Package {actuarialfitdist}

actuarialfitdist: Actuarial Severity Fitting with Limits and Deductibles

Description

Fits severity distributions to ground-up insurance losses with deductible truncation and limit censoring, then carries fitted models through to limited expected severity, LER, ILF, deductible, and combined rating-factor analyses.

Ground-up losses are required

The core fitting functions assume the loss column is ground-up severity on a consistent valuation basis. Do not supply insurer payments, net-of- deductible amounts, excess losses, or depreciated ACV payments unless the analyst has first transformed them to the intended ground-up basis.

Documentation and first steps

Start with vignette("actuarialfitdist") for a worked example and vignette("candidate-comparisons") for model comparison, plotting, and conversion to rating factors. See ?fit_severity and ?severity_factors for the different meanings of a policy-limit input.

Supported families

Weibull, gamma, lognormal, Pareto II/Lomax, Burr XII, normal, exponential, log-logistic, inverse Gaussian, and generalized Pareto. Spliced body-tail combinations may use any supported family on either side of the threshold.

Author(s)

Maintainer: Greg Sollenberger yagreg7@yahoo.com [copyright holder]

Authors:

• Greg Sollenberger yagreg7@yahoo.com [copyright holder]

See Also

Useful links:

• https://github.com/gs-actuary/actuarialfitdist

• Report bugs at https://github.com/gs-actuary/actuarialfitdist/issues

Inspect fitted actuarial severity models

Description

These standard R methods display model results and provide access to coefficients, log-likelihood, information criteria and (when available) the estimated covariance matrix and confidence intervals. summary() gives natural-scale estimates and their standard errors. A Hessian-based variance estimate can be unavailable for numerically difficult fits; in that case vcov() and confint() require a successful refit with hessian = TRUE.

Details

plot(fit) calls plot_fit(fit). See ?predict.actuarialfitdist_fit and ?simulate.actuarialfitdist_fit for prediction and simulation.

Examples

set.seed(1)
d <- data.frame(loss = rlnorm(150, 9, 0.8))
fit <- fit_severity(d, "loss", hessian = FALSE)
summary(fit)
coef(fit)
logLik(fit)

Bootstrap a fitted severity model

Description

Provides a deliberately lightweight bootstrap. Parametric bootstrap retains the fitted portfolio's deductible, limit, scaling, and weight structure, simulates observed claims conditional on exceeding the deductible, and refits the model. Case bootstrap resamples claim rows with replacement.

Usage

bootstrap_fit(
  object,
  R = 200,
  type = c("parametric", "case"),
  seed = NULL,
  refit_threshold = FALSE
)

Arguments

Value

An actuarialfitdist_bootstrap list containing estimates (one row per replicate, including coefficients, convergence and any error), success_rate, R, type, and original (the input fit). Inspect failures before using the empirical distribution of bootstrap estimates.

Examples

set.seed(123)
d <- data.frame(loss = rlnorm(120, log(10000), 0.8))
fit <- fit_severity(d, "loss", distribution = "lognormal", hessian = FALSE)
boot <- bootstrap_fit(fit, R = 3, type = "case", seed = 1)
boot$success_rate

Data for comparing several candidate severity distributions

Description

Recreates each candidate's row-level deductible truncation and limit censoring, then returns actual and simulated observed claim amounts with the same scale-range filter. Inspect or modify the data with ggplot2/plotly.

Usage

candidate_plot_data(
  object,
  scale_range = NULL,
  nsim = 3,
  seed = NULL,
  output = c("raw", "plot_ready"),
  type = c("density", "histogram", "cdf", "survival"),
  bins = 40,
  points = 160,
  x_scale = c("log10", "linear"),
  xlim = NULL
)

Arguments

Value

A data frame with a distribution column for each successful candidate. output = "raw" returns actual and simulated claim-level observations with observed_loss, censoring flags and weights. output = "plot_ready" returns source, x, value, lower, upper, and distribution, matching the default candidate plot; source = "modeled" denotes expected portfolio probabilities, not Monte Carlo simulations.

Examples

set.seed(11)
d <- data.frame(loss = rlnorm(120, log(10000), 0.8))
candidates <- fit_severity_candidates(d, loss = "loss",
  distributions = c("lognormal", "gamma"), hessian = FALSE)
head(candidate_plot_data(candidates, nsim = 1, seed = 1))

Compare factor outputs side by side

Description

Evaluates the same rating scenarios for each successful candidate fit and reshapes one selected factor metric into a distribution-by-distribution table.

Usage

compare_factors(object, metric = "rating_factor", ...)

Arguments

Value

A wide data frame with the coverage scenario columns used by severity_factors() and one ⁠value.<distribution>⁠ column for each successful candidate, for the chosen metric.

Examples

set.seed(123)
d <- data.frame(loss = rlnorm(120, log(10000), 0.8))
candidates <- fit_severity_candidates(d, "loss",
  distributions = c("lognormal", "gamma"), hessian = FALSE)
compare_factors(candidates, deductible = 1000, limit = c(25000, 50000))

Diagnose fit within a severity layer

Description

Compares actual and simulated claim behavior within a user-selected observed severity layer, optionally restricted to a range of scaling values.

Usage

diagnose_fit(
  object,
  lower = 0,
  upper = Inf,
  scale_range = NULL,
  nsim = 100,
  seed = NULL
)

Arguments

Value

A data frame with one row for actual and one for simulated observed claims. Columns include source, rows, layer_count, layer_proportion, layer_mean, and censoring_rate. Simulated counts are averaged over replicates; results reflect observed (possibly censored) severity, not uncensored ground-up losses.

Examples

set.seed(123)
d <- data.frame(loss = rlnorm(120, log(10000), 0.8))
fit <- fit_severity(d, "loss", distribution = "lognormal", hessian = FALSE)
diagnose_fit(fit, lower = 1000, upper = 30000, nsim = 1)

Exceedance probabilities from a fitted model

Description

Returns fitted ground-up probabilities of exceeding specified severity thresholds, optionally at supplied values of the scaling variable.

Usage

exceedance_probability(object, threshold, scale_value = NULL)

Arguments

Value

Numeric vector of fitted probabilities that positive ground-up severity exceeds each threshold.

Examples

set.seed(123)
d <- data.frame(loss = rlnorm(120, log(10000), 0.8))
fit <- fit_severity(d, "loss", distribution = "lognormal", hessian = FALSE)
exceedance_probability(fit, 100000)

Expected payment under deductible, limit, and valuation terms

Description

Computes the expectation of pmin(pmax(v * X - d, 0), L), where X is positive ground-up severity, v is valuation_factor, d is deductible, and L is limit.

Usage

expected_payment(
  object,
  deductible = 0,
  limit = Inf,
  scale_value = NULL,
  valuation_factor = 1
)

Arguments

Value

Numeric vector of expected insurer payments, in loss currency units, calculated as the expectation of pmin(pmax(valuation_factor * X - deductible, 0), limit) for positive ground-up severity X. Here limit is a payment cap after deductible, not the ground-up observation censoring limit used while fitting.

Examples

set.seed(123)
d <- data.frame(loss = rlnorm(120, log(10000), 0.8))
fit <- fit_severity(d, "loss", distribution = "lognormal", hessian = FALSE)
expected_payment(fit, deductible = 1000, limit = 25000)

Data underlying observed-versus-modeled severity plots

Description

Produces a censoring- and truncation-aware comparison data set. Modeled values are simulated under the fitted model using each selected row's actual deductible, limit, and scaling value. This avoids the misleading practice of overlaying one unconditional fitted density on a heterogeneous portfolio of deductible-truncated and limit-censored claims.

Usage

fit_plot_data(
  object,
  scale_range = NULL,
  nsim = 20,
  seed = NULL,
  output = c("raw", "plot_ready"),
  type = c("density", "histogram", "cdf", "survival"),
  bins = 40,
  points = 160,
  x_scale = c("log10", "linear"),
  xlim = NULL
)

Arguments

Value

A data frame. For output = "raw", each selected original claim and each simulated replicate has row, source, simulation, observed_loss, censored, deductible, limit, scale_value, and weight. For output = "plot_ready", columns source, x, value, lower, and upper give the deterministic observed and modeled values used in analytic plots. Histograms/densities use density per displayed coordinate (per log10-severity unit when x_scale = "log10"); CDF/survival values are probabilities. The analytic output does not depend on nsim or seed.

Examples

set.seed(123)
d <- data.frame(loss = rlnorm(120, log(10000), 0.8))
fit <- fit_severity(d, "loss", distribution = "lognormal", hessian = FALSE)
head(fit_plot_data(fit, nsim = 1, seed = 1))

Fit an actuarial severity distribution

Description

Fits a parametric severity distribution to ground-up insurance losses using maximum likelihood. Claims below the deductible are treated as unobserved (left truncation) and observations at the policy limit are treated as right-censored.

Usage

fit_severity(
  data,
  loss,
  deductible = NULL,
  limit = NULL,
  distribution = "lognormal",
  scale_by = NULL,
  scale_intercept = FALSE,
  weights = NULL,
  fixed = list(),
  control = list(),
  hessian = TRUE,
  invalid_rows = c("warn_drop", "error")
)

Arguments

Value

An actuarialfitdist_fit object. Important components include coefficients (named estimates on their natural scales), logLik, AIC, BIC, convergence, and optimizer_counts. data contains the retained observations; excluded_rows records original row positions excluded during validation, and excluded_details explains why. vcov is a covariance matrix when it can be estimated (hessian = TRUE); otherwise it is NULL. convergence = 0 is an optimizer diagnostic, not proof that the chosen distribution adequately describes the claim tail.

Critical ground-up-loss assumption

loss must contain ground-up claim severities on a consistent valuation basis. It must not contain insurer payments, losses net of deductible, excess-of-deductible amounts, or ACV/depreciated payments unless the analyst has first converted those observations to the intended ground-up basis. The package deliberately does not guess or reconstruct this basis.

Observation mechanism versus payment factors

For fitting, deductible and limit are column names giving each claim's left-truncation threshold and ground-up censoring threshold. A claim recorded exactly at its finite limit is right-censored. In expected_payment() and severity_factors(), limit instead means a post-deductible insurer payment cap, supplied as an amount. These definitions must not be interchanged.

Examples

set.seed(123)
d <- data.frame(loss = rlnorm(120, log(10000), 0.8))
fit <- fit_severity(d, "loss", distribution = "lognormal")
summary(fit)

Fit and compare candidate severity distributions

Description

Fits several supported families to the same ground-up-loss data and returns both the fitted models and a comparison table with per-distribution optimization runtimes, evaluation counts, and convergence codes. The function intentionally does not choose a winner automatically; actuarial tail behavior and rating factor stability can matter even when information criteria are close.

Usage

fit_severity_candidates(
  data, loss, deductible = NULL, limit = NULL,
  distributions = c("weibull", "gamma", "lognormal",
    "pareto2", "burr", "normal", "exponential",
    "loglogistic", "invgauss", "gpd"),
  scale_by = NULL, scale_intercept = FALSE,
  weights = NULL, fixed = list(), control = list(),
  hessian = TRUE, invalid_rows = c("warn_drop", "error")
)

Arguments

Value

An actuarialfitdist_candidates list with fits (named fitted objects or errors), comparison (one row per requested family), excluded_rows, and excluded_details. comparison includes converged, logLik, AIC, BIC, error, and per-family fitting time and optimizer evaluations. Failed fits have missing fit statistics. No winning model is selected automatically; compare tail behavior and payment factors as well.

Choosing a distribution

Fit criteria are comparable only for fits using the same data and observation likelihood. Check converged and error before comparing AIC/BIC. Prefer a distribution with credible tail and layer behavior, rather than selecting the smallest AIC mechanically.

Examples

set.seed(123)
d <- data.frame(loss = rlnorm(120, log(10000), 0.8))
candidates <- fit_severity_candidates(d, "loss",
  distributions = c("lognormal", "gamma"), hessian = FALSE)
candidates$comparison
candidates$fits$lognormal
plot_candidate_fits(candidates)

Fit a spliced body-tail severity model

Description

Fits a two-component severity model with one family below a threshold and a second family above it. Each component is normalized on its side of the threshold and a fitted splice probability controls the probability mass in the body. Density continuity at the threshold is not imposed.

Usage

fit_spliced_severity(
  data,
  loss,
  deductible = NULL,
  limit = NULL,
  body = "lognormal",
  tail = "pareto2",
  threshold = NULL,
  threshold_method = c("fixed", "search"),
  threshold_probs = c(0.65, 0.95),
  threshold_grid = 15L,
  scale_by = NULL,
  scale_intercept = FALSE,
  weights = NULL,
  fixed = list(),
  control = list(),
  hessian = TRUE,
  invalid_rows = c("warn_drop", "error"),
  min_tail_exact = 25L
)

Arguments

Details

The same critical ground-up-loss assumption as fit_severity() applies. The loss column must contain ground-up severities. Deductibles define left truncation and limits define right censoring.

Value

An actuarialfitdist_fit object with body and tail coefficients, fitted splice probability, chosen threshold, fit statistics, and the excluded-row audit. If threshold_method = "search", threshold_search records attempted thresholds, exact uncensored tail counts, convergence, fit statistics, and reasons for rejecting candidates. A successful optimizer code does not guarantee a stable extrapolated tail.

Examples

set.seed(123)
d <- data.frame(loss = rlnorm(50, log(10000), 0.8))
fit <- fit_spliced_severity(d, "loss", body = "lognormal", tail = "pareto2",
  threshold = as.numeric(stats::quantile(d$loss, 0.75)), hessian = FALSE,
  min_tail_exact = 5)
fit$threshold

Increased limits factor

Description

Computes the ratio of expected payments at a target limit to expected payments at a base limit, holding the deductible and valuation basis fixed.

Usage

increased_limits_factor(
  object,
  limit,
  base_limit,
  scale_value = NULL,
  deductible = 0,
  valuation_factor = 1
)

Arguments

Value

Numeric vector of increased limits factors: expected payment at each target limit divided by the payment at base_limit, for the same deductible and valuation assumptions.

Examples

set.seed(123)
d <- data.frame(loss = rlnorm(120, log(10000), 0.8))
fit <- fit_severity(d, "loss", distribution = "lognormal", hessian = FALSE)
increased_limits_factor(fit, limit = 50000, base_limit = 25000)

Limited expected severity

Description

Computes the expectation of pmin(X, limit) for positive ground-up severity X. For models fitted with a scaling variable, supply the corresponding scale_value.

Usage

limited_expected_value(object, limit, scale_value = NULL)

Arguments

Value

Numeric vector of expected ground-up severity limited at each supplied limit, in the same currency units as the loss data. Inf requests the unlimited mean when it exists.

Examples

set.seed(123)
d <- data.frame(loss = rlnorm(120, log(10000), 0.8))
fit <- fit_severity(d, "loss", distribution = "lognormal", hessian = FALSE)
limited_expected_value(fit, 25000)

Loss elimination ratio

Description

Calculates one minus the expected payment after deductible divided by the expected positive ground-up severity. Infinite-mean models return NA when the denominator is not finite.

Usage

loss_elimination_ratio(
  object,
  deductible,
  scale_value = NULL,
  valuation_factor = 1
)

Arguments

Value

Numeric vector of loss elimination ratios: one minus expected post-deductible payment divided by expected payment without a deductible, holding the valuation factor fixed. Returns NA when the denominator is not finite and positive.

Examples

set.seed(123)
d <- data.frame(loss = rlnorm(120, log(10000), 0.8))
fit <- fit_severity(d, "loss", distribution = "lognormal", hessian = FALSE)
loss_elimination_ratio(fit, deductible = 1000)

Compare observed and fitted severity across candidate distributions

Description

Facets or overlays observed severity against modeled severity histograms, densities, CDFs or survival curves. The default uses expected probabilities, not random simulations. Uses a shared log10 axis by default. Fitted comparisons reproduce the observation mechanism, not unconditional ground-up densities. Returned ggplot can be customized.

Usage

plot_candidate_fits(
  object,
  type = c("histogram", "density", "cdf", "survival"),
  scale_range = NULL,
  nsim = 3,
  seed = NULL,
  bins = 40,
  x_scale = c("log10", "linear"),
  xlim = NULL,
  facet = TRUE,
  method = c("analytic", "simulation"),
  points = 160,
  x_breaks = NULL,
  x_text_angle = if (facet) 45 else 0,
  x_text_size = 9,
  y_text_size = 9
)

Arguments

Value

A ggplot2 plot, faceted by distribution unless facet = FALSE. Only successfully fitted candidates are plotted. The default is analytic (deterministic); candidate_plot_data(output = "plot_ready") returns the exact plotting values for custom charts.

Interpretation

Analytic curves compare the empirical observed severity distribution to the fitted distribution after the same observation rules. They are not unconditional ground-up density curves. nsim and seed affect only method = "simulation". Models that fail fitting are omitted, and their errors remain in object$comparison.

Examples

set.seed(2)
d <- data.frame(loss = rlnorm(150, log(9000), 0.9))
fits <- fit_severity_candidates(d, "loss",
  distributions = c("lognormal", "weibull"), hessian = FALSE)
plot_candidate_fits(fits)

Plot censoring-aware goodness of fit

Description

The default log10 severity axis reveals the body of heavy-tailed claim distributions without discarding large losses. For histograms, ggplot computes density in log-severity coordinates, ensuring simulated and observed bars use the same normalization. Axis limits only zoom the view.

Usage

plot_fit(
  object,
  type = c("histogram", "density", "cdf", "survival"),
  scale_range = NULL,
  nsim = 20,
  seed = NULL,
  bins = 30,
  x_scale = c("log10", "linear"),
  xlim = NULL,
  method = c("analytic", "simulation"),
  points = 160,
  x_breaks = NULL,
  x_text_angle = 0,
  x_text_size = 9,
  y_text_size = 9
)

Arguments

Value

A ggplot2 plot comparing observed severity with modeled observations on the same deductible, limit and scaling basis. The default analytic method uses deterministic expected probabilities; choose method = "simulation" for a Monte Carlo comparison. To customize the underlying analytic values, use fit_plot_data(output = "plot_ready").

Analytic versus simulation plots

method = "analytic" (the default) calculates expected observed-claim probabilities across the actual mix of deductibles, limits, and scaling values. It is deterministic and ignores nsim and seed. Use method = "simulation" when you want to see Monte Carlo variability; nsim controls the number of simulated portfolios in that mode.

Examples

set.seed(123)
d <- data.frame(loss = rlnorm(120, log(10000), 0.8))
fit <- fit_severity(d, "loss", distribution = "lognormal", hessian = FALSE)
plot_fit(fit, x_scale = "log10")

Plot the fitted scaling relationship

Description

Compares empirical observed mean severity by scale bin with simulated observed means and the fitted ground-up mean relationship.

Usage

plot_scaling_fit(
  object,
  bins = 10,
  bin_method = c("quantile", "width"),
  scale_range = NULL,
  nsim = 50,
  seed = NULL,
  x_breaks = NULL,
  x_text_angle = 0,
  x_text_size = 9,
  y_text_size = 9
)

Arguments

Value

A ggplot2 object showing observed means, simulated observed means, and fitted ground-up means by scaling-variable bin. The plotted data can be obtained with scaling_plot_data(output = "plot_ready").

Examples

set.seed(2)
d <- data.frame(cov_a = rep(c(200000, 400000, 600000), each = 80))
d$loss <- rlnorm(nrow(d), log(.07*d$cov_a), .8)
f <- fit_severity(d, "loss", scale_by = "cov_a", hessian = FALSE)
plot_scaling_fit(f, bins = 3, nsim = 1)

Predict severity quantities

Description

Evaluates fitted means, quantiles, survival probabilities, CDF values, or densities for single-family and spliced severity models.

Usage

## S3 method for class 'actuarialfitdist_fit'
predict(
  object,
  newdata = NULL,
  scale_value = NULL,
  type = c("mean", "quantile", "survival", "cdf", "density"),
  p = 0.5,
  x = NULL,
  ...
)

Arguments

Value

Numeric fitted values. Means and quantiles are in ground-up severity units; survival and CDF results are probabilities, and density results are probability densities. Results are conditional on positive ground-up severity.

Examples

set.seed(1)
d <- data.frame(loss = rlnorm(120, log(10000), 0.8))
fit <- fit_severity(d, "loss", hessian = FALSE)
predict(fit, type = "mean")
predict(fit, type = "quantile", p = 0.95)
predict(fit, type = "survival", x = 25000)

Data underlying the scaling relationship diagnostic

Description

Bins the fitted scaling variable and compares actual mean observed severity with the mean of simulated observed severities generated under the same row- level deductibles and limits. It also reports the fitted ground-up mean at a representative scaling value in each bin. The first two series are directly comparable on the observed/censored basis; the ground-up mean is included to display the model's implied severity-scaling relationship.

Usage

scaling_plot_data(
  object,
  bins = 10,
  bin_method = c("quantile", "width"),
  scale_range = NULL,
  nsim = 50,
  seed = NULL,
  output = c("wide", "plot_ready")
)

Arguments

Value

A data frame with scale bins. For output = "wide", columns include bin, scale_value, n, actual_observed_mean, modeled_observed_mean, and fitted_ground_up_mean. For output = "plot_ready", columns bin, scale_value, mean, and series give the exact long-format data used by plot_scaling_fit(). Observed and modeled observed means incorporate policy terms; the ground-up mean does not.

Examples

set.seed(2)
d <- data.frame(cov_a = rep(c(200000, 400000, 600000), each = 80))
d$loss <- rlnorm(nrow(d), log(.07*d$cov_a), .8)
f <- fit_severity(d, "loss", scale_by = "cov_a", hessian = FALSE)
scaling_plot_data(f, bins = 3, nsim = 1)

Generate actuarial severity rating factors

Description

Takes either one fitted severity model or a candidate-comparison object to the business endpoint. Outputs expected payments, limited expected severity, LERs, ILFs, and base-relative combined rating factors. If a candidate object is supplied, every successful candidate is evaluated using the same coverage scenarios so factor sensitivity can be compared directly.

Usage

severity_factors(
  object,
  deductible,
  limit,
  scale_value = NULL,
  valuation_factor = 1,
  base_deductible = 0,
  base_limit = Inf,
  base_valuation_factor = 1,
  grid = c("cross", "paired")
)

Arguments

Details

A valuation_factor below one applies a multiplicative ACV/depreciation adjustment to ground-up replacement-cost severity before the deductible and limit. Fitting remains agnostic to depreciation: historical losses must have already been placed on the analyst's chosen ground-up basis.

Value

A long-format data frame with one row per coverage scenario and successful distribution. Columns include distribution, model, scale_value, deductible, limit, valuation_factor, expected_payment, limited_expected_severity, unlimited_mean, LER, ILF, rating_factor, and the three ⁠base_*⁠ assumptions. A value can be NA when the relevant expectation or denominator does not exist. With grid = "cross", input vectors form a Cartesian product; with "paired", they form positionally matched scenarios.

What the factor limit means

Here limit is the maximum payment after applying the deductible. It is not the ground-up censoring threshold in fit_severity(). rating_factor compares each scenario's expected payment against the supplied base deductible, limit and valuation terms. grid = "cross" can create many scenarios when several input vectors are long.

Examples

set.seed(123)
d <- data.frame(loss = rlnorm(120, log(10000), 0.8))
fit <- fit_severity(d, "loss", distribution = "lognormal", hessian = FALSE)
severity_factors(fit, deductible = c(500, 1000),
  limit = c(25000, 50000), grid = "paired")

Severity quantiles from a fitted model

Description

Returns ground-up severity quantiles implied by a fitted single-family or spliced model, including scale-dependent fits when scale_value is supplied.

Usage

severity_quantile(object, p, scale_value = NULL)

Arguments

Value

Numeric vector of fitted positive ground-up severity quantiles at probabilities p, in the original loss units.

Examples

set.seed(123)
d <- data.frame(loss = rlnorm(120, log(10000), 0.8))
fit <- fit_severity(d, "loss", distribution = "lognormal", hessian = FALSE)
severity_quantile(fit, c(.5, .9, .99))

Simulate from a fitted severity model

Description

Simulates either positive ground-up severities or the observed claims that result after reproducing row-level deductible truncation and limit censoring.

Usage

## S3 method for class 'actuarialfitdist_fit'
simulate(
  object,
  nsim = 1,
  seed = NULL,
  type = c("observed", "ground_up"),
  newdata = object$data,
  n = NULL,
  scale_value = NULL,
  ...
)

Arguments

Value

A data frame. In type = "observed", rows contain row, simulation, observed_loss, censored, deductible, limit, and scale_value after reproducing each row's observation mechanism. In type = "ground_up", rows contain simulation, ground_up, and scale_value without censoring or truncation.

Examples

set.seed(1)
d <- data.frame(loss = rlnorm(120, log(10000), 0.8))
fit <- fit_severity(d, "loss", hessian = FALSE)
head(simulate(fit, nsim = 1, seed = 123))
head(simulate(fit, nsim = 1, seed = 123, type = "ground_up", n = 5))