ineq.weighted.boot {wINEQ}

Weighted inequality measures with bootstrap

Description

For weighted mean and weighted total of X (or median of X) as well as for each relevant inequality measure, returns outputs from ineq.weighted and bootstrap outcomes: expected value, bias (in %), standard deviation, coefficient of variation, lower and upper bound of confidence interval.

Usage

ineq.weighted.boot(
  X,
  W = rep(1, length(X)),
  B = 100,
  AF.norm = TRUE,
  Atkinson.e = 1,
  Jenkins.alfa = 0.8,
  Entropy.e = 0.5,
  Kolm.p = 1,
  Kolm.scale = "Standardization",
  Leti.norm = T,
  AN_Y.a = 1,
  AN_Y.b = 1,
  Apouey.a = 2/(1 - length(W[!is.na(W) & !is.na(X)])),
  Apouey.b = length(W[!is.na(W) & !is.na(X)])/(length(W[!is.na(W) & !is.na(X)]) - 1),
  BL.withsqrt = FALSE,
  keepSamples = FALSE,
  keepMeasures = FALSE,
  conf.alpha = 0.05,
  calib.boot = FALSE,
  Xs = rep(1, length(X)),
  total = sum(W),
  calib.method = "truncated",
  bounds = c(low = 0, upp = 10)
)

Arguments

X

is a data vector

W

is a vector of weights

B

is a number of bootstrap samples.

AF.norm

(logical). If TRUE (default) then index is divided by its maximum possible value

Atkinson.e

is a parameter for Atkinson coefficient

Jenkins.alfa

is a parameter for Jenkins coefficient

Entropy.e

is a generalized entropy index parameter

Kolm.p

is a parameter for Kolm index

Kolm.scale

method of data standardization before computing

Leti.norm

(logical). If TRUE (default) then Leti index is divided by a maximum possible value

AN_Y.a

is a positive parameter for Abul Naga and Yalcin inequality measure

AN_Y.b

is a parameter for Abul Naga and Yalcin inequality measure

Apouey.a

is a parameter for Apouey inequality measure

Apouey.b

is a parameter for Apouey inequality measure

BL.withsqrt

if TRUE function returns index given by BL2, elsewhere by BL (default). See more in details of BL function.

keepSamples

if TRUE, it returns bootstrap samples of data (Xb) and weights (Wb)

keepMeasures

if TRUE, it returns values of all inequality measures for each bootstrap sample

conf.alpha

significance level for confidence interval

calib.boot

if FALSE, then naive bootstrap is performed, calibrated bootstrap elsewhere

Xs

matrix of calibration variables. By default it is a vector of 1's, applied if calib.boot is TRUE

total

vector of population totals. By default it is a sum of weights, applied if calib.boot is TRUE

calib.method

weights' calibration method for function calib (sampling)

bounds

vector of bounds for the g-weights used in the truncated and logit methods; 'low' is the smallest value and 'upp' is the largest value

Details

By default, naive bootstrap is performed, that is no weights calibration is conducted. You can choose calibrated bootstrap to calibrate weights with respect to provided variables (Xs) and totals (total). Confidence interval is simply derived with quantile of order \alpha and 1-\alpha where \alpha is a significance level for confidence interval.

Value

This functions returns a data frame from ineq.weighted extended with bootstrap results: expected value, bias (in %), standard deviation, coefficient of variation, lower and upper bound of confidence interval. If keepSamples=TRUE or keepMeasures==TRUE then the output becomes a list. If keepSamples=TRUE, the functions returns Xb and Wb, which are the samples of vector data and the samples of weights, respectively. If keepMeasures==TRUE, the functions returns Mb, which is a set of inequality measures from bootstrapping.

Examples

# Inequality measures with additional statistics for numeric variable
X=1:10
W=1:10
ineq.weighted.boot(X,W,B=10)

# Inequality measures with additional statistics for ordered factor variable
X=factor(c('H','H','M','M','L','L'),levels = c('L','M','H'),ordered = TRUE)
W=c(2,2,3,3,8,8)
ineq.weighted.boot(X,W,B=10)