Lognormal Parameter Conversion Calculator
Converts an arithmetic mean and standard deviation into the normal parameters of a lognormal model. The form displays sigma²=ln(1+v/m²); mu=ln(m)−sigma²/2 beside lognormal parameters, using a worked condition that can be recalculated with the labeled inputs.
Enter the source values under the stated assumptions
Lognormal parameters
Scope of the lognormal parameter conversion method
The lognormal parameter conversion page converts an arithmetic mean and standard deviation into the normal parameters of a lognormal model.
Lognormal parameters is limited to the statistical quantity named by the result panel. The lognormal parameters calculation does not silently add a population, time horizon, causal direction, or decision threshold that is absent from the fields.
Before entering the lognormal parameter conversion data
- Arithmetic mean: For lognormal parameters, the worked value for arithmetic mean is 10 units. Treat the arithmetic mean entry (10 units) explicitly as a count, proportion, rate, estimate, or model parameter before comparing lognormal parameters conditions. The form enforces minimum 1e-06.
- Arithmetic SD: For lognormal parameters, the worked value for arithmetic sd is 6 units. Treat the arithmetic sd entry (6 units) explicitly as a count, proportion, rate, estimate, or model parameter before comparing lognormal parameters conditions. The form enforces minimum 1e-06.
The entries used for lognormal parameters must refer to one coherent analysis condition. Combining incompatible populations, periods, or measurement definitions can produce valid lognormal parameters arithmetic for a nonexistent study.
How lognormal parameters is calculated
For lognormal parameters, match every symbol in the relationship to a labeled field before substituting numbers. Lognormal parameters is reported in log units.
While checking lognormal parameters, inspect every denominator in sigma²=ln(1+v/m²); mu=ln(m)−sigma²/2. For lognormal parameters, a zero or near-zero denominator can make lognormal parameters undefined or unstable.
A reproducible lognormal parameter conversion case
The default lognormal parameters condition is Arithmetic mean = 10 units, Arithmetic SD = 6 units.
Mean 10 and SD 6 give mu about 2.149 and sigma about .555.
The live calculator reports Log-scale mean 2.1488427 · Log-scale SD 0.55451303. Repeating one intermediate step from sigma²=ln(1+v/m²); mu=ln(m)−sigma²/2 provides a fixed lognormal parameters reference check for later code changes.
Conditions attached to lognormal parameters
Both arithmetic inputs must be positive and describe the same population scale.
For lognormal parameter conversion, distribution calculations depend on parameterization and support. For lognormal parameter conversion, two programs can use the same distribution name while assigning different meanings to a rate, scale, or tail probability.
Reading lognormal parameters in context
When interpreting lognormal parameter conversion, confirm the parameter convention and whether the requested quantity is a density, probability, quantile, moment, or standardized value.
As a second check for lognormal parameters, reversing the numerator and denominator answers a different question, so retain the direction printed in sigma²=ln(1+v/m²); mu=ln(m)−sigma²/2.
A controlled sensitivity check for lognormal parameters
Change arithmetic mean while holding the remaining entries fixed, then state why the direction and size of the lognormal parameters change are plausible from sigma²=ln(1+v/m²); mu=ln(m)−sigma²/2.
Repeat the lognormal parameters exercise with arithmetic sd. If a modest defensible change materially alters the interpretation, report both conditions rather than presenting that lognormal parameters scenario as exact.
When the analysis changes, compare lognormal mean median and mode.
Reporting lognormal parameters reproducibly
Report lognormal parameters using sigma²=ln(1+v/m²); mu=ln(m)−sigma²/2, followed by the entered values, units, exclusions, and analysis date. Name the lognormal parameters population or dataset boundary instead of leaving it implicit.
Keep the full calculator output with the record, including Log-scale mean 2.1488427 · Log-scale SD 0.55451303. A later lognormal parameters review can then distinguish a changed input from a different convention or software implementation.
Questions about lognormal parameters
How should lognormal parameters be rounded?
Keep the unrounded lognormal parameters for subsequent arithmetic, then report only the precision supported by the source measurements and the decision context. Extra digits in lognormal parameters do not correct sampling or model error.
Which input deserves the closest boundary check?
For lognormal parameters, start with arithmetic sd and then arithmetic mean. Confirm the lognormal parameters units and allowed domain because a valid-looking entry can still describe the wrong statistical setup.
Why could another program report a different lognormal parameters?
A different convention for rounding, tails, ties, interpolation, parameterization, or missing values can change lognormal parameters. Compare the printed lognormal parameters formula and its input definitions before treating either output as wrong.
What does lognormal parameters represent on this page?
It is the quantity produced by sigma²=ln(1+v/m²); mu=ln(m)−sigma²/2 from the displayed arithmetic mean, arithmetic sd. This page converts an arithmetic mean and standard deviation into the normal parameters of a lognormal model.
What should be saved with lognormal parameters?
Save the entered values and units for arithmetic mean, arithmetic sd, along with the analysis date, exclusions, software or formula version, and the relationship sigma²=ln(1+v/m²); mu=ln(m)−sigma²/2. That record is sufficient to rebuild this specific lognormal parameters calculation.
Does lognormal parameters establish a causal or population conclusion?
No. The displayed lognormal parameter conversion value is conditional on the entered data and named method. The lognormal parameters design, measurement process, and assumptions determine what can be concluded beyond those values.