asymmetry.measures (version 0.2)

eta.s: Strong asymmetry measure \(eta(X)\).

Description

Returns the strong asymmetry measure \(eta(X)\) of Patil, Bagkavos and Wood (2014).

Usage

eta.s(xin, dist, GridLength, p1, p2)

Arguments

xin

A vector of data points - the available sample.

dist

Character string, specifies selected distribution function.

GridLength

A non-negative number, which will be rounded up if fractional.Desired length of the sequence.

p1

A scalar. Parameter 1 (vector or object) of the selected distribution.

p2

A scalar. Parameter 2 (vector or object) of the selected distribution.

Value

Returns a scalar, the value of the strong asymmetry measure \(\eta(X)\).

Details

Implements $$\eta(X)= -0.5 sign(\rho_1)\max|\rho_p + \rho_p^*|$$ with \(1/2 \le p \le 1\).

Uses maximum likehood estimates for the unknown functionals in the definition of the measure.

References

• Patil P.N., Bagkavos D. and Wood A.T.A., (2014). A measure of asymmetry based on a new necessary and sufficient condition for symmetry, Sankhya A, 76, 123--145.

• Bagkavos D., Patil P.N., Wood A.T.A. (2016), A Numerical Study of the Power Function of a New Symmetry Test. In: Cao R., Gonzalez Manteiga W., Romo J. (eds), Nonparametric Statistics. Springer Proceedings in Mathematics and Statistics, vol 175, Springer.

See Also

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

Examples

# NOT RUN {
selected.dist <- "norm" #select norm as the distribution
m.use <- mean(GDP.Per.head.dist.2005)
sd.use<- sd(GDP.Per.head.dist.2005)
grid <- 50

s.use<- GDP.Per.head.dist.1995
eta.s(GDP.Per.head.dist.2005,selected.dist,grid,m.use,sd.use)
    
# }