Inverse transform sampling (original) (raw)
Die Inversionsmethode ist ein Simulationsverfahren, um aus gleichverteilten Zufallszahlen andere Wahrscheinlichkeitsverteilungen zu erzeugen.
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| dbo:abstract | Die Inversionsmethode ist ein Simulationsverfahren, um aus gleichverteilten Zufallszahlen andere Wahrscheinlichkeitsverteilungen zu erzeugen. (de) El método de la transformada (o transformación) inversa, también conocido como método de la transformada integral de probabilidad inversa, es un método para la generación de números aleatorios de cualquier distribución de probabilidad continua cuando se conoce la inversa de su función de distribución (cdf). Este método es en general aplicable, pero puede resultar muy complicado obtener una expresión analítica de la inversa para algunas distribuciones de probabilidad. El método de Box-Muller es un ejemplo de algoritmo que aunque menos general, es más eficiente desde el punto de vista computacional. El método se utiliza para simular valores de las distribuciones exponencial, Cauchy, triangular, de Pareto y Weibull. (es) Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, Smirnov transform, or the golden rule) is a basic method for pseudo-random number sampling, i.e., for generating sample numbers at random from any probability distribution given its cumulative distribution function. Inverse transformation sampling takes uniform samples of a number between 0 and 1, interpreted as a probability, and then returns the largest number from the domain of the distribution such that . For example, imagine that is the standard normal distribution with mean zero and standard deviation one. The table below shows samples taken from the uniform distribution and their representation on the standard normal distribution. We are randomly choosing a proportion of the area under the curve and returning the number in the domain such that exactly this proportion of the area occurs to the left of that number. Intuitively, we are unlikely to choose a number in the far end of tails because there is very little area in them which would require choosing a number very close to zero or one. Computationally, this method involves computing the quantile function of the distribution — in other words, computing the cumulative distribution function (CDF) of the distribution (which maps a number in the domain to a probability between 0 and 1) and then inverting that function. This is the source of the term "inverse" or "inversion" in most of the names for this method. Note that for a discrete distribution, computing the CDF is not in general too difficult: we simply add up the individual probabilities for the various points of the distribution. For a continuous distribution, however, we need to integrate the probability density function (PDF) of the distribution, which is impossible to do analytically for most distributions (including the normal distribution). As a result, this method may be computationally inefficient for many distributions and other methods are preferred; however, it is a useful method for building more generally applicable samplers such as those based on rejection sampling. For the normal distribution, the lack of an analytical expression for the corresponding quantile function means that other methods (e.g. the Box–Muller transform) may be preferred computationally. It is often the case that, even for simple distributions, the inverse transform sampling method can be improved on: see, for example, the ziggurat algorithm and rejection sampling. On the other hand, it is possible to approximate the quantile function of the normal distribution extremely accurately using moderate-degree polynomials, and in fact the method of doing this is fast enough that inversion sampling is now the default method for sampling from a normal distribution in the statistical package R. (en) La méthode de la transformée inverse est une méthode permettant d'échantillonner une variable aléatoire X de loi donnée à partir de l'expression de sa fonction de répartition F et d'une variable uniforme sur [0, 1]. (fr) Il metodo dell'inversione, noto anche come trasformazione integrale di probabilità, è una tecnica per generare un campione di numeri casuali distribuiti secondo una data distribuzione casuale, nota la sua funzione di distribuzione di probabilità. Questo metodo è sufficientemente generico, ma può essere computazionalmente troppo oneroso in pratica per talune distribuzioni di probabilità. Una metodologia che applica un algoritmo meno generico ma computazionalmente più efficiente è la trasformata di Box-Muller. (it) 逆関数法（ぎゃくかんすうほう、英: inversion method, inverse transform method）とは、累積分布関数の逆関数を用いて、標準一様分布に従う確率変数から、所望の分布に従う確率変数を生成させる方法。逆関数サンプリング法（ぎゃくかんすうサンプリングほう、英: inverse transform sampling）とも呼ばれる。計算機シミュレーションにおいて、一様分布に従う乱数から、所望の乱数を生成させるのに用いられる。 (ja) Ме́тод обра́тного преобразова́ния (Преобразование Н. В. Смирнова) — способ генерации случайных величин с заданной функцией распределения, путём модификации работы генератора равномерно распределённых чисел. (ru) 逆变换采样（英語：inverse transform sampling），又称为逆万流齐一（inversion sampling）、逆概率积分变换（inverse probability integral transform）、逆变换法（inverse transformation method）、斯米尔诺夫变换（Smirnov transform）、黄金法则（golden rule）等，是的一种基本方法。在已知任意概率分布的累积分布函数时，可用于从该分布中生成随机样本。 假设为一个连续随机变量，其累积分布函数为。此时，随机变量服从区间[0, 1]上的均匀分布。逆变换采样即是将该过程反过来进行：首先对于随机变量，我们从0至1中随机均匀抽取一个数。之后，由于随机变量与有着相同的分布，即可看作是从分布中生成的随机样本。 (zh) |
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| rdfs:comment | Die Inversionsmethode ist ein Simulationsverfahren, um aus gleichverteilten Zufallszahlen andere Wahrscheinlichkeitsverteilungen zu erzeugen. (de) La méthode de la transformée inverse est une méthode permettant d'échantillonner une variable aléatoire X de loi donnée à partir de l'expression de sa fonction de répartition F et d'une variable uniforme sur [0, 1]. (fr) Il metodo dell'inversione, noto anche come trasformazione integrale di probabilità, è una tecnica per generare un campione di numeri casuali distribuiti secondo una data distribuzione casuale, nota la sua funzione di distribuzione di probabilità. Questo metodo è sufficientemente generico, ma può essere computazionalmente troppo oneroso in pratica per talune distribuzioni di probabilità. Una metodologia che applica un algoritmo meno generico ma computazionalmente più efficiente è la trasformata di Box-Muller. (it) 逆関数法（ぎゃくかんすうほう、英: inversion method, inverse transform method）とは、累積分布関数の逆関数を用いて、標準一様分布に従う確率変数から、所望の分布に従う確率変数を生成させる方法。逆関数サンプリング法（ぎゃくかんすうサンプリングほう、英: inverse transform sampling）とも呼ばれる。計算機シミュレーションにおいて、一様分布に従う乱数から、所望の乱数を生成させるのに用いられる。 (ja) Ме́тод обра́тного преобразова́ния (Преобразование Н. В. Смирнова) — способ генерации случайных величин с заданной функцией распределения, путём модификации работы генератора равномерно распределённых чисел. (ru) 逆变换采样（英語：inverse transform sampling），又称为逆万流齐一（inversion sampling）、逆概率积分变换（inverse probability integral transform）、逆变换法（inverse transformation method）、斯米尔诺夫变换（Smirnov transform）、黄金法则（golden rule）等，是的一种基本方法。在已知任意概率分布的累积分布函数时，可用于从该分布中生成随机样本。 假设为一个连续随机变量，其累积分布函数为。此时，随机变量服从区间[0, 1]上的均匀分布。逆变换采样即是将该过程反过来进行：首先对于随机变量，我们从0至1中随机均匀抽取一个数。之后，由于随机变量与有着相同的分布，即可看作是从分布中生成的随机样本。 (zh) Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, Smirnov transform, or the golden rule) is a basic method for pseudo-random number sampling, i.e., for generating sample numbers at random from any probability distribution given its cumulative distribution function. (en) El método de la transformada (o transformación) inversa, también conocido como método de la transformada integral de probabilidad inversa, es un método para la generación de números aleatorios de cualquier distribución de probabilidad continua cuando se conoce la inversa de su función de distribución (cdf). Este método es en general aplicable, pero puede resultar muy complicado obtener una expresión analítica de la inversa para algunas distribuciones de probabilidad. El método de Box-Muller es un ejemplo de algoritmo que aunque menos general, es más eficiente desde el punto de vista computacional. (es) |
| rdfs:label | Inversionsmethode (de) Método de la transformada inversa (es) Méthode de la transformée inverse (fr) Inverse transform sampling (en) Metodo dell'inversione (it) 逆関数法 (ja) Метод обратного преобразования (ru) 逆变换采样 (zh) |
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