It’s (close to) a Weibull — again!

You recall that in my last post, I went through an involved process of showing how one could generate storm losses for individuals over years.  That process, which underlies a project to examine the effect of legal change on the sustainability of a catastrophe insurer, involved the copulas of beta distributions and a parameter mixture distribution in which the underlying distribution was also a beta distribution. It was not for the faint of heart.

One purpose of this effort was to generate a histogram that looks like the one below that shows the distribution of scaled claim sizes for non-negligible claims. This histogram was obtained by taking one draw from the copula distribution for each of the [latex]y[/latex] years in the simulation and using it to constrain the distribution of losses suffered by each of the [latex]n[/latex] policyholders in each of those [latex]y[/latex] years.  Thus, although the underlying process created an [latex]y \times n[/latex] matrix, the histogram below is for a single “flattened” [latex]y \times n[/latex] vector of values.

Histogram of individual scaled non-negligible claim sizes

Histogram of individual scaled non-negligible claim sizes

But, if we stare at that histogram for a while, we recognize the possibility that it might be approximated by a simple statistical distribution.  If that were the case, we could simply use the simple statistical distribution rather than the elaborate process for generating individual storm loss distributions. In other words, there might be a computational shortcut that could approximate the elaborate proces.  If that were the case, to get the experience of all [latex]n[/latex] policyholders — including those who did not have a claim at all — we could just upsample random variates drawn from our hypothesized simple distribution and add zeros; alternatively, we could create a mixture distribution in which most of the time one drew from a distribution that was always zero and, when there was a positive claim, one drew from this hypothesized simple distribution.

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Why I blog on Texas Windstorms

I am blogging because Texas, and other coastal states, have set themselves up for disaster by engineering flimsy legal and financial regimes to address the risks of tropical cyclones.  I read accounts in the press or on the Internet that are based on incredible misinformation and wishful thinking that nature will not respect. I see many politicians in a cycle of untruths with their constituents that leave coastal residents and businesses at significant risk of a catastrophe. Selfishly, I know that I, a semi-coastal resident, will be asked, one way or another to help pick up the pieces in an expensive way if a major storm hits a densely populated part of the Texas Coast.

I am also blogging because, immodestly, I have considerable expertise in this area and can’t just submit every thought to the Houston Chronicle and hope that they publish it. As a law professor at the University of Houston Law Center with a deep interest in actuarial science and finance, I’ve studied the legal and financial operations of the Texas Windstorm Insurance Association for many years.

Finally, I guess I am blogging because I want to give some courage to people who want to look at the Texas insurance scene with an open mind.  I have seen one Texas political figure, Insurance Commissioner Eleanor Kitzman, vilified by many coastal politicians and residents for daring to tell the truth about the risks now being run.  That is just wrong.   We say we want politicians to tell us the truth.  But do we really?  So, my hope is to give useful information and analysis to people who dare to look without prejudice at Texas windstorm situation. 

I’ll be using several tools to present information.  WordPress supports text and pictures and all the usual stuff.  I’ll  use those modes of expression to the best of my ability. But it also supports interactive tools (CDF technology) that let you, the reader, really explore the situation and make up your own mind.  And, ultimately, I suspect that is how we will all learn best.

So, enjoy, read and think.