What Is the Lognormal Distribution Calculator?
A lognormal distribution calculator evaluates central tendency and dispersion for positive-valued right-skewed variables.
How Does the Lognormal Distribution Calculator Work?
Applies exponentiated moment-generating equations from underlying Gaussian variables.
Lognormal Distribution Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Mean = exp(μ + σ²/2) · Median = exp(μ) · Mode = exp(μ - σ²)
Converts logarithmic parameters into real arithmetic values through exponentiation.
How to Use the Lognormal Distribution Calculator
- Input log-scale location parameter μ and scale parameter σ.
Step-by-Step Example Calculation
Standard parameters μ = 0, σ = 1
Input Values:
mu:0
sigma:1
Understanding Your Result
Shows true arithmetic mean, geometric median, peak probability mode, and standard deviation.
Factors That Affect the Result
- Scale parameter σ dictates rightward skewness and disparity between mode and mean.
When Should You Use This Calculator?
- Quantitative finance asset returns, biological incubation periods, and geological mineral concentrations.
Assumptions & Limitations
- Applies strictly to positive continuous random variables.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard mathematical lognormal parametric formulations.