| eta.w.breve {asymmetry.measures} | R Documentation |
Asymmetry coefficient \breve{\eta}
Description
Implements the asymmetry coefficient \breve{\eta} of Patil, Patil and Bagkavos (2012).
Usage
eta.w.breve(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.
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.bc, eta.w.tilde,eta.w.tilde.bc
Examples
eta.w.breve(GDP.Per.head.dist.1995,Epanechnikov)
0.329707 #estimate of etabreve