Inverse transform sampling

Inverse transform sampling is a method for generating random numbers from a probability distribution by inverting its cumulative distribution function (CDF). This method is also known as the inverse probability integral transform or the inverse transformation method. It can be used for any probability distribution as long as its CDF can be analytically or numerically inverted. The algorithm is used to generate independent and identically distributed (i.i.d.) random samples for each distribution under consideration.From: Numerical Methods, Algorithms and Tools in C# [2019], Solving inventory routing with transshipment and substitution under dynamic and stochastic demands using genetic algorithm and deep reinforcement learning [2022]

Acoustic Wave Propagation

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Published in Indrakshi Dey, Propagation Modeling for Wireless Communications, 2022

Indrakshi Dey

Inverse transform sampling allows us to generate an arbitrary probability distribution from a uniform distribution. In this case, letting F(fm)=u to be a uniform distribution in [0,1], the transformation fm=−α[∑k=01/β−1(k+1)!W{1k((mod(2u,1))β2β−1)1/k}]1/β

Application of continuous Markov-chain Monte-Carlo method to multi-unit risk evaluations considering interdependence of accident progression among multiple units

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Published in Journal of Nuclear Science and Technology, 2021

Kento Sawada, Akio Yamamoto, Tomohiro Endo, Chikahiro Sato, Keisuke Maeda, Sunghyon Jang

The inverse transform sampling is effective, but there are several potential limitations. First, the cumulative probability should be given as a function or a numerical table before samplings in the CMMC coupling method. Therefore, when the cumulative probability depends on an accident sequence, the direct application of the inverse transform sampling may be difficult. Second, the application of the inverse transform sampling will be more complicated when many parameters are simultaneously considered.

Solving inventory routing with transshipment and substitution under dynamic and stochastic demands using genetic algorithm and deep reinforcement learning

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Published in International Journal of Production Research, 2022

Fatima Ezzahra Achamrah, Fouad Riane, Sabine Limbourg

We used the Inverse Transform Sampling (Algorithm 2) to generate independent and identical distributed (i.i.d.) random sample for realizations for each distribution under consideration.

Inverse transform sampling

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Acoustic Wave Propagation

Application of continuous Markov-chain Monte-Carlo method to multi-unit risk evaluations considering interdependence of accident progression among multiple units

Solving inventory routing with transshipment and substitution under dynamic and stochastic demands using genetic algorithm and deep reinforcement learning