eta.w.breve: Asymmetry coefficient \breve{eta}

In asymmetry.measures: Asymmetry Measures for Probability Density Functions

Description

Implements the asymmetry coefficient \breve{η} 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, …, X_n from a continuous density function f(x) and distribution function F(x), \breve{η} is defined by

\breve{η}=-\frac{∑_{i=1}^n {U_iW_i}-n\bar{U}\bar{W}}{√{(∑_{i=1}^n {U_i^2-n\bar{U^2}})(∑_{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}∑_{i=1}^n U_i, \; \bar{W}=n^{-1} ∑_{i=1}^{n} W_i.

Value

Returns a scalar, the estimate of \breve{η}.

Author(s)

Dimitrios Bagkavos and Lucia Gamez Gallardo

R implementation and documentation: Dimitrios Bagkavos <[e-mail]>, Lucia Gamez Gallardo <[e-mail]>

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.tilde,eta.w.tilde.bc

Examples

eta.w.breve(GDP.Per.head.dist.1995,Epanechnikov)
0.329707 #estimate of etabreve

  

asymmetry.measures documentation built on July 22, 2020, 9:06 a.m.