July 2017 – Life, the universe and cat modelling

Notes on visiting Phillip Island

This post has some tips for people wanting to visit the MotoGP race at Phillip Island. Those with plenty of time on their hands will be better off renting a bike and riding the coastal roads. This post is aimed more at those making a flying visit (acknowledging that those without much time on their hands are unlikely to be reading this blog)

Phillip Island itself may be famous for its fauna, but anyone who likes cities will want to stay in Melbourne.

The Phillip Island circuit is about a two hour drive from Melbourne. It isn’t really possible to get there any quicker as the Victoria police are (in)famous for their merciless treatment of people caught speeding. This is clear – even to the casual visitor – by the number of sport bikes on the way to the circuit sticking religiously to the speed limit.

Upon reaching Phillip Island proper there may be a bit of a tailback but nothing major compared to other international motorsport events. The organisers seem to do a decent job of getting spectators into the circuit. Perhaps this is because attendance is about 35,000.

Phillip Island is in southern Australia and the MotoGP takes place in their spring. But it’s still Australia: spectators need Factor 50 even if it looks cloudy.

Long left hander onto the Gardner straight

Watching from top of the Gardner straight it is possible to see the drop down from Lukey heights to MG and most of the long left onto the straight. There is also the added bonus of one of Dorna’s video screens showing the global feed.

The final race itself starts relatively late, presumably to better accommodate global TV audiences. After the slow down lap, the marshals open the track promptly to let spectators make their way towards the podium ceremony. The podium ceremony finishes at about 17:00 by which time all the trackside vendors, official or otherwise, seem to have closed their stalls.

Getting out of the car park is not as easy as entering, so it would be wise to find something else to do. Unfortunately this is tricky because, as mentioned above, all merchandise, food and drink stalls seem to shut the second the final race finishes. Those needing either sustenance or souvenirs would be advised to make purchases before the final race starts.

Notes on visiting Mugello

MotoGP at Mugello is one of those “classic” European rounds, so camping at the circuit will be a lot of fun for those not planning on getting much sleep. Expect loud music, drinking and, of course, novel applications of the unsilenced internal combustion engine.

Camping between Savelli and Arrabbiata 1

Conventional wisdom says those wanting a comfortable bed should stay in Florence. Florence may be closer to the circuit and much prettier, but Bologna is a bigger city and easier to get to if you’re flying in from afar. Plus, of course, Ducatisti will want to make some sort of pilgrimage to Bologna before or after the race.

Bologna Fiera to Mugello takes about an hour on the main highway (E35). Navigating is easy enough but this is the 21st century so satnav and smartphones make this pretty much idiot-proof. The E35 is a toll road which costs about €6 each way.

Circuit entrances (“ingressi”) are generally well signposted but the flow of traffic invariably leads to the fields nearest to Ingresso Palagio. Those wishing to watch from San Donato to Arrabbiata 1 will probably want to use Ingresso Luco. However, the signposting for Luco seemed to disappear somewhere around the small town of Scarperia e San Piero. That said, this diversion does seem to provide a route avoiding some of the traffic and leading back towards Ingresso Palagio.

On race day 2017, there was a 10km tailback at 08:30. This may have been racegoers with fake passes trying to access Ingresso Paddock because once that turn had been cleared traffic seemed to start moving again. Nonetheless this last 10km took 2½ hours in a car.

Parking in a field near Ingresso Palagio will cost €10-20 and it’s a short walk to the circuit. The closer you park to Ingresso Palagio the shorter the walk, but the longer you wait after the race while the fields further away are cleared first. There will probably be a good two hour wait for the traffic to move, followed by diversions enforcing a circuitous route around the local landscape back to E35. Go on a bike if you can.

Perimeter road between San Donato and Luco

The circuit itself is easy, if long, to navigate. There is a well tarmacked perimeter road almost all the way round the circuit. The exception being the south side of the circuit: there is no way to get from from Ingresso Luco to Ingresso Arrabiatta without leaving the circuit.

This is Italy so food at the circuit is plentiful and good: nary a doughnut to be seen. Merchandise is plentiful if a little uniform: it is hard to buy anything without a yellow 46 on it. It is even harder to find anyone willing to sell it when they’re busy selling VR46 merch.

It would be surprising if there were anywhere at Mugello that wasn’t a good vantage point to watch the racing. The landscape means several parts of the track are visible from most locations. A grandstand seat isn’t necessary but it does guarantee a degree of comfortable viewing and, perhaps more importantly, screens which show the global TV feed.

Inferring point weights on the severity distribution (Part 1)

Some catastrophe models compensate for the inadequacies of two parameter severity distributions by including point weights at zero and total loss. These are generally undocumented but appear to be non-zero values of probability density corresponding to mean damage ratios of zero and unity. The severity distribution between zero and unity is invariably represented by a two parameter probability distribution. Therefore, at least theoretically, we have a four parameter severity distribution.

At the time of writing these parameters are not well documented but can be inferred as described below.

For a single event, the general form for the calculation of “gross” expected loss net of deductible D and limit L is:

$\mu_{GR} = \displaystyle\int_D^{D+L} \! x.P(x-D)\mathrm{d}x \ + \ L.P(x>D\!+\!L)$

this is true for both continuous and discrete forms of the original (or “ground up”) severity distribution P(x). Considering two different limits, L₁ and L₂, on the same ground up distribution, we can say that

$\mu_1 - \mu_2 = \displaystyle\int_{L_2}^{L_1} \! x.P(x)\mathrm{d}x \ + \ L_1.P(x>L_1) \ - \ L_2.P(x>L_2)$

if both cases have no deductible. As L₁ → L₂, we can say that P(x>L₁) → P(x>L₂) so that

$\mu_1 - \mu_2 \simeq (L_1 - L_2).P(x>L_1)$

assuming that

$P(x>L_1) \gg P(L_2<x<L_1)$

which should certainly be true in the case where we have a significant probability density at x = 1. If we know we have a significant point weight corresponding to total loss, we can infer that point weight by comparing ground up (GU) and gross (GR) expected losses considering a limit L close to the insured value T:

$P(x=1) = \cfrac{\mu_{GU}-\mu_{GR}}{T-L}$