Publications by arthur charpentier
MAT8886 Fisher-Tippett theorem and limiting distribution for the maximum
Tomorrow, we will discuss Fisher-Tippett theorem. The idea is that there are only three possible limiting distributions for normalized versions of the maxima of i.i.d. samples . For bounded distribution, consider e.g. the uniform distribution on the unit interval, i.e. on the unit interval. Let and . Then, for all and , i.e. the limiting dist...
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Infidelity and econometrics
On http://www.bakadesuyo.com, there was recently an interesting discussion about infidelity, the key question being “at what ages are men and women most likely to have affairs?” The discussion is based on some graphs, e.g. The source is a paper by Donald Cox. Based on a sample of 36 men and 22 women. And to be honest, I have been surprised ...
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Gold price and fear
Via @theEconomist, I understood that there might be connections between the price of Gold (which is said to be extremely high nowadays) and the VIX SP500 index (the option volatility index, i.e. the so-called “fear index“, as discussed – in French- a few months ago). This has been discussed also on several blogs, e.g. http://etfdailynews.co...
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MAT8886 Extremes and sums (of i.i.d. random variables)
Yesterday, we have discussed briefly sums and maximas of i.i.d. random variables using the concept of subexponential distributions. Today, we will introduce the concept of regular variation: a positive function is said to be regularly varying (at infinity), denoted , for some , if for all . An this concept can be related to sums and maxima (see...
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Even odds
This evening, I found a nice probabilistic puzzle on http://www.futilitycloset.com/ “A bag contains 16 billiard balls, some white and some black. You draw two balls at the same time. It is equally likely that the two will be the same color as different colors. What is the proportion of colors within the bag?“ To be honest, I did not understoo...
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It is "simply" the average value
for some obscure reasons, simple things are usually supposed to be simple. Recently, on the internet, I saw a lot of posts on the “average time in which you hold a stock“, and two rather different values are mentioned “Take any stock in the United States. The average time in which you hold a stock is – it’s gone up from 20 seconds to 22...
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MAT886 mean excess function (and reinsurance)
Tomorrow, in the course on extreme value, we will focus on applications. We will discuss reinsurance pricing. Consider a random variable , a threshold and define the mean excess function. This function is known in life insurance as the average remaining life time of someone alive at age . This function can be written For instance, if has a Gen...
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On linear models with no constant and R2
In econometrics course we always say to our students that “if you fit a linear model with no constant, then you might have trouble. For instance, you might have a negative R-squared“. So I tried to find databases on the internet such that, when we compute a linear regression, we actually obtain a negative R squared. I have generated hundreds ...
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MAT8886 a short word on profile likelihood
Profile likelihood is an interesting theory to visualize and compute confidence interval for estimators (see e.g. Venzon & Moolgavkar (1988)). As we will use is, we will plot But more generally, it is possible to consider where . Then (under standard suitable conditions) which can be used to derive confidence intervals.> base1=read.table( + "h...
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MAT8886 exchangeability, credit risk and risk measures
Exchangeability is an extremely concept, since (most of the time) analytical expressions can be derived. But it can also be used to observe some unexpected behaviors, that we will discuss later on with a more general setting. For instance, in a old post, I discussed connexions between correlation and risk measures (using simulations to illustrate...
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