1 Duration Models

1.1 Composition of the portfolio

Analyse the composition of the portfolio: covariates, frequency by covariates.

First, load the training and testing sets, located in the following folder: data/canada_panel/ (CanadaPanelTrain.csv and CanadaPanelTest.csv, respectively).

library(tidyverse)
canada_train <- readr::read_csv("./data/canada_panel/CanadaPanelTrain.csv")
canada_test <- readr::read_csv("./data/canada_panel/CanadaPanelTest.csv")
nrow(canada_train)
canada_train

Define a function that computes summary statistics for a vector of numerics:

Average
Standard deviation
Min and Max
Median
Other percentiles (e.g., 10th, 25th, 75th, and 90th)

Try to account for possible NA values. Name the function my_summary.

#' my_summary
#' Returns a tibble with summary statistics for a numerical vector
#' @param x vector of numerics
my_summary <- function(x) {
  tibble(
    Average = mean(x, na.rm=TRUE),
    Min = min(x, na.rm = TRUE),
    Max = max(x, na.rm = TRUE),
    `10th percentile` = quantile(x, probs = .1, names = FALSE),
    `25th percentile` = quantile(x, probs = .25, names = FALSE),
    Median = median(x, na.rm = TRUE),
    `75th percentile` = quantile(x, probs = .75, names = FALSE),
    `90th percentile` = quantile(x, probs = .9, names = FALSE)
  )
}

Use the function on a single variable from the training sample:

my_summary(canada_train$RA_EXPOSURE_TIME)

Apply this function to multiple variables of your choice to explore the dataset and put the results in a table. You may either use a for loop, lapply() or map() (pick the option you are more comfortable with). Do not forget to add the variable name to be able to identify the variables.

some_variables <- c("RA_DISTANCE_DRIVEN", "RA_NBTRIP", "RA_HOURS_DRIVEN")

# Using a for loop
summary_table_canada <- NULL
for( var in some_variables ) {
  summary_table_canada <- 
    summary_table_canada %>% 
    bind_rows(
      my_summary(canada_train[[var]])
    )
}
summary_table_canada$variable <- some_variables
summary_table_canada


# Using lapply
summary_table_canada <- 
  lapply(some_variables, function(var) my_summary(canada_train[[var]])) %>% 
  bind_rows()
summary_table_canada$variable <- some_variables
summary_table_canada

# Using map
summary_table_canada <-
  canada_train %>% 
  dplyr::select(!!some_variables) %>% 
  purrr::map(my_summary) %>% 
  bind_rows(.id = "variable")
summary_table_canada

Plot the distribution of claims on a barplot. You may display the distribution of gender among each claims levels (by showing the proportion of each gender within the bars). The result may look like the figure displayed below:

p_distribution_claims_gender <- 
  canada_train %>% 
  dplyr::group_by(RA_ACCIDENT_IND, RA_GENDER) %>% 
  dplyr::tally() %>% 
  mutate(RA_GENDER = factor(RA_GENDER, levels = c("2", "1", "3"),
                             labels = c("Female", "Male", "Unknown"))) %>%
  ggplot(data = ., aes(x = reorder(RA_ACCIDENT_IND, -n), y = n, fill = RA_GENDER)) +
  geom_col() +
  scale_fill_manual(name = "Gender",
                    values = c("Female" = "#66c2a5",
                               "Male" = "#fc8d62",
                               "Unknown" = "#8da0cb")) +
  labs(x = "Number of Claims", y = "Frequency",
       title = "Distribution of Number of Claims and Gender") +
  # Legend below the graph
  theme(legend.position = "bottom")

ggsave(p_distribution_claims_gender,
       file = "figs/p_distribution_claims_gender.png", width = 10, height = 6)

p_distribution_claims_gender

Plot a boxplot of exposure time depending on marital status and vehicle use. Use faceting to separate the data according to vehicule use. The resulting plot should look like the one below:

Telematics - Exercises (solutions)

Insurance Data Science: Use and Value of Unusual Data

August 2019

1 Duration Models

1.1 Composition of the portfolio