eta.s.exact {asymmetry.measures}

Strong asymmetry measure eta(X).

Description

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

Usage

  eta.s.exact(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.

Details

Implements

\eta(X)= -0.5 sign(\rho_1)\max|\rho_p + \rho_p^*|

with 1/2 \le p \le 1 This version uses exact p.d.f. and c.d.f. evaluation and not estimates of the unknown functionals.

Value

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

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., 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., González 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,eta.s

Examples

selected.dist <- "norm" #select norm as the distribution
m.use <- 2
sd.use<- 2
grid <- 50
s.use<- rnorm(100)
eta.s.exact(s.use,selected.dist,grid,m.use,sd.use)  # calculate eta.s at xout