| eta.w.hat {asymmetry.measures} | R Documentation |
Asymmetry coefficient \hat{\eta}
Description
Implements the asymmetry coefficient \hat{\eta} 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,\dots, X_n from a continuous density function f(x) and distribution function F(x), \hat{\eta} is defined by
\hat{\eta}=-\frac{\sum_{i=1}^n {U_iV_i}-n\bar{U}\bar{V}}{\sqrt{(\sum_{i=1}^n{U_i^2-n\bar{U^2}})(\sum_{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}\sum_{i=1}^n U_i, \; \bar{V}=n^{-1}\sum_{i=1}^n V_i.
Value
Returns a scalar, the estimate of \hat{\eta}.
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
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