| VMS | R Documentation |
Compute the covariance matrix of M and S given q_\mathrm{min}. Define the vector of four moment expectations
E_{i\in 1,2} = Ψ\bigl(Φ^{(-1)}(q_\mathrm{min}), i\bigr)\mbox{,}
where Ψ(a,b) is the gtmoms function and Φ^{(-1)} is the inverse of the standard normal distribution. Define the scalar quantity Es = EMS(n,r,qmin)[2] as the expectation of S using the EMS function, and define the scalar quantity E_s^2 = E_2 - E_1^2 as the expectation of S^2. Finally, compute the covariance matrix COV of M and S using the V function:
COV_{1,1} = V_{1,1}\mbox{,}
COV_{1,2} = COV_{2,1} = V_{1,2}/2Es\mbox{,}
COV_{2,2} = E_s^2 - (E_s)^2\mbox{.}
VMS(n, r, qmin)
n |
The number of observations; |
r |
The number of truncated observations; and |
qmin |
A nonexceedance probability threshold for X > q_\mathrm{min}. |
A 2-by-2 covariance matrix.
Because the gtmoms function is naturally vectorized and TAC sources provide no protection if qmin is a vector (see Note under EMS). For the implementation here, only the first value in qmin is used and a warning issued if it is a vector.
W.H. Asquith consulting T.A. Cohn sources
LowOutliers_jfe(R).txt, LowOutliers_wha(R).txt, P3_089(R).txt—Named VMS
Cohn, T.A., 2013–2016, Personal communication of original R source code: U.S. Geological Survey, Reston, Va.
EMS, V, gtmoms
VMS(58,2,.5) # Note that [1,1] is the same as [1,1] for Examples under V(). # [,1] [,2] #[1,] 0.006488933 0.003279548 #[2,] 0.003279548 0.004682506