CondMomsChi2 {MGBT}

Conditional Moments: N.B. Moments employ only observations above Xsi

Description

Compute the \chi^2-conditional moments (Chi-squared distributed moments) based on only those (n - r) observations above a threshold X_{si} for a sample size of n and r number of truncated observations. The first moment is (gtmoms(xsi,2) - gtmoms(xsi,1)^2) that is in the first returned column. The second moment (variance of S-squared) is V(n,r,pnorm(xsi))[2,2] that is in the second returned column. Further mathematical details are available under functions gtmoms and V.

Usage

CondMomsChi2(n, r, xsi)

Arguments

n

The number of observations;

r

The number of truncated observations; and

xsi

The lower threshold (see gtmoms).

Value

The value a two-column, one-row R matrix.

Note

TAC sources define a CondMomsZ function along with this function. However, the CondMomsZ function appears to not be used for any purpose. Only the CondMomsChi2 is needed for the MGBT test.

Author(s)

W.H. Asquith consulting T.A. Cohn sources

Source

LowOutliers_jfe(R).txt, LowOutliers_wha(R).txt, P3_089(R).txt—Named CondMomsChi2

References

Cohn, T.A., 2013–2016, Personal communication of original R source code: U.S. Geological Survey, Reston, Va.

See Also

CondMomsZ, gtmoms

Examples

CondMomsChi2(58, 2, -3.561143)
#          [,1]       [,2]
#[1,] 0.9974947 0.03574786

# Note that CondMomsChi2(58, 2, -3.561143)[2] == V(58, 2, pnorm(-3.561143))[2,2]