Inverse Transformationsstichprobe
Inverse Transform Sampling is a statistical technique used to generate random samples from a specified probability distribution. The method utilizes the kumulative Verteilungsfunktion (CDF) of the distribution, which describes the probability that a random variable takes a value less than or equal to a given point.
Der Prozess beginnt damit, eine gleichverteilte Zufallszahl zu generieren, U, from the interval [0, 1]. This value represents a probability. The next step is to apply the inverse of the CDF, denoted as F-1(U), to this random number. The result is a sample X gezogen aus der gewünschten Verteilung.
Zum Beispiel, wenn Sie aus einer exponentiellen Verteilung with rate parameter λ, you would first generate a uniform random number, U. Then, you would compute the inverse CDF (or quantile function) for the exponential distribution, which is X = -ln(1 – U) / λ. This will yield a random sample from the exponential distribution.
Inverse Transform Sampling is particularly useful because it provides a straightforward way to sample from various distributions, making it a popular choice in Monte Carlo simulations and probabilistische Modelle. However, it is important to note that this method may not be efficient for all distributions, especially those without a simple or computable inverse CDF.