Hi, In chapter 3 page 6, the paragraph under heading normal distribution states that loss distribution tends to be asymmetrical. Could someone tell why is it so? Thanks for the insight! Regards, Shyam
Hi Shyam, In principle, a variable described by a normal distribution could take any possible value for an appropriate mean and sd. However, this isn't true for insurance losses. I can think of three reasons to illustrate, but am sure there are more: 1) In general (i.e. ignoring salvage / subrogation / reinsurance recoveries) a loss amount will always be positive. From a purely mathematical perspective, restricting the domain of values this way means that the resulting distribution will inherently include an element of asymmetry. 2) Insurance loss information taken from a company's database are typically impacted by truncation (e.g. deductibles before the policyholder can claim) or censoring (typically affects life policies). As a result, any distribution used to infer the behaviour of the losses will have asymmetry. 3) Even if you had full visibility of the loss - e.g. there was no deductible so policyholders submitted each and every claim, there would still be an element of asymmetry, because events with extreme severity don't happen often (think catastrophe), so there is a natural aspect to asymmetry. HTH D