pub(all) suberror CopulaError {
  InvalidInput(String)
  BudgetExceeded(String)
  NumericalFailure(String)
} derive(
@moonbitlang/core/debug.Debug
Debug)

pub struct BootstrapReplicate {
  model : Copula
  log_likelihood : Double
  at_boundary : Bool
  upper_joint_probability : Double
}

pub struct BootstrapResult {
  replicates : Array[BootstrapReplicate]
  theta : SampleSummary
  upper_joint_probability : SampleSummary
  boundary_fits : Int
}

pub struct CalibrationPoint {
  threshold : Pair
  forecast : Double
  observed : RateInterval
  residual : Double
}

pub(all) struct Candidate {
  label : String
  family : Family
  rotation : Rotation
  options : FitOptions
}

pub struct Concordance {
  concordant : Int
  discordant : Int
  x_only_ties : Int
  y_only_ties : Int
  both_ties : Int
  tau_b : Double
} derive(
@moonbitlang/core/debug.Debug
Debug)

pub struct Copula {
  family : Family
  theta : Double
  rotation : Rotation
} derive(
@moonbitlang/core/debug.Debug
Debug)

pub struct EmpiricalCopula {
  // private fields
}

pub struct EmpiricalMargin {
  // private fields
}

pub(all) enum Family {
  Independence
  Clayton
  Gumbel
  Frank
} derive(
@moonbitlang/core/debug.Debug
Debug)

pub(all) struct FitOptions {
  lower : Double
  upper : Double
  tolerance : Double
  iterations : Int
}

pub struct FitResult {
  model : Copula
  log_likelihood : Double
  aic : Double
  bic : Double
  observations : Int
  evaluations : Int
  converged : Bool
  at_boundary : Bool
}

pub struct GridDiagnostic {
  points : Int
  maximum_absolute : Double
  root_mean_square : Double
  sample_scaled_mean_square : Double
}

pub struct Inversion {
  value : Double
  residual : Double
  iterations : Int
} derive(
@moonbitlang/core/debug.Debug
Debug)

pub struct JointRisk {
  lower_both : Double
  upper_both : Double
  upper_either : Double
  x_above_y_below : Double
  x_below_y_above : Double
} derive(
@moonbitlang/core/debug.Debug
Debug)

pub(all) struct Pair {
  x : Double
  y : Double
} derive(
@moonbitlang/core/debug.Debug
Debug)

pub struct RankedModel {
  label : String
  fit : FitResult
  delta_aic : Double
  weight : Double
}

pub struct RateInterval {
  successes : Int
  trials : Int
  observed : Double
  lower : Double
  upper : Double
}

pub struct RosenblattDiagnostic {
  first : UniformDiagnostic
  second : UniformDiagnostic
  residual_spearman : Double
}

pub(all) enum Rotation {
  R0
  R90
  R180
  R270
} derive(
@moonbitlang/core/debug.Debug
Debug)

pub struct SampleSummary {
  count : Int
  mean : Double
  standard_deviation : Double
  lower : Double
  median : Double
  upper : Double
}

pub struct TailDiagnostic {
  threshold : Double
  lower_joint : Double
  upper_joint : Double
  lower_coefficient : Double
  upper_coefficient : Double
  observations : Int
} derive(
@moonbitlang/core/debug.Debug
Debug)

pub(all) enum ThresholdEvent {
  LowerBoth
  UpperBoth
  UpperEither
  FirstUpperSecondLower
  FirstLowerSecondUpper
}

pub(all) enum TiePolicy {
  Midrank
  Ordinal
  RejectTies
} derive(
@moonbitlang/core/debug.Debug
Debug)

pub struct UniformDiagnostic {
  count : Int
  mean : Double
  variance : Double
  ks_distance : Double
  cramer_von_mises : Double
}

fn bootstrap_raw(family : Family, raw : Array[Pair], plans : Array[Array[Int]], threshold : Pair, rotation? : Rotation, options? : FitOptions, coverage? : Double) -> BootstrapResult raise CopulaError

fn checked_probability(x : Double) -> Double raise CopulaError

fn checkerboard_cdf(raw : Array[Pair], u : Double, v : Double) -> Double raise CopulaError

fn compare_models(candidates : Array[Candidate], data : Array[Pair]) -> Array[RankedModel] raise CopulaError

fn concordance(data : Array[Pair]) -> Concordance raise CopulaError

fn default_fit_options(family : Family) -> FitOptions

fn empirical_tails(data : Array[Pair], threshold : Double) -> TailDiagnostic raise CopulaError

fn fit(family : Family, data : Array[Pair], rotation? : Rotation, options? : FitOptions) -> FitResult raise CopulaError

fn fit_raw(family : Family, raw : Array[Pair], rotation? : Rotation) -> FitResult raise CopulaError

fn independence() -> Copula

fn probability_grid(divisions : Int) -> Array[Pair] raise CopulaError

fn pseudo_observations(data : Array[Pair], policy? : TiePolicy) -> Array[Pair] raise CopulaError

fn ranks(values : Array[Double], policy? : TiePolicy) -> Array[Double] raise CopulaError

fn resample_pairs(data : Array[Pair], indices : Array[Int]) -> Array[Pair] raise CopulaError

fn restore_margins(data : Array[Pair], x_margin : EmpiricalMargin, y_margin : EmpiricalMargin) -> Array[Pair] raise CopulaError

fn return_period(event_probability : Double, period_length : Double) -> Double? raise CopulaError

fn sample_summary(values : Array[Double], coverage? : Double) -> SampleSummary raise CopulaError

fn spearman(data : Array[Pair]) -> Double raise CopulaError

fn standard_candidates() -> Array[Candidate]

fn tie_counts(data : Array[Pair]) -> (Int, Int) raise CopulaError

fn uniform_diagnostic(values : Array[Double]) -> UniformDiagnostic raise CopulaError

fn validate_uniforms(data : Array[Pair], minimum : Int) -> Unit raise CopulaError

fn wilson_interval(successes : Int, trials : Int, z? : Double) -> RateInterval raise CopulaError