MGBT (version 1.0.7)

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 $$H(x)=\varphi (x)/(1-\mathrm{\Phi }(x))\text{,}$$ where $\varphi (x)$ is the standard normal density function and $\mathrm{\Phi }(x)$ is the standard normal distribution (cumulative) function. For a truncation index, $r$, define the recursion formula, $\mathrm{\Psi }$ for gtmoms as $$\mathrm{\Psi }(x_{si},r)=(r-1)\mathrm{\Psi }(x_{si},r-2)+x_{si}^{r-1}H(x_{si})\text{,}$$ for which $\mathrm{\Psi }(x_{si},0)=1$ and $\mathrm{\Psi }(x_{si},1)=H(x_{si})$.

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
# }