Joint_RP_2D: Calculates joint return periods
In rjaneUCF/MultiHazard: Tools for modeling compound events

Joint_RP_2D

R Documentation

Calculates joint return periods

Description

Calculates joint return periods via simulation. A large number of realizations are simulated from the copulas fit to the conditioned samples, in proportion with the sizes of the conditional samples. The realizations are transformed to the original scale and the relevant probabilities estimated empirically.

Usage

Joint_RP_2D(
  Data,
  Data_Con1,
  Data_Con2,
  u1,
  u2,
  Thres1 = NA,
  Thres2 = NA,
  Copula_Family1,
  Copula_Family2,
  Marginal_Dist1,
  Marginal_Dist2,
  Con1 = "Rainfall",
  Con2 = "OsWL",
  mu = 365.25,
  Var1 = NA,
  Var2 = NA,
  x_lab = "Rainfall (mm)",
  y_lab = "O-sWL (mNGVD 29)",
  x_lim_min = NA,
  x_lim_max = NA,
  y_lim_min = NA,
  y_lim_max = NA,
  DecP = 2,
  N
)

Arguments

`Data`	Data frame of dimension `nx2` containing two co-occurring time series of length `n`.
`Data_Con1`	Data frame containing the conditional sample (declustered excesses paired with concurrent values of other variable), conditioned on the variable in the first column.
`Data_Con2`	Data frame containing the conditional sample (declustered excesses paired with concurrent values of other variable), conditioned on the variable in the second column. Can be obtained using the `Con_Sampling_2D` function.
`u1`	Numeric vector of length one specifying the (quantile) threshold above which the variable in the first column was sampled in Data_Con1.
`u2`	Numeric vector of length one specifying the (quantile) threshold above which the variable in the second column was sampled in Data_Con2.
`Thres1`	Numeric vector of length one specifying the threshold above which the variable in the first column was sampled in Data_Con1. Only one of `u1` and `Thres1` should be supplied. Default is `NA`.
`Thres2`	Numeric vector of length one specifying the threshold above which the variable in the second column was sampled in Data_Con2. Only one of `u2` and `Thres2` should be supplied. Default is `NA`.
`Copula_Family1`	Numeric vector of length one specifying the copula family used to model the `Data_Con1` dataset.
`Copula_Family2`	Numeric vector of length one specifying the copula family used to model the `Data_Con2` dataset. Best fitting of 40 copulas can be found using the `Copula_Threshold_2D` function.
`Marginal_Dist1`	Character vector of length one specifying (non-extreme) distribution used to model the marginal distribution of the non-conditioned variable in `Data_Con1`.
`Marginal_Dist2`	Character vector of length one specifying (non-extreme) distribution used to model the marginal distribution of the non-conditioned variable in `Data_Con2`.
`Con1`	Character vector of length one specifying the name of variable in the first column of `Data`.
`Con2`	Character vector of length one specifying the name of variable in the second column of `Data`.
`mu`	Numeric vector of length one specifying the (average) occurrence frequency of events in `Data`. Default is `365.25`, daily data.
`x_lab`	Character vector specifying the x-axis label.
`y_lab`	Character vector specifying the y-axis label.
`x_lim_min`	Numeric vector of length one specifying x-axis minimum. Default is `NA`.
`x_lim_max`	Numeric vector of length one specifying x-axis maximum. Default is `NA`.
`y_lim_min`	Numeric vector of length one specifying y-axis minimum. Default is `NA`.
`y_lim_max`	Numeric vector of length one specifying y-axis maximum. Default is `NA`.
`DecP`	Numeric vector of length one specifying the number of decimal places to round the data in the conditional samples to in order to identify observations in both conditional samples. Default is `2`.
`N`	Numeric vector of length one specifying the size of the sample from the fitted joint distributions used to estimate the density along an isoline. Samples are collected from the two joint distribution with proportions consistent with the total number of extreme events conditioned on each variable. Default is `10^6`
`Val1`	Numeric vector specifying the values of the variable in the first column of `Data`.
`Val2`	Numeric vector specifying the values of the variable in the second column of `Data`.

Value

Console output is a vector RP_Copula of the joint return period of the specified (Var1,Var2) events according to the conditional sampling - copula theory approach.

Examples

#Joint excedence probability of a 5 inch rainfall and 2 ft O-sWL at S-22.
Joint_RP_2D(Data=S22.Detrend.df,
            Data_Con1=con.sample.Rainfall$Data, Data_Con2=con.sample.OsWL$Data,
            u1=0.98, u2=0.98,
            Copula_Family1=cop.Rainfall,Copula_Family2=cop.OsWL,
            Marginal_Dist1="Logis", Marginal_Dist2="BS",
            Con1 = "Rainfall", Con2 = "OsWL",
            mu = 365.25,
            Con_Var="Rainfall",
            RP_Con=10, RP_Non_Con=10,
            x_lab = "Rainfall (Inches)", y_lab = "O-sWL (ft NGVD 29)",
            y_lim_max = 10,
            N=10^7)

rjaneUCF/MultiHazard documentation built on April 20, 2024, 12:48 a.m.