The inverse transform is a mathematical technique used to generate random samples from a probability distribution by applying the inverse of its cumulative distribution function (CDF) to uniformly distributed random numbers. This method is particularly useful in simulations and is applicable when the CDF is invertible, allowing for straightforward implementation in generating random variates from continuous distributions.

Inverse Transform

inverse transform

mathematical technique

random samples

A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment. It is fundamental in statistics and data analysis, helping to model and predict real-world phenomena by describing how probabilities are distributed over values of a random variable.

probability distribution

A Cumulative Distribution Function (CDF) represents the probability that a random variable takes on a value less than or equal to a specific value, providing a complete description of the probability distribution of a real-valued random variable. The CDF is a non-decreasing, right-continuous function that ranges from 0 to 1, capturing the cumulative probability across the entire range of possible values.

cumulative distribution function

uniformly distributed random numbers

Simulations are computational models that replicate real-world processes or systems to predict outcomes, analyze scenarios, and enhance understanding without the risks or costs of real-world experimentation. They are crucial in fields ranging from physics and engineering to economics and healthcare, providing insights that guide decision-making and innovation.

simulations

Invertible CDF

random variates

Continuous distributions describe the probabilities of outcomes for continuous random variables, where the set of possible outcomes is uncountably infinite. These distributions are characterized by probability density functions (PDFs) and are integral in fields like statistics and machine learning for modeling real-world phenomena.

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