eta.w.hat.bc {asymmetry.measures}R Documentation

Asymmetry coefficient \hat{η} using boundary correction

Description

Implements the asymmetry coefficient \hat{η} of Patil, Patil and Bagkavos (2012)

Usage

  eta.w.hat.bc(xin, kfun)

Arguments

xin

A vector of data points - the available sample.

kfun

The kernel to use in the density estimate.

Details

Given a sample X_1, X_2, …, X_n from a continuous density function f(x) and distribution function F(x), \hat{η} is defined by

\hat{η}=-\frac{∑_{i=1}^{n} {U_i V_i}-n\bar{U}\bar{V}}{√{(∑_{i=1}^n{U_i^2-n\bar{U^2}})(∑_{i=1}^n {V_i^2-n\bar{V^2}})}}

where

U_i = \hat{f}(X_i), \; V_i =\hat{F}(X_i), \; \bar{U}=n^{-1}∑_{i=1}^n U_i, \; \bar{V}=n^{-1}∑_{i=1}^n V_i.

eta.w.hat.bc uses reflection to correct the boundary bias issue of the kernel estimate kde.

Value

Returns a scalar, the estimate of \hat{η}.

Author(s)

Dimitrios Bagkavos and Lucia Gamez Gallardo

R implementation and documentation: Dimitrios Bagkavos <dimitrios.bagkavos@gmail.com>, Lucia Gamez Gallardo <gamezgallardolucia@gmail.com>

References

Patil, P.N., Patil, P.P. and Bagkavos, D., (2012), A measure of asymmetry. Stat. Papers, 53, 971-985.

See Also

eta.w.hat, eta.w.breve, eta.w.breve.bc, eta.w.tilde,eta.w.tilde.bc

Examples

eta.w.hat.bc(GDP.Per.head.dist.1995,Epanechnikov)
0.3463025 #estimate of etahat.bc
  

[Package asymmetry.measures version 0.2 Index]