distributions
- Thread starter Rajiv28
- Start date
Hi Rajiv,
That's a big topic, but I will post a summary of distributions mentioned in the FRM (just give me a few days). For exam purposes, I assume you know the foundational ones are in Gujarati.
see middle of this newsletter for applications of normal, student's t, chi-square and F: http://www.bionicturtle.com/learn/article/frm_episode_2_quant_b_econometrics/
but of course, several others are mentioned/referred (e.g., GPD/GEV in EVT, subexponential in OpRisk). Sometimes the distribution is mathematically implied by the problem; e.g., GEV distributions are mathematically implied (derived) by the peaks over threshold setup. In other cases (e.g., DB LDA OpRisk), practitioners are "merely" trying to fit a distribution to messy data; in this case, there is more art than science.
The Pareto, in addition to having its own properties, was considered by DB because it can give the fat tails (this is often the motive, to get fat tails). The Pareto has fatter tails than the t-distribution; i.e., greater kurtosis for (almost?) any degrees of freedom. The t distribution is almost normal looking, its excess kurtosis is 6/(df -4) so, for example, at 22 df, excess kurtosis is 3 and the pareto can be much fatter.
David
That's a big topic, but I will post a summary of distributions mentioned in the FRM (just give me a few days). For exam purposes, I assume you know the foundational ones are in Gujarati.
see middle of this newsletter for applications of normal, student's t, chi-square and F: http://www.bionicturtle.com/learn/article/frm_episode_2_quant_b_econometrics/
but of course, several others are mentioned/referred (e.g., GPD/GEV in EVT, subexponential in OpRisk). Sometimes the distribution is mathematically implied by the problem; e.g., GEV distributions are mathematically implied (derived) by the peaks over threshold setup. In other cases (e.g., DB LDA OpRisk), practitioners are "merely" trying to fit a distribution to messy data; in this case, there is more art than science.
The Pareto, in addition to having its own properties, was considered by DB because it can give the fat tails (this is often the motive, to get fat tails). The Pareto has fatter tails than the t-distribution; i.e., greater kurtosis for (almost?) any degrees of freedom. The t distribution is almost normal looking, its excess kurtosis is 6/(df -4) so, for example, at 22 df, excess kurtosis is 3 and the pareto can be much fatter.
David
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