asymmetry.measures (version 0.2)

eta.w.tilde.bc: Asymmetry coefficient $\tilde{\eta }$ using boundary correction

Description

Implements the asymmetry coefficient $\tilde{\eta }$ of Patil, Patil and Bagkavos (2012).

Usage

eta.w.tilde.bc(xin, kfun)

Arguments

xin

A vector of data points - the available sample.

kfun

The kernel to use in the density estimate.

Value

Returns a scalar, the estimate of $\tilde{\eta }$.

Details

Given a sample $X_1,X_2,\dots ,X_n$ from a continuous density function $f(x)$ and distribution function $F(x)$, $\tilde{\eta }$ is defined by $$\tilde{\eta }=-\frac{\sum _{i=1}^n{U}_i{V}_i-(n/2)\overline{U}}{\sqrt{(n/12)(\sum _{i=1}^n{U}_i^2-n\overline{U^2})}}$$

where $$U_i=\hat{f}(X_i),V_i=F(X_i),\overline{U}=n^{-1}\sum _{i=1}^n{U}_i,\overline{V}=n^{-1}\sum _{i=1}^n{V}_i.$$

eta.w.tilde.bc uses reflection to correct the boundary bias of kde.

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

Examples

# NOT RUN {
eta.w.tilde.bc(GDP.Per.head.dist.1995,Epanechnikov)
0.3333485 #estimate of etatile.bc
  
# }