gtmoms {MGBT} | R Documentation |
Moments of Observations Above the Threshold
Description
Moments of observations above the threshold (xsi
, ), which has been standardized to a zero mean and unit standard deviation. Define the standard normal hazard function as
where is the standard normal density function and
is the standard normal distribution (cumulative) function. For a truncation index,
, define the recursion formula,
for
gtmoms
as
for which and
.
Usage
gtmoms(xsi, r)
Arguments
xsi |
The lower threshold; and |
r |
The number of truncated observations. |
Value
The moments.
Note
AUTHOR TODO—Note that is it not clear in TAC documentation that is a scalar or vector quantity, and
gtmoms
is automatically vectoral in the R idioms if is. Also it is not immediately clear
is or is not one of the order statistics. Based on MGBT operation in USGS-PeakFQ output (USGS, 2014), the threshold is “known” no better in accuracy than one of the sample order statistics, so
might be written
. But this answer could be only restricted to a implementation in software and perhaps not theory. Finally, although the computations involve the standard normal distribution, the standardization form of
is not yet confirmed during the WHA porting process.
Author(s)
W.H. Asquith consulting T.A. Cohn sources
Source
LowOutliers_jfe(R).txt
, LowOutliers_wha(R).txt
, P3_089(R).txt
—Named gtmoms
References
Cohn, T.A., 2013–2016, Personal communication of original R source code: U.S. Geological Survey, Reston, Va.
U.S. Geological Survey (USGS), 2018, PeakFQ—Flood frequency analysis based on Bulletin 17B and recommendations of the Advisory Committee on Water Information (ACWI) Subcommittee on Hydrology (SOH) Hydrologic Frequency Analysis Work Group (HFAWG), version 7.2: Accessed November 29, 2018, at https://water.usgs.gov/software/PeakFQ/.
See Also
Examples
gtmoms(-3.561143, 2) # Is this a meaningful example?
#[1] 0.9974952