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Inverse transform sampling

Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, or the Smirnov transform) 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.

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Overview

Smirnov Pseudo-random number sampling Random Probability distribution Cumulative distribution function

17 related topics

Formal statement

Continuous random variables Inverse probability Probability integral transform Continuous random variable Uniform

5 related topics

The method

Generate a random number Power series

2 related topics

Proof of correctness

Infimum Right-continuous

2 related topics

Topics to explore

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Overview

Smirnov Nikolai Smirnov (mathematician)
Pseudo-random number sampling
Random
Probability distribution
Cumulative distribution function
Uniform samples Continuous uniform distribution
Normal distribution
Standard deviation
Quantile function
Inverting Inverse function
Discrete distribution
Continuous distribution
Probability density function
Rejection sampling
Analytical expression Closed-form expression
Box–Muller transform
Ziggurat algorithm

Formal statement

Continuous random variables Random variable
Inverse probability
Probability integral transform
Continuous random variable
Uniform Uniform distribution (continuous)

Intuition

Increasing function Monotonic function

The method

Generate a random number Pseudorandom number generator
Power series

Examples

Exponential distribution

Proof of correctness

Infimum
Right-continuous Càdlàg

Truncated distribution

Truncated distributions Truncated distribution

Reduction of the number of inversions

Polynomial chaos

Software implementations

Scipy.stats SciPy

Advanced semantic analysis

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Map overview Semantic statistics

Inverse transform sampling

Nodes41

Edges40

Triples9

Avg. degree1.95

Density0.04878

Components1

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Inverse transform sampling

Top relations

related to The method · 3

Inverse transform sampling → Let, The, We

related to Truncated distribution · 1

Inverse transform sampling → Inverse

Important terminology Word statistics

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Important terminology

distribution displaystyle function inverse number method sampling random uniform cumulative cdf transform normal variable probability -1 distributions generate samples example

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
those based on rejection sampling.For the normal distribution	instance of	it is a useful method for building more generally applicable samplers	0.80	text
the lack of an analytical expression for the corresponding quantile function means that other methods	instance of	it is a useful method for building more generally applicable samplers	0.80	text
the PDF or the CDF.C library UNU.RANR library RunuranPython subpackage sampling in scipy.stats See alsoProbability integral transformCopula	instance of	an approximation of the inverse can be computed if the user provides some information about the distributions	0.80	text
defined by means of probability integral transform.Quantile function	instance of	an approximation of the inverse can be computed if the user provides some information about the distributions	0.80	text
for the explicit construction of inverse CDFs.Inverse distribution function for a precise mathematical definition for distributions with discrete components.Rejection sampling is another common technique to generate random variates that does not rely on inversion of the CDF	instance of	an approximation of the inverse can be computed if the user provides some information about the distributions	0.80	text
Inverse transform sampling	related to The method	The	0.60	section
Inverse transform sampling	related to The method	Let	0.60	section
Inverse transform sampling	related to The method	We	0.60	section
Inverse transform sampling	related to Truncated distribution	Inverse	0.60	section

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