The following table shows a few statistics related to the loss amount distribution for a risk over the period 2014 to 2023. The loss amounts from which these statistics are derived were generated from a lognormal distribution with parameters 10.3 and 1.5. For each year, a fixed number of 500 losses were generated, and a 5% loss inflation was superimposed on each successive year, so that, for example, the loss amounts for 2017 were derived by sampling losses from a lognormal distribution with the parameters above and then multiplying each amount by 1.052007−2004 = 1.16.

2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 Mean 93,396 107,148 93,523 93,754 108,782 88,764 105,208 119,736 118,352 139,733 Median 27,008 35,398 33,892 31,944 37,930 34,966 42,755 44,157 41,747 43,156 10th largest 680,164 591,770 812,676 976,665 783,431 977,358 763,855 937,060 1,088,360 1,050,619 Trimmed mean (90%)

26,950 35,205 33,510 31,948 38,325 35,545 42,388 44,618 41,913 43,776 i. Make a chart of the mean, median, and trimmed mean against the year and calculate the year-on-year inflation for each statistic, commenting on the stability of the statistic.

ii. Calculate the loss inflation based on the four statistics provided and compare it with the true inflation.

iii. Run your own experiment with the same parameters as specified above and see if you get similar results. Also, run the same experiment with 100 losses only and with a variable number of losses, based on a Poisson distribution with a Poisson rate equal to 100.