
  complete = getOption("pipster.return_complete"),
  lorenz = NULL,
  n_bins = 100
)

Arguments

params: list of parameters from pipgd_validate_lorenz()
welfare: numeric vector of cumulative share of welfare (income/consumption)
weight: numeric vector of cumulative share of the population
mean: numeric scalar of distribution mean. Default is 1
times_mean: numeric factor that multiplies the mean to create a relative poverty line. Default is 1
popshare: numeric: range (0,1). Share of population. Provide share of population instead of poverty line
povline: numeric: value of poverty line. Default is the mean value
complete: logical: If TRUE, returns a list a cumulative returns from previously used get_gd functions. Default is FALSE
lorenz: character or NULL. Lorenz curve selected. It could be "lq" for Lorenz Quadratic or "lb" for Lorenz Beta
n_bins: atomic double vector of length 1: number of points on the lorenz curve

Value

Returns a list which contains:

numeric lorenz curve,
corresponding points on x-axis,
whether lq or lb parameterization, and
if complete=TRUE, also returns all params.

Examples

# Example 1: Generating a Lorenz Curve with default settings
pipgd_lorenz_curve(welfare = pip_gd$L,
                   weight = pip_gd$P)
#> $lorenz_curve
#> $lorenz_curve$output
#>   [1] 0.000000000 0.003286780 0.006735991 0.010341921 0.014099338 0.018003439
#>   [7] 0.022049809 0.026234377 0.030553393 0.035003389 0.039581162 0.044283744
#>  [13] 0.049108392 0.054052559 0.059113890 0.064290199 0.069579464 0.074979810
#>  [19] 0.080489502 0.086106939 0.091830640 0.097659242 0.103591492 0.109626241
#>  [25] 0.115762440 0.121999134 0.128335458 0.134770637 0.141303978 0.147934869
#>  [31] 0.154662779 0.161487251 0.168407907 0.175424439 0.182536613 0.189744269
#>  [37] 0.197047313 0.204445726 0.211939559 0.219528932 0.227214038 0.234995141
#>  [43] 0.242872579 0.250846764 0.258918183 0.267087401 0.275355065 0.283721901
#>  [49] 0.292188723 0.300756433 0.309426025 0.318198590 0.327075321 0.336057517
#>  [55] 0.345146589 0.354344068 0.363651612 0.373071013 0.382604208 0.392253285
#>  [61] 0.402020503 0.411908294 0.421919287 0.432056318 0.442322452 0.452721002
#>  [67] 0.463255550 0.473929981 0.484748506 0.495715698 0.506836539 0.518116455
#>  [73] 0.529561380 0.541177812 0.552972888 0.564954470 0.577131250 0.589512865
#>  [79] 0.602110052 0.614934816 0.628000656 0.641322826 0.654918667 0.668808034
#>  [85] 0.683013823 0.697562671 0.712485868 0.727820580 0.743611525 0.759913326
#>  [91] 0.776793891 0.794339470 0.812662487 0.831914312 0.852307416 0.874157041
#>  [97] 0.897968756 0.924654900 0.956235231 1.000000000
#> 
#> $lorenz_curve$points
#>   [1] 0.00000000 0.01010101 0.02020202 0.03030303 0.04040404 0.05050505
#>   [7] 0.06060606 0.07070707 0.08080808 0.09090909 0.10101010 0.11111111
#>  [13] 0.12121212 0.13131313 0.14141414 0.15151515 0.16161616 0.17171717
#>  [19] 0.18181818 0.19191919 0.20202020 0.21212121 0.22222222 0.23232323
#>  [25] 0.24242424 0.25252525 0.26262626 0.27272727 0.28282828 0.29292929
#>  [31] 0.30303030 0.31313131 0.32323232 0.33333333 0.34343434 0.35353535
#>  [37] 0.36363636 0.37373737 0.38383838 0.39393939 0.40404040 0.41414141
#>  [43] 0.42424242 0.43434343 0.44444444 0.45454545 0.46464646 0.47474747
#>  [49] 0.48484848 0.49494949 0.50505051 0.51515152 0.52525253 0.53535354
#>  [55] 0.54545455 0.55555556 0.56565657 0.57575758 0.58585859 0.59595960
#>  [61] 0.60606061 0.61616162 0.62626263 0.63636364 0.64646465 0.65656566
#>  [67] 0.66666667 0.67676768 0.68686869 0.69696970 0.70707071 0.71717172
#>  [73] 0.72727273 0.73737374 0.74747475 0.75757576 0.76767677 0.77777778
#>  [79] 0.78787879 0.79797980 0.80808081 0.81818182 0.82828283 0.83838384
#>  [85] 0.84848485 0.85858586 0.86868687 0.87878788 0.88888889 0.89898990
#>  [91] 0.90909091 0.91919192 0.92929293 0.93939394 0.94949495 0.95959596
#>  [97] 0.96969697 0.97979798 0.98989899 1.00000000
#> 
#> $lorenz_curve$lorenz
#> [1] "lq"
#> 
#> 

# Example 2: Specifying the number of bins for the Lorenz Curve
pipgd_lorenz_curve(welfare = pip_gd$L,
                   weight = pip_gd$P,
                   n_bins = 50)
#> $lorenz_curve
#> $lorenz_curve$output
#>  [1] 0.000000000 0.006808033 0.014255849 0.022302075 0.030911793 0.040055347
#>  [7] 0.049707427 0.059846372 0.070453613 0.081513244 0.093011673 0.104937348
#> [13] 0.117280536 0.130033146 0.143188589 0.156741666 0.170688490 0.185026418
#> [19] 0.199754014 0.214871027 0.230378386 0.246278213 0.262573861 0.279269957
#> [25] 0.296372487 0.313888885 0.331828163 0.350201075 0.369020310 0.388300749
#> [31] 0.408059777 0.428317676 0.449098123 0.470428821 0.492342315 0.514877054
#> [37] 0.538078796 0.562002505 0.586714954 0.612298402 0.638855924 0.666519417
#> [43] 0.695462132 0.725919329 0.758224630 0.792879765 0.830705384 0.873231159
#> [49] 0.924071589 1.000000000
#> 
#> $lorenz_curve$points
#>  [1] 0.00000000 0.02040816 0.04081633 0.06122449 0.08163265 0.10204082
#>  [7] 0.12244898 0.14285714 0.16326531 0.18367347 0.20408163 0.22448980
#> [13] 0.24489796 0.26530612 0.28571429 0.30612245 0.32653061 0.34693878
#> [19] 0.36734694 0.38775510 0.40816327 0.42857143 0.44897959 0.46938776
#> [25] 0.48979592 0.51020408 0.53061224 0.55102041 0.57142857 0.59183673
#> [31] 0.61224490 0.63265306 0.65306122 0.67346939 0.69387755 0.71428571
#> [37] 0.73469388 0.75510204 0.77551020 0.79591837 0.81632653 0.83673469
#> [43] 0.85714286 0.87755102 0.89795918 0.91836735 0.93877551 0.95918367
#> [49] 0.97959184 1.00000000
#> 
#> $lorenz_curve$lorenz
#> [1] "lq"
#> 
#> 

# Example 3: Using pre-calculated parameters
use_params <- pipgd_params(welfare = pip_gd$L,
                           weight = pip_gd$P)
pipgd_lorenz_curve(params = use_params)
#> $lorenz_curve
#> $lorenz_curve$output
#>   [1] 0.000000000 0.003286780 0.006735991 0.010341921 0.014099338 0.018003439
#>   [7] 0.022049809 0.026234377 0.030553393 0.035003389 0.039581162 0.044283744
#>  [13] 0.049108392 0.054052559 0.059113890 0.064290199 0.069579464 0.074979810
#>  [19] 0.080489502 0.086106939 0.091830640 0.097659242 0.103591492 0.109626241
#>  [25] 0.115762440 0.121999134 0.128335458 0.134770637 0.141303978 0.147934869
#>  [31] 0.154662779 0.161487251 0.168407907 0.175424439 0.182536613 0.189744269
#>  [37] 0.197047313 0.204445726 0.211939559 0.219528932 0.227214038 0.234995141
#>  [43] 0.242872579 0.250846764 0.258918183 0.267087401 0.275355065 0.283721901
#>  [49] 0.292188723 0.300756433 0.309426025 0.318198590 0.327075321 0.336057517
#>  [55] 0.345146589 0.354344068 0.363651612 0.373071013 0.382604208 0.392253285
#>  [61] 0.402020503 0.411908294 0.421919287 0.432056318 0.442322452 0.452721002
#>  [67] 0.463255550 0.473929981 0.484748506 0.495715698 0.506836539 0.518116455
#>  [73] 0.529561380 0.541177812 0.552972888 0.564954470 0.577131250 0.589512865
#>  [79] 0.602110052 0.614934816 0.628000656 0.641322826 0.654918667 0.668808034
#>  [85] 0.683013823 0.697562671 0.712485868 0.727820580 0.743611525 0.759913326
#>  [91] 0.776793891 0.794339470 0.812662487 0.831914312 0.852307416 0.874157041
#>  [97] 0.897968756 0.924654900 0.956235231 1.000000000
#> 
#> $lorenz_curve$points
#>   [1] 0.00000000 0.01010101 0.02020202 0.03030303 0.04040404 0.05050505
#>   [7] 0.06060606 0.07070707 0.08080808 0.09090909 0.10101010 0.11111111
#>  [13] 0.12121212 0.13131313 0.14141414 0.15151515 0.16161616 0.17171717
#>  [19] 0.18181818 0.19191919 0.20202020 0.21212121 0.22222222 0.23232323
#>  [25] 0.24242424 0.25252525 0.26262626 0.27272727 0.28282828 0.29292929
#>  [31] 0.30303030 0.31313131 0.32323232 0.33333333 0.34343434 0.35353535
#>  [37] 0.36363636 0.37373737 0.38383838 0.39393939 0.40404040 0.41414141
#>  [43] 0.42424242 0.43434343 0.44444444 0.45454545 0.46464646 0.47474747
#>  [49] 0.48484848 0.49494949 0.50505051 0.51515152 0.52525253 0.53535354
#>  [55] 0.54545455 0.55555556 0.56565657 0.57575758 0.58585859 0.59595960
#>  [61] 0.60606061 0.61616162 0.62626263 0.63636364 0.64646465 0.65656566
#>  [67] 0.66666667 0.67676768 0.68686869 0.69696970 0.70707071 0.71717172
#>  [73] 0.72727273 0.73737374 0.74747475 0.75757576 0.76767677 0.77777778
#>  [79] 0.78787879 0.79797980 0.80808081 0.81818182 0.82828283 0.83838384
#>  [85] 0.84848485 0.85858586 0.86868687 0.87878788 0.88888889 0.89898990
#>  [91] 0.90909091 0.91919192 0.92929293 0.93939394 0.94949495 0.95959596
#>  [97] 0.96969697 0.97979798 0.98989899 1.00000000
#> 
#> $lorenz_curve$lorenz
#> [1] "lq"
#> 
#> 


# Example 4: Generating Lorenz Curve with a specific Lorenz model(e.g. Lorenz beta)
pipgd_lorenz_curve(params = use_params,
                   lorenz = "lb")
#> $lorenz_curve
#> $lorenz_curve$output
#>   [1] 0.000000000 0.002359208 0.005529581 0.009030258 0.012766584 0.016694612
#>   [7] 0.020788888 0.025032840 0.029414865 0.033926425 0.038561009 0.043313520
#>  [13] 0.048179882 0.053156792 0.058241540 0.063431882 0.068725953 0.074122193
#>  [19] 0.079619304 0.085216200 0.090911983 0.096705914 0.102597394 0.108585948
#>  [25] 0.114671213 0.120852923 0.127130905 0.133505068 0.139975397 0.146541950
#>  [31] 0.153204853 0.159964294 0.166820523 0.173773849 0.180824638 0.187973311
#>  [37] 0.195220344 0.202566265 0.210011658 0.217557159 0.225203457 0.232951296
#>  [43] 0.240801475 0.248754849 0.256812330 0.264974888 0.273243555 0.281619425
#>  [49] 0.290103658 0.298697483 0.307402198 0.316219176 0.325149871 0.334195817
#>  [55] 0.343358638 0.352640049 0.362041866 0.371566009 0.381214512 0.390989529
#>  [61] 0.400893345 0.410928383 0.421097220 0.431402595 0.441847427 0.452434826
#>  [67] 0.463168118 0.474050857 0.485086857 0.496280210 0.507635324 0.519156952
#>  [73] 0.530850234 0.542720746 0.554774551 0.567018266 0.579459137 0.592105126
#>  [79] 0.604965026 0.618048584 0.631366666 0.644931449 0.658756669 0.672857922
#>  [85] 0.687253062 0.701962704 0.717010891 0.732425994 0.748241930 0.764499898
#>  [91] 0.781250867 0.798559334 0.816509188 0.835213413 0.854831234 0.875601306
#>  [97] 0.897914640 0.922509170 0.951207864 1.000000000
#> 
#> $lorenz_curve$points
#>   [1] 0.00000000 0.01010101 0.02020202 0.03030303 0.04040404 0.05050505
#>   [7] 0.06060606 0.07070707 0.08080808 0.09090909 0.10101010 0.11111111
#>  [13] 0.12121212 0.13131313 0.14141414 0.15151515 0.16161616 0.17171717
#>  [19] 0.18181818 0.19191919 0.20202020 0.21212121 0.22222222 0.23232323
#>  [25] 0.24242424 0.25252525 0.26262626 0.27272727 0.28282828 0.29292929
#>  [31] 0.30303030 0.31313131 0.32323232 0.33333333 0.34343434 0.35353535
#>  [37] 0.36363636 0.37373737 0.38383838 0.39393939 0.40404040 0.41414141
#>  [43] 0.42424242 0.43434343 0.44444444 0.45454545 0.46464646 0.47474747
#>  [49] 0.48484848 0.49494949 0.50505051 0.51515152 0.52525253 0.53535354
#>  [55] 0.54545455 0.55555556 0.56565657 0.57575758 0.58585859 0.59595960
#>  [61] 0.60606061 0.61616162 0.62626263 0.63636364 0.64646465 0.65656566
#>  [67] 0.66666667 0.67676768 0.68686869 0.69696970 0.70707071 0.71717172
#>  [73] 0.72727273 0.73737374 0.74747475 0.75757576 0.76767677 0.77777778
#>  [79] 0.78787879 0.79797980 0.80808081 0.81818182 0.82828283 0.83838384
#>  [85] 0.84848485 0.85858586 0.86868687 0.87878788 0.88888889 0.89898990
#>  [91] 0.90909091 0.91919192 0.92929293 0.93939394 0.94949495 0.95959596
#>  [97] 0.96969697 0.97979798 0.98989899 1.00000000
#> 
#> $lorenz_curve$lorenz
#> [1] "lb"
#> 
#>