Beispiel: Monte-Carlo-Simulation

Funktionen > Statistische Versuchsplanung > Monte-Carlo-Simulation > Beispiel: Monte-Carlo-Simulation

Generieren Sie mit der Funktion montecarlo Zufallsstichproben, um eine Funktion zu simulieren.

1. Definieren Sie eine zu simulierende Funktion.

2. Definieren Sie die Verteilung jedes Parameters.

Die beiden Einträge im Vektor dist verweisen auf die Funktionen Normal und Uniform.

3. Definieren Sie den Mittelwert und die Standardabweichung jeder Verteilung. Verzeichnen Sie die Ergebnisse in Matrix Rvals.

4. Legen Sie einen oberen Grenzwert für Parameter Y fest.

5. Definieren Sie die Anzahl der zu generierenden Stichproben.

6. Rufen Sie montecarlo auf, um die Stichproben zu erzeugen.

Die Ausgabe der Funktion montecarlo ist eine Matrix mit drei Spalten:

Die ersten beiden Spalten enthalten die Stichproben, die für jeden Parameter erzeugt wurden. Die letzte Spalte ist die Ausgabe der Funktion f bei diesen Parametern.

7. Zeichnen Sie die generierten Werte in getrennten Vektoren auf.

Sie können prüfen, ob es sich bei dem letzten Vektor R1 tatsächlich um das Ergebnis der Funktion f handelt:

8. Stellen Sie die einzelnen Parameter und deren Mittelwert nebeneinander grafisch dar.

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Die Stichproben wurden an der Y-Achse gleichmäßig verteilt und an der X-Achse entsprechend der Normalverteilung angetragen. Strichproben mit einem y-Wert größer 8.5 wurden weggelassen.

9. Rufen Sie histogram auf, um die y-Werte in 10 Bins zu trennen. Plotten Sie ein Histogramm der y-Werte.

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Die y-Werte sind gleichmäßig verteilt. Die Stichproben werden erzeugt und enthalten auf beiden Seiten des Mittelwerts 6 Sigmas:

Wenn die generierten Stichproben größer als der obere Grenzwert sind, werden sie verworfen:

10. Rufen Sie histogram auf, um die x-Werte in 10 Bins zu trennen. Plotten Sie ein Histogramm der y-Werte und fügen Sie eine Normalverteilung hinzu.

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Die x-Werte sind normal verteilt.

11. Plotten Sie die Ergebnisse für jeden der Parameter.

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12. Rufen Sie das Spezialkonstrukt if auf, um Nebenbedingungen zu definieren und die Ergebnisse durch NaN-Werte zu ersetzen, wenn sie nicht den Nebenbedingungen entsprechen.

13. Stellen Sie die einzelnen Parameter nebeneinander grafisch dar.

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14. Plotten Sie die Ergebnisse für jeden der Parameter.

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