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Lognormal Distribution Calculator — result sheet
Calculate lognormal density, cumulative probability, reliability, mean, and median from a median scale and shape parameter.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: CDF=Φ((ln(x)−ln(T50))/σ); PDF=exp(−z²/2)/(σx√(2π)); mean=T50 exp(σ²/2); median=T50.
The two-parameter lognormal model treats the natural logarithm of the positive variable as normally distributed.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Median or T50 scale — minimum 1.0E-6; maximum 1000000000000
- Log-space shape sigma — minimum 1.0E-6; maximum 100
- Evaluation value — minimum 1.0E-6; maximum 1000000000000
Worked example
| Input | Value |
|---|---|
| Median or T50 scale | 10 |
| Log-space shape sigma | 0.5 |
| Evaluation value | 12 |
CDF ≈ 0.642; PDF ≈ 0.062; mean ≈ 11.331; median = 10.
Assumptions and limits
- The evaluated value, scale, and shape are positive.
- The model is a two-parameter lognormal distribution with zero location shift.
- Distribution fit, censoring, failure mechanisms, and forecast validity are not inferred.
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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