fit_truncated_dist: Fit a distribution to truncated severity (loss) data

In insurancerating: Analytic Insurance Rating Techniques

Fit a distribution to truncated severity (loss) data

Description

Estimate the original distribution from truncated data. Truncated data arise frequently in insurance studies. It is common that only claims above a certain threshold are known.

Usage

fit_truncated_dist(
  y,
  dist = c("gamma", "lognormal"),
  left = NULL,
  right = NULL,
  start = NULL,
  print_initial = TRUE
)

Arguments

y	vector with observations of losses
dist	distribution for severity ("gamma" or "lognormal"). Defaults to "gamma".
left	numeric. Observations below this threshold are not present in the sample.
right	numeric. Observations above this threshold are not present in the sample. Defaults to Inf.
start	list of starting parameters for the algorithm.
print_initial	print attempts for initial parameters.

Value

fitdist returns an object of class "fitdist"

Author(s)

Martin Haringa

Examples

## Not run: 
# Original observations for severity
set.seed(1)
e <- rgamma(1000, scale = 148099.5, shape = 0.4887023)

# Truncated data (only claims above 30.000 euros)
threshold <- 30000
f <- e[e > threshold]

library(dplyr)
library(ggplot2)
data.frame(value = c(e, f),
variable = rep(c("Original data", "Only claims above 30.000 euros"),
               c(length(e), length(f)))) %>%
               filter(value < 5e5) %>%
               mutate(value = value / 1000) %>%
               ggplot(aes(x = value)) +
               geom_histogram(colour = "white") +
               facet_wrap(~variable, ncol = 1) +
               labs(y = "Number of observations",
                    x = "Severity (x 1000 EUR)")

# scale = 156259.7 and shape = 0.4588. Close to parameters of original
# distribution!
x <- fit_truncated_dist(f, left = threshold, dist = "gamma")

# Print cdf
autoplot(x)

# CDF with modifications
autoplot(x, print_dig = 5, xlab = "loss", ylab = "cdf", ylim = c(.9, 1))

est_scale <- x$estimate[1]
est_shape <- x$estimate[2]

# Generate data from truncated distribution (between 30k en 20 mln)
rg <- rgammat(10, scale = est_scale, shape = est_shape, lower = 3e4,
 upper = 20e6)

# Calculate quantiles
quantile(rg, probs = c(.5, .9, .99, .995))

## End(Not run)

insurancerating documentation built on Dec. 28, 2022, 2:53 a.m.