## FANDOM

32.681 Seiten

Angaben zur Quelle [Bearbeiten]

 Autor Richard L. Smith Titel Statistics of extremes, with applications in environment, insurance and finance Jahr 2003 URL http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.75.1919&rep=rep1&type=pdf Literaturverz. ja Fußnoten ja Fragmente 2

Fragmente der Quelle:
 Zuletzt bearbeitet: 2012-08-11 14:50:29 Hindemith

 Typus Verschleierung Bearbeiter Graf Isolan Gesichtet
Untersuchte Arbeit:
Seite: 129, Zeilen: 24-35
Quelle: Smith 2003
Seite(n): 50, Zeilen: 15-18, 22-28
We are interested in the extremal properties of this process. Without loss of generality, we consider the case where all marginal distributions have unit Frèchet [sic!] distribution.

Definition 5.2.1. The process Yij is called max-stable if all finite dimensional distributions are max-stable, i.e., for any n ≥ 1, r ≥ 1

${\scriptstyle \mathbb P}$(Yij ≤ ruij: 1≤i≤n, 1≤j≤d)r = ${\scriptstyle \mathbb P}$(Yij ≤ uij: 1≤i≤n, 1≤j≤d).

Furthermore, a process Xij for i = 1,...,n, j = 1,...,d, is said to be in the domain of attraction of a max-stable process Yij if there exist normalising constants anij > 0, bnij such that for any finite r

${\scriptstyle \lim\limits_{n\to\infty}\mathbb{P}\left(\frac{X_{ij}-b_{nij}}{a_{nij}}\le ru_{ij}:1\le i\le n, 1\le j\le j [sic!] \right)^r}$
${\scriptstyle = \mathbb{P}(Y_{ij}\le u_{ij}: 1\le i\le n, 1\le j\le d). \qquad (5.2.1)}$

Since we assume a priori that the process Xij also has unit Frèchet [sic!], then we may take anij = n, bnij = 0.

If we are interested in the extremal properties of this process, then for the same reasons as with multivariate extremes, it suffices to consider the case where all the marginal distributions have been transformed to unit Fréchet. Such a process is called max-stable if all the finite-dimensional distributions are max-stable, i.e. for any n ≥ 1, r ≥ 1

[...]

Pr(Yid ≤ nyid: 1≤i≤r, 1≤d≤D)n = Pr(Yid ≤ yid: 1≤i≤r, 1≤d≤D). (7.7)

Corresponding to this, a process {Xid : i = 1,2,...; 1≤d≤D} is said to be in the domain of attraction of a max-stable process {Yid : i = 1,2,...; 1≤d≤D} if there exist normalising constants anid > 0, bnid such that for any finite r

${\scriptstyle \lim\limits_{n\to\infty}Pr\left\{\frac{X_{id}-b_{nid}}{a_{nid}}\le ny_{id}:1\le i\le r, 1\le d\le D \right\}^n}$
${\scriptstyle = Pr(Y_{id}\le y_{id}: 1\le i\le r, 1\le d\le D). \qquad (7.8)}$

If we assume a priori that the X process also has unit Fréchet margins, then we may take anid = n, bnid = 0.

 Anmerkungen Keine Kennzeichnung der Übernahme, kein Hinweis auf die Quelle. Obwohl es sich hier im Wesentlichen um eine Definition handelt, so sind doch auch erklärende Bemerkungen wörtlich übernommen worden. Fréchet ist in der Quelle richtig geschrieben; bei der Übernahme ist das Wort "margins" verlorengegangen Sichter (Graf Isolan) Plagiatsfischer

 Zuletzt bearbeitet: 2012-08-01 18:12:50 Hindemith

 Typus Verschleierung Bearbeiter Graf Isolan Gesichtet
Untersuchte Arbeit:
Seite: 160, Zeilen: 15-19, 20-23
Quelle: Smith 2003
Seite(n): 58, Zeilen: 13-15, 16-19
We simulate a sample of size 20.000 to test if the fitted M4 process is a realistic representation of the Frèchet-transformed time series and if it can be utilized in common measures in risk management. In a first look at the quality of the simulated data, we displayed a scatterplot among the sample paths simulated from the fitted process and observed if this sample looks similar to those from the original series. [...] One point to note here is that the data was generated so that the marginal distributions were exactly unit Frèchet. In order to provide a fair comparison with the original estimation procedure, the axes were rescaled so that a considerable number of points were present. One test of whether the fitted M4 process is a realistic representation of the Fréchet-transformed time series is whether the sample paths simulated from the fitted process look similar to those from the original series. [...] One point to note here is that although the data were generated so that the marginal distributions were exactly unit Fréchet, in order to provide a fair comparison with the original estimation procedure, the marginal distributions were re-estimated, and transformed according to the estimated parameters, before drawing the scatterplots in Fig. 43 and 44.
 Anmerkungen Keine Kennzeichnung der übernommenen Passagen; keine Quellenangabe. Im Rahmen der Anwendung der von Smith beschriebenen Methodik wurde Originaltext uebernommen. Fréchet ist in der Quelle richtig geschrieben. Sichter (Graf Isolan, KnallErbse) Plagiatsfischer