How likely is Cynthia to live to 100?
Being an R stats lover Cynthia enjoyed her first explorations of the life table for the year 1999. Using R she wants to gain more insights. Cynthia is particularly interested in the probability to become a centenarian. What is this probability for a zero-year-old, using the data of 1999? And for an 18-year-old? Can you figure out how to calculate those probabilities? Then do a visualization of \((k,\ _kp_{18})\).
In the following exercises, the 1999 period life table for females in Belgium is again preloaded and stored in the object life_table
and the lx
column has been extracted for you.
This exercise is part of the course
Life Insurance Products Valuation in R
Exercise instructions
- Use
lx
to compute the probability for a zero-year-old to become a centenarian (i.e. to reach age 100). Make sure to extract by index. - Compute the same probability for an 18-year-old.
- Calculate and plot the probabilities for an 18-year-old to survive until ages 18, 19, … up to 100. Define
k
as a vector from 0 to 82. Usek
to calculate the probabilities.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Compute the probabilty for (0) to reach the age 100
___
# Compute the probabilty for (18) to reach the age 100
___
# Plot the survival probabilties for (18) up to age 100
k <- ___
plot(k, ___,
pch = 20,
xlab = "k",
ylab = expression(paste(""[k], "p"[18])),
main = "Survival probabilities for (18)")