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THE ART OF CONJECTURING (ARS CONJECTANDI) ON THE HISTORICAL ORIGIN OF NORMAL DISTRIBUTION (Rodowod rozkladu normalnego)

100%
Laudanski L.
Didactics of Mathematics
|
2010
|
issue 7(10)
67-79
EN
The paper offers a range of historic investigations regarding the normal distribution, frequently also referred to as the Gaussian distribution. The first one is the Error Analysis, the second one is the Probability Theory with its old exposition called the Theory of Chance. The latter regarded as the essential, despite the fact that the origin of the Error Theory can be associated with Galileo Galilei and his Dialogo sopra i due massimi sistemi del mondo Tolemaico e Copernico. However, the normal distribution regarded in this way was not found before 1808-9 as a result of the combined efforts of Robert Adrain and his Researches Concerning Isotomous Curves on the one hand and Carl F. Gauss and his Theoria motus corporum coelestium in sectionibus conicis Solem ambienitum on the other. While considering the Theory of Chance - it is necessary to acknowledge The Doctrine of Chances of Abraham de Moivre - 1733 and the proof contained in this work showing the normal distribution derived as the liming case of the binomial distribution with the number of Bernoulli trials tending to infinity. Therefore the simplest conclusion of the paper is: the normal distribution should be rather attributed to Abraham de Moivre than to Carl Friedrich Gauss.
2

MODELING A DISTRIBUTION OF MORTGAGE CREDIT LOSSES

88%
Gapko P., Šmíd M.
Ekonomický časopis (Journal of Economics)
|
2012
|
vol. 60
|
issue 10
1005 – 1023
EN
In our paper, we focus on the credit risk quantification methodology. We demonstrate that the current regulatory standards for credit risk management are at least not perfect. Generalizing the well-known KMV model, standing behind Basel II, we build a model of a loan portfolio involving a dynamics of the common factor, influencing the borrowers’ assets, which we allow to be non-normal. We show how the parameters of our model may be estimated by means of past mortgage delinquency rates. We give statistical evidence that the non-normal model is much more suitable than the one which assumes the normal distribution of risk factors. We point out in what way the assumption that risk factors follow a normal distribution can be dangerous. Especially during volatile periods comparable to the current crisis, the normal-distribution-based methodology can underestimate the impact of changes in tail losses caused by underlying risk factors.
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