Пример: Моделирование методом Монте-Карло

Функции > План эксперимента > Моделирование методом Монте-Карло > Пример: Моделирование методом Монте-Карло

Используйте функцию montecarlo для генерирования случайных выборок, моделирующих функцию.

1. Задайте моделируемую функцию.

2. Задайте распределение каждого параметра.

Два элемента вектора dist относятся к функциям Normal и Uniform.

3. Задайте среднее значение и среднеквадратическое отклонение для каждого распределения. Сохраните результаты в матрице Rvals.

4. Задайте верхний предел параметра Y.

5. Задайте число генерируемых выборок.

6. Вызовите функцию montecarlo для генерации выборок.

Функция montecarlo возвращает матрицу из трех столбцов:

Щелкните для копирования этого выражения

Первые два столбца являются выборками, созданными для каждого из параметров. Последний столбец состоит из значений функции f для данных параметров.

7. Сохраните созданные значения в отдельных векторах.

Можно проверить, что последний вектор R1 действительно состоит из значений функции f.

8. Постройте график зависимости параметров друг от друга и покажите среднее значение.

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Выборки равномерно распределены по оси y и нормально распределены по оси x. Выборки со значением y больше 8.5 отброшены.

9. Вызовите функцию histogram для разделения значений y на 10 столбцов. Постройте гистограмму значений y.

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Значения y распределены равномерно. Выборки создаются в диапазоне 6 среднеквадратичных отклонений с каждой стороны среднего значения.

Если сгенерированные выборки выходят за верхний предел, они отбрасываются.

10. Вызовите функцию histogram для разделения значений x на 10 столбцов. Постройте гистограмму значений y и добавьте нормальное распределение.

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Значения x распределены в соответствии с нормальным распределением.

11. Постройте графики результатов для каждого из параметров.

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12. Вызовите конструкцию if для определения ограничений и замены результатов на значения NaN, если они не соответствуют ограничениям.

13. Постройте график зависимости параметров друг от друга.

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14. Постройте графики результатов для каждого из параметров.

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