Overview
Inverse transform sampling is exact when the inverse cumulative distribution function is available or easy to approximate.
CoreSource checked
Inverse Transform Sampling
Samples a target distribution by applying its inverse CDF to uniform random values.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Randomness & Sampling
- Difficulty
- Intermediate
- Family
- Distribution Sampling
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 6
- Code example
- Ready
- Visualization
- Ready
Core Concepts
uniform random valuecumulative distributioninverse cdfdistribution transform
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(1)
Average
O(sample count)
Worst
O(sample count)
Space
O(1)
When to Use
- Use when monte Carlo simulation needs uniform random value.
- Use when the input matches the assumptions behind distribution Sampling.
When Not to Use
- Avoid when independence, reproducibility, or distribution quality cannot be checked.
- Avoid when a simpler algorithm gives the required result with less setup.
What It Does
- Samples a target distribution by applying its inverse CDF to uniform random values
- Uses uniform random value and cumulative distribution to guide the work.
- Produces samples.
Use Cases
- Monte Carlo simulation
- Randomized algorithms
- Sampling distributions
Inputs
- Random source
- Distribution or weights
- Sample count
Outputs
- Samples
- Estimated statistic
- Randomized selection
Key Formulas (1)
Inverse transform sample
x = Finverse(u)
x = F_inverse(u)Transforms a uniform random value into a sample from the target distribution.
Pseudocode
- 1.Initialize the random source, sequence state, or sampler parameters
- 2.Generate the next candidate, variate, or structured random choice
- 3.Accept, transform, weight, or record the value according to the method
- 4.Repeat until the requested sample count or stopping rule is reached
Canonical Example
- Input
- seed = 7, sample count = 5, and a small target distribution or domain
- Output
- Samples
- Explanation
- Inverse Transform Sampling applies uniform random value to produce samples.
Implementation Notes
- Expose seed handling when reproducibility is important.
- Keep the uniform random value step separate enough to test independently.
- Separate the random source from the sampler so tests can use fixed seeds and distribution checks.
Common Pitfalls
- Using a biased random source can quietly invalidate downstream estimates.
- Test edge cases, not only clean examples.
- Uncontrolled seeds or biased random choices can make results irreproducible or statistically misleading.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryPlot generated samples against the target distribution or domain.
Step 1 of 4: Initialize the random source, sequence state, or sampler parameters
randomness-sampling-mechanismNotes
Inverse Transform Sampling should be used with the assumptions and tradeoffs of distribution Sampling in mind.
Sources (1)
What each reference supports for this entry.
Non-Uniform Random Variate Generation
BookRandom variate generation reference for Inverse Transform Sampling inverse CDF sampling and random variate transformation.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Alternative toAlias Method
Randomness & Sampling · Core
For discrete distributions, alias tables provide faster repeated sampling.
Compare with thisAlternativesAlias Table Construction
Randomness & Sampling · Core
Inverse transform can sample from cumulative weights, while alias tables preprocess for constant-time draws.
Compare with thisRelationships
View full relationship pageAlternative toAlias Method
For discrete distributions, alias tables provide faster repeated sampling.
Alternative toRejection Sampling
Inverse transform sampling uses an inverse CDF instead of proposal rejection.
Related Algorithms
Tags
Randomness & SamplingInverse TransformSamplingProbability