This repository contains several projects related to actuarial science & statistics, with codes in R.
A retailer, wishes to estimate the effects of super discounts, which occur on around 40% of the time, on their earnings. Given a sample of 100 data points, showing the daily sales (assumed to be normally distributed) for 100 days (with and without super discount), we will perform a Baysesian analysis to find out if super discounts increase sales.
A phone manufacturer, Apricot, has 3 class of products, low, medium, and high class phones, and is planning to offer lifetime warranties for its customers. For each class of phone, a replacement will be issued when a phone experiences a fault and can't be repaired on the same day. Further, a replacement will also be given if a phone reaches a certain number of faults (2 for low class, and 3 for middle & high class). Given the probabilities and costs associated to faults, same-day repairs, and replacements, how can the phone company optimise its warranty scheme to minimise costs?
An insurance company wishes to estimate the required reserve for the upcoming year, using the total aggregated claims for the previous 4 years. To do this, we will perform a Bayesian analysis to predict the necessary capital the company should hold such that we are 95% certain that the claims will not exceed this amount of reserve. We were told that the amount of the aggregated claim follows a given Rayleigh distribution with unknown parameter θ, and that the previous 4 total annual claims were 1.1, 0.7, 0.45, and 1.3 million GBP.