Description Usage Arguments Details Value Author(s) References See Also Examples
Implements the asymmetry coefficient \hat{η} of Patil, Patil and Bagkavos (2012)
1 | eta.w.hat.bc(xin, kfun)
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xin |
A vector of data points - the available sample. |
kfun |
The kernel to use in the density estimate. |
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
.
Returns a scalar, the estimate of \hat{η}.
Dimitrios Bagkavos and Lucia Gamez Gallardo
R implementation and documentation: Dimitrios Bagkavos <dimitrios.bagkavos@gmail.com>, Lucia Gamez Gallardo <gamezgallardolucia@gmail.com>
eta.w.hat, eta.w.breve, eta.w.breve.bc, eta.w.tilde,eta.w.tilde.bc
1 2 3 | eta.w.hat.bc(GDP.Per.head.dist.1995,Epanechnikov)
0.3463025 #estimate of etahat.bc
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