Title: logarithmic normal distribution
Long Title: IUPAC Gold Book - logarithmic normal distribution
DOI: 10.1351/goldbook.L03611
Status: current

Definition
A continuous distribution with the differential mass-distribution function of the form: \[f_{\rm{w}}(x)\ \rm{d}x = \frac{1}{a\ \sqrt{\pi \ x}}\ \exp (- \frac{1}{a^{2}}\ \ln ^{2}\frac{x}{b})\ \rm{d}x\] where \(x\) is a parameter characterizing the chain length, such as relative molecular mass or degree of polymerization and \(a\) and \(b\) are positive adjustable parameters.

Related Terms
- chain length: https://goldbook.iupac.org/terms/view/C00956
- degree of polymerization: https://goldbook.iupac.org/terms/view/D01569
- mass-distribution function: https://goldbook.iupac.org/terms/view/M03716
- relative molecular mass: https://goldbook.iupac.org/terms/view/R05271

Source
- Purple Book, 1st ed., p. 57 (http://old.iupac.org/publications/books/author/metanomski.html)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/L03611/html
- json: https://goldbook.iupac.org/terms/view/L03611/json
- xml: https://goldbook.iupac.org/terms/view/L03611/xml

Citation: Citation: 'logarithmic normal distribution' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.L03611
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Accessed: 2026-08-10T01:52:03+00:00