MGBT (version 1.0.4)

gtmoms: Moments of Observations Above the Threshold

Description

Moments of observations above the threshold (xsi, \(x_{si}\)), which has been standardized to a zero mean and unit standard deviation. Define the standard normal hazard function as $$H(x) = \phi(x) / (1 - \Phi(x))\mbox{,}$$ where \(\phi(x)\) is the standard normal density function and \(\Phi(x)\) is the standard normal distribution (cumulative) function. For a truncation index, \(r\), define the recursion formula, \(\Psi\) for gtmoms as $$\Psi(x_{si}, r) = (r-1)\Psi(x_{si}, r-2) + x_{si}^{r-1}H(x_{si})\mbox{,}$$ for which \(\Psi(x_{si}, 0) = 1\) and \(\Psi(x_{si}, 1) = H(x_{si})\).

Usage

gtmoms(xsi, r)

Arguments

xsi

The lower threshold; and

r

The number of truncated observations.

Value

The moments.

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

CondMomsChi2, gtmoms

Examples

# NOT RUN {
gtmoms(-3.561143, 2)  # Is this a meaningful example?
#[1] 0.9974952
# }