| eta.w.breve.bc {asymmetry.measures} | R Documentation |
Asymmetry coefficient \breve{\eta} using boundary correction
Description
Implements the asymmetry coefficient \breve{\eta} of Patil, Patil and Bagkavos (2012).
Usage
eta.w.breve.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,\dots, X_n from a continuous density function f(x) and distribution function F(x). \breve{\eta} is defined by
\breve{\eta}=-\frac{\sum_{i=1}^n {U_iW_i}-n\bar{U}\bar{W}}{\sqrt{(\sum_{i=1}^n {U_i^2-n\bar{U^2}})(\sum_{i=1}^n {W_i^2-n\bar{W^2}})}}
where
U_i = \hat{f}(X_i), \; W_i =F_n(X_i), \; \bar{U}=n^{-1}\sum_{i=1}^n U_i, \; \bar{W}=n^{-1}\sum_{i=1}^n W_i.
eta.w.breve.bc uses reflection to correct the boundary bias of the kernel density estimate kde
Value
Returns a scalar, the estimate of \breve{\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.hat, eta.w.breve, eta.w.tilde,eta.w.tilde.bc
Examples
eta.w.breve.bc(GDP.Per.head.dist.1995,Epanechnikov)
0.329707 #estimate of etabreve