Description Usage Arguments Details Value Note Author(s) Source References See Also Examples
Compute peta
, which is the survival probability of the t-distribution for eta =
η.
Define b_r as the inverse (quantile) of the Beta distribution for nonexceedance probability F \in (0,1) having two shape parameters (α and β) as
b_r = \mathrm{Beta}^{(-1)}(F; α, β) = \mathrm{Beta}^{(-1)}(F; r, n+1-r)\mbox{,}
for sample size n and number of truncated observations r and note that b_r \in (0,1). Next, define z_r as the Z-score for b_r
z_r = Φ^{(-1)}(b_r)\mbox{,}
where Φ^{(-1)}(\cdots) is the inverse of the standard normal distribution.
Compute the covariance matrix COV of M and S from VMS
as in COV = VMS(n, r, qmin=br)
, and from which define
λ = COV_{1,2} / COV_{2,2}\mbox{,}
which is a covariance divided by a variance, and then define
η_p = λ + η\mbox{.}
Compute the expected values of M and S from EMS
as in EMp = EMp = EMS(n, r, qmin=br)
, and from which define
μ_{Mp} = EMp_1 - λ\times EMp_2\mbox{,}
σ_{Mp} = √{COV_{1,1} - COV_{1,2}^2/COV_{2,2}}\mbox{.}
Compute the conditional moments from CondMomsChi2
as in momS2 = CondMomsChi2(n,r,zr)
, and from which define
df = 2 momS2_1^2 / momS2_2\mbox{,}
α = momS2_2 / momS2_1\mbox{,}
1 | peta(pzr, n, r, eta)
|
pzr |
The probability level of a Beta distribution having shape1 α = r and shape2 β = n+1-r; |
n |
The number of observations; |
r |
The number of truncated observations; and |
eta |
The Grubbs–Beck statistic (GB_r, see |
Currently (2019), context is lost on the preformatted note of code note below. It seems possible that the intent by WHA was to leave a trail for future revisitation of the Beta distribution and its access, which exists in native R code.
1 2 |
The probability of the eta
value.
Testing a very large streamgage dataset in Texas with GRH, shows at least one failure of the following computation was encountered for a short record streamgage numbered 08102900.
1 2 3 4 5 6 | # USGS 08102900 (data sorted, 1967--1974)
#https://nwis.waterdata.usgs.gov/nwis/peak?site_no=08102900&format=hn2
Peaks <- c(40, 45, 53, 55, 88) # in cubic feet per second (cfs)
MGBT(Peaks)
# Here is the line in peta(): SigmaMp <- sqrt(CV[1,1] - CV[1,2]^2/CV[2,2])
# *** In sqrt(CV[1, 1] - CV[1, 2]^2/CV[2, 2]) : NaNs produced
|
In implementation, a suppressWarnings()
is wrapped on the SigmaMp
. If the authors make no action in response to NaN
, then the low-outlier threshold is 53 cubic feet per second (cfs) with a p-value for 40 cfs as 0.81 and 45 cfs as 0.0. This does not seem logical. The is.finite
catch in the next line (see sources) is provisional under a naïve assumption that the negative in the square root has barely undershot. The function is immediately exited with the returned p-value set to unity. Testing indicates that this is a favorable innate trap here within the MGBT package and will avoid higher up error trapping in larger application development.
W.H. Asquith consulting T.A. Cohn source
LowOutliers_jfe(R).txt
, LowOutliers_wha(R).txt
, P3_089(R).txt
—Named peta
Cohn, T.A., 2013–2016, Personal communication of original R source code: U.S. Geological Survey, Reston, Va.
EMS
, VMS
, CondMomsChi2
, gtmoms
1 2 | peta(0.4, 58, 2, -2.3006)
#[1] 0.298834
|
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