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Combine a fitted bivariate (copula) analysis with an M x N response surface Z = f(X, Y) to derive the annual-exceedance-probability curve of Z via the conditional-frequency law of total probability. Wraps the shared C++ CoincidentFrequencyAnalysis (which internally fits the bivariate analysis from the same marginal/copula spec).

Usage

coincident_frequency_analysis(
  marginal_x_family,
  marginal_x_data,
  marginal_x_parameters,
  marginal_y_family,
  marginal_y_data,
  marginal_y_parameters,
  x_values,
  y_values,
  response,
  number_of_bins = 50L,
  copula = "Normal",
  estimation_method = "InferenceFromMargins",
  sampler = "DEMCz",
  iterations = 3000L,
  output_length = 10000L,
  credible_level = 0.9,
  seed = 12345L,
  number_of_chains = 4L,
  thinning_interval = -1L
)

Arguments

marginal_x_family, marginal_y_family

marginal distribution family names.

marginal_x_data, marginal_y_data

numeric vectors of the marginal samples.

marginal_x_parameters, marginal_y_parameters

numeric fixed marginal parameter vectors.

x_values, y_values

numeric ascending vectors of the primary (X) / secondary (Y) ordinates.

response

numeric M x N matrix of the response surface Z[i, j] = f(x_i, y_j).

number_of_bins

number of Z output bins (default 50).

copula

copula family name (e.g. "Normal", "Clayton", "Gumbel").

estimation_method

copula estimation method (default "InferenceFromMargins").

sampler

MCMC sampler: "DEMCz" (default), "DEMCzs", "ARWMH", or "NUTS".

iterations

number of post-warmup MCMC iterations.

output_length

number of posterior samples used to build the credible band.

credible_level

credible-interval width (e.g. 0.90 for a 90% band).

seed

PRNG seed for the sampler (fixed for reproducibility).

number_of_chains

number of MCMC chains (default 4).

thinning_interval

MCMC thinning interval; -1 (default) keeps the sampler's own default.

Value

A named list: z_output_values (the Z bins), mode_curve, mean_curve, lower_ci, upper_ci (the AEP curve + credible band, one entry per Z bin).