page_title: ProbOnto
section_title: Log-normal distribution
hierarchical_section_title: ProbOnto / Knowledge base / Alternative parameterizations / Log-normal distribution
caption_attribution_description: English: seven parameterizations of the log-normal distribution
context_page_description: ProbOnto is a knowledge base and ontology of probability distributions. ProbOnto 2.5 contains over 150 uni- and multivariate distributions and alternative parameterizations, more than 220 relationships and re-parameterization formulas, supporting also the encoding of empirical and univariate mixture distributions.
context_section_description: In the case of the log-normal distribution there are more options. This is due to the fact that it can be parameterized in terms of parameters on the natural and log scale, see figure.
   
   
  The available forms in ProbOnto 2.0 are
  LogNormal1(μ,σ) with mean, μ, and standard deviation, σ, both on the log-scale
  LogNormal2(μ,υ) with mean, μ, and variance, υ, both on the log-scale
  LogNormal3(m,σ) with median, m, on the natural scale and standard deviation, σ, on the log-scale
  LogNormal4(m,cv) with median, m, and coefficient of variation, cv, both on the natural scale
  LogNormal5(μ,τ) with mean, μ, and precision, τ, both on the log-scale
  LogNormal6(m,σg) with median, m, and geometric standard deviation, σg, both on the natural scale
  LogNormal7(μN,σN) with mean, μN, and standard deviation, σN, both on the natural scale
  ProbOnto knowledge base stores such re-parameterization formulas to allow for a correct translation of models between tools.
caption: Overview of parameterizations of the log-normal distributions.
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