Probability of exceedance and return period of an annual rate

Usage

convertAEP(AEP, IT)

Arguments

AEP: Annual rates of exceedance in 1/year.
IT: Investigation time in years, finite and positive: one value or one per AEP.

Value

A data.table with POE (probability within IT) and TR (years), one row per AEP.

Mathematics

Under Poisson occurrence an annual rate $AEP$ gives, over an investigation time $IT$, the probability of at least one exceedance and the return period $$POE = 1 - e^{-IT \cdot AEP}, \qquad TR = 1/AEP .$$ The conversion is exact; it carries no dispersion.

Examples

convertAEP(AEP = 1 / unique(VancouverSpectra$TR), IT = 50)
#>            POE         TR
#>          <num>      <num>
#>  1: 0.01999735 2475.24752
#>  2: 0.02498264 1976.28458
#>  3: 0.03497377 1404.49438
#>  4: 0.05019635  970.87379
#>  5: 0.06993425  689.65517
#>  6: 0.09967548  476.19048
#>  7: 0.13972227  332.22591
#>  8: 0.19948499  224.71910
#>  9: 0.29917706  140.64698
#> 10: 0.39950442   98.03922