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Fitting and Comparing Severity
Candidates
Workflow and data interpretation
fit_severity_candidates() fits competing parametric
ground-up severity families and returns a list with fits, a
comparison data frame, and excluded_rows /
excluded_details. The observations must be
ground-up; net paid losses should not be substituted without
reconstructing that basis. A finite policy censoring limit means values
at the limit are right-censored; no limit or deductible column is needed
if it does not apply.
set.seed(128)
n <- 750
latent <- rlnorm(n, log(14000), 1.0)
limits <- sample(c(20000, 50000, 100000, Inf), n, replace = TRUE)
dat <- data.frame(ground_up_loss = pmin(latent, limits),
censor_limit = limits)
Fit, compare, and extract a selected fit
candidates <- fit_severity_candidates(dat, loss = "ground_up_loss",
limit = "censor_limit", distributions = c("lognormal", "gamma", "weibull"),
hessian = FALSE)
print(candidates$comparison)
#> distribution converged logLik AIC BIC parameters n n_censored
#> 1 lognormal TRUE -7254.734 14513.47 14522.71 2 750 85
#> 2 gamma TRUE -7306.483 14616.97 14626.21 2 750 85
#> 3 weibull TRUE -7311.927 14627.85 14637.09 2 750 85
#> error elapsed_seconds function_evaluations gradient_evaluations
#> 1 <NA> 0.03 25 5
#> 2 <NA> 0.22 103 29
#> 3 <NA> 0.06 35 11
#> convergence_code
#> 1 0
#> 2 0
#> 3 0
candidates$comparison[order(candidates$comparison$AIC), ]
#> distribution converged logLik AIC BIC parameters n n_censored
#> 1 lognormal TRUE -7254.734 14513.47 14522.71 2 750 85
#> 2 gamma TRUE -7306.483 14616.97 14626.21 2 750 85
#> 3 weibull TRUE -7311.927 14627.85 14637.09 2 750 85
#> error elapsed_seconds function_evaluations gradient_evaluations
#> 1 <NA> 0.03 25 5
#> 2 <NA> 0.22 103 29
#> 3 <NA> 0.06 35 11
#> convergence_code
#> 1 0
#> 2 0
#> 3 0
fit_lognormal <- candidates$fits$lognormal
summary(fit_lognormal)
#> Actuarial severity model summary
#>
#> Model: single
#> Distribution: lognormal
#> Observations: 750 (effective weighted count: 750)
#> Right-censored: 85
#> LogLik: -7254.734 AIC: 14513.47 BIC: 14522.71
#>
#> estimate std.error
#> scale 13642.397983 NA
#> sdlog 1.015471 NA
#>
#> The internal scale is exp(meanlog). With scale_by, mean severity is proportional to scale_coef * scale_by + scale_intercept.
Lower AIC/BIC is better relative to other fits on the same
observation model. A higher log likelihood is better. These are
not absolute goodness-of-fit measures and can hide tail or layer errors.
Not every distribution should be forced onto every loss dataset; inspect
convergence and factor stability.
Visual comparison
Modeled portfolio probabilities reproduce row-level censoring limits
and deductibles. Thus the histogram comparisons are made on the
observed basis. The new analytic default computes
expected bin counts without Monte Carlo simulation;
method = "simulation" restores the stochastic plot. The
default horizontal axis is logarithmic, and specifying xlim
changes only the displayed range. Use
scale_range = c(lower, upper) when fitting with
scale_by.
plot_candidate_fits(candidates, type = "histogram",
x_scale = "log10", xlim = c(500, 200000),
x_text_angle = 45, x_text_size = 8)
# Deterministic summaries: the very same bins drawn in the default plot.
head(candidate_plot_data(candidates, output = "plot_ready",
type = "histogram", xlim = c(500, 200000)))
#> source x value lower upper distribution
#> 1 actual 538.8846 0.00000000 500.0000 580.7932 lognormal
#> 2 actual 625.9610 0.02049658 580.7932 674.6414 lognormal
#> 3 actual 727.1077 0.02049658 674.6414 783.6543 lognormal
#> 4 actual 844.5984 0.02049658 783.6543 910.2821 lognormal
#> 5 actual 981.0740 0.06148974 910.2821 1057.3713 lognormal
#> 6 actual 1139.6021 0.02049658 1057.3713 1228.2280 lognormal
# Old row-level simulations remain available when requested.
head(candidate_plot_data(candidates, nsim = 1, seed = 22, output = "raw"))
#> row source simulation observed_loss censored deductible limit scale_value
#> 1 1 actual 0 20000.00 TRUE 0 2e+04 NA
#> 2 2 actual 0 22684.22 FALSE 0 1e+05 NA
#> 3 3 actual 0 20000.00 TRUE 0 2e+04 NA
#> 4 4 actual 0 13640.75 FALSE 0 1e+05 NA
#> 5 5 actual 0 20000.00 TRUE 0 2e+04 NA
#> 6 6 actual 0 25013.35 FALSE 0 Inf NA
#> weight distribution
#> 1 1 lognormal
#> 2 1 lognormal
#> 3 1 lognormal
#> 4 1 lognormal
#> 5 1 lognormal
#> 6 1 lognormal
Convert fits to rating factors and assess sensitivity
limit in severity_factors() is a
payment limit after the deductible:
E[min(max(v*X-d,0),L)]. This is distinct from the ground-up
censoring limit used for fitting. In particular, with
valuation_factor = 1, finite payment limits require
integrated survival between d and d + L.
factors <- severity_factors(candidates, deductible = c(500, 1000),
limit = c(25000, 50000, Inf), base_deductible = 500, base_limit = 25000)
head(factors)
#> distribution model scale_value deductible limit valuation_factor
#> lognormal.1 lognormal single NA 500 25000 1
#> lognormal.2 lognormal single NA 1000 25000 1
#> lognormal.3 lognormal single NA 500 50000 1
#> lognormal.4 lognormal single NA 1000 50000 1
#> lognormal.5 lognormal single NA 500 Inf 1
#> lognormal.6 lognormal single NA 1000 Inf 1
#> expected_payment limited_expected_severity unlimited_mean
#> lognormal.1 14234.88 14598.73 22845.93
#> lognormal.2 13868.96 14598.73 22845.93
#> lognormal.3 18369.59 18819.74 22845.93
#> lognormal.4 17919.71 18819.74 22845.93
#> lognormal.5 22345.99 22845.93 22845.93
#> lognormal.6 21847.17 22845.93 22845.93
#> LER ILF rating_factor base_deductible base_limit
#> lognormal.1 0.02188308 1.000000 1.0000000 500 25000
#> lognormal.2 0.04371713 1.000000 0.9742944 500 25000
#> lognormal.3 0.02188308 1.290463 1.2904632 500 25000
#> lognormal.4 0.04371713 1.292073 1.2588593 500 25000
#> lognormal.5 0.02188308 1.569805 1.5698055 500 25000
#> lognormal.6 0.04371713 1.575256 1.5347634 500 25000
#> base_valuation_factor
#> lognormal.1 1
#> lognormal.2 1
#> lognormal.3 1
#> lognormal.4 1
#> lognormal.5 1
#> lognormal.6 1
compare_factors(candidates, metric = "rating_factor",
deductible = c(500, 1000), limit = c(25000, 50000),
base_deductible = 500, base_limit = 25000)
#> scale_value deductible limit valuation_factor base_deductible
#> lognormal.1 NA 500 25000 1 500
#> base_limit base_valuation_factor value.lognormal value.gamma
#> lognormal.1 25000 1 1 1
#> value.weibull
#> lognormal.1 1
By default, the grid is Cartesian. Use grid = "paired"
to match vectors positionally, allowing scalar recycling. This prevents
unexpectedly generating 10,000 scenarios from two vectors of length
100.
Excluded claims
Rows with below-deductible or above-censor-limit losses are excluded
by default with a warning. The original positions and reasons are
retained. This behavior is not a claim that these payments were
necessarily erroneous: extra-contractual payments, bad-faith
settlements, and mismatched ground-up definitions require specific
analyst investigation, not silent censoring.
bad <- dat
bad$ground_up_loss[2] <- bad$censor_limit[2] + 1000
# Use a guaranteed finite limit in the example.
bad$censor_limit[2] <- 10000
bad$ground_up_loss[2] <- 10500
fit <- suppressWarnings(fit_severity(bad, loss = "ground_up_loss",
limit = "censor_limit", distribution = "lognormal", hessian = FALSE))
fit$excluded_rows
#> [1] 2
fit$excluded_details
#> row reason
#> 1 2 loss above censoring limit
Optimization diagnostics
Inspect the candidate table for outlying runtimes or optimizer
evaluation counts. When fitting scale_intercept = TRUE, the
optimizer automatically scales its intercept parameter; it does not
constrain its value. A caller can still supply
control$parscale explicitly. The displayed fit coefficients
remain in their original units.
candidates$comparison[, c("distribution", "elapsed_seconds",
"function_evaluations", "gradient_evaluations", "convergence_code")]
#> distribution elapsed_seconds function_evaluations gradient_evaluations
#> 1 lognormal 0.03 25 5
#> 2 gamma 0.22 103 29
#> 3 weibull 0.06 35 11
#> convergence_code
#> 1 0
#> 2 0
#> 3 0
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.