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Rayleigh Distribution PDF and CDF Calculator — result sheet
Calculate the probability density, cumulative probability, mean, and standard deviation for a Rayleigh value.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: PDF=(x/σ²)e^(−x²/(2σ²)); CDF=1−e^(−x²/(2σ²)); mean=σ√(π/2); SD=σ√((4−π)/2).
The page exposes the Rayleigh model’s density and cumulative probability at one value along with its two summary measures.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Value x — minimum 0; maximum 1000000
- Scale parameter σ — minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Value x | 2 |
| Scale parameter σ | 1 |
PDF ≈0.2707; CDF ≈0.8647; mean ≈1.2533; SD ≈0.6551.
Assumptions and limits
- Value is nonnegative and scale is positive.
- The continuous Rayleigh distribution applies to the supplied scale.
- Data fitting, censoring, uncertainty, and alternative distributions are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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