LogNormal Distribution Fitting

A lognormal distribution represents a statistical distribution of logarithmic values derived from a related normal distribution. In probability theory, it characterizes a continuous probability distribution of a random variable whose logarithm conforms to a normal distribution. Therefore, if the random variable X follows a lognormal distribution, then its natural logarithm, denoted as Y = ln(X), exhibits a normal distribution. Conversely, if Y adheres to a normal distribution, then the exponential function of Y, denoted as X = exp(Y), demonstrates a lognormal distribution. Notably, a random variable governed by a lognormal distribution exclusively assumes positive real values.

This distribution serves as a convenient and versatile model across diverse domains, including exact and engineering sciences, medicine, economics, and beyond. It finds application in various contexts, such as representing energies, concentrations, lengths, financial returns, and other quantities. The lognormal distribution's versatility stems from its ability to capture phenomena where values exhibit exponential growth or decay, making it a valuable tool for analyzing real-world data across a wide range of fields.

LogNormal Distribution


  • μ is the mean of samples in distribution or continuous location parameter

  • σ is the standard deviation or continuous shape parameter (> 0)

How To Cite

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Calculate the probability of the fitted distribution on: LogNormal Distribution Calculator

Paste the column data(>0) here. Use Excel, text, or any suitable format, with each sample on a separate line.

LogNormal Distribution:

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