cdf.cox: \insertCitecox2005;textualWData distribution estimator

In WData: Statistical Inference for Weighted Data

\insertCitecox2005;textualWData distribution estimator

Description

This function computes \insertCitecox2005;textualWData distribution estimator given a sample and the corresponding biased function.

Usage

cdf.cox(
  y,
  w = function(y) {
     ifelse(y >= 0, y, NA)
 }
)

Arguments

y	A numeric vector containing the biased sample.
w	A function representing the bias function applied to the data points. It must be evaluable and positive in each point of the sample y. By default, it is set to the length-biased function.

Details

\insertCite

cox2005;textualWData distribution estimator is expressed as

\widehat{F}_n(y) = \frac{\widehat{\mu}_w}{n}\sum_{i=1}^{n} \frac{1}{w(Y_i)} \mathbb{I}(Y_i \leq y), \quad \text{where} \quad \widehat{\mu}_w = n \left(\sum_{i=1}^{n} \frac{1}{w(Y_i)} \right)^{-1}.

Value

A function of class ecdf, inheriting from the stepfun class, and hence inheriting a knots method.

References

\insertAllCited

Examples

cdf.cox(y = shrub.data$Width)

WData documentation built on Nov. 2, 2026, 1:10 a.m.