eta.w.hat: Asymmetry coefficient \hat{eta}

In asymmetry.measures: Asymmetry Measures for Probability Density Functions

Description

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

Usage

  eta.w.hat(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_iV_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.

Value

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

Author(s)

Dimitrios Bagkavos and Lucia Gamez Gallardo

R implementation and documentation: Dimitrios Bagkavos <[e-mail]>, Lucia Gamez Gallardo <[e-mail]>

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

Examples

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

  

asymmetry.measures documentation built on July 22, 2020, 9:06 a.m.