Log-Normal Distribution
A distribution of a random variable whose logarithm is normally distributed. Common in finance and biology.
Probability Density FunctionPDF = f(x)
Cumulative Distribution FunctionCDF = F(x)
Probability in an Interval
Compute the probability that X falls between two values. For continuous distributions, this is the shaded area under the PDF (≤ vs < doesn't matter).
P(a ≤ X ≤ b)
Quantiles (Inverse CDF)
Pick a probability p and read the corresponding quantile xₚ where F(xₚ) = p.
Quantile xₚ (where F(xₚ) = p)
In Log-Normal Distribution, selected probability p: 0.9500 (95.00%)
Parameters
Adjust the parameters and (optionally) add up to 3 curves to compare different settings side‑by‑side.
0 curves shown
Estimating parameters from data
If you’re fitting this distribution to observed data, these are common plug‑in estimates you can start with.
Mean (log-space) (μ)
Take the mean of the log-transformed data: μ = mean(ln(x)).
Standard Deviation (log-space) (σ)
Take the standard deviation of the log-transformed data: σ = std(ln(x)).