International Journal of
Psychology and Counselling

  • Abbreviation: Int. J. Psychol. Couns.
  • Language: English
  • ISSN: 2141-2499
  • DOI: 10.5897/IJPC
  • Start Year: 2009
  • Published Articles: 222

Full Length Research Paper

Lognormal distribution for social researchers: A probability classic

José Moral de la Rubia
  • José Moral de la Rubia
  • School of Psychology, Facultad de Psicología, Universidad Autónoma de Nuevo León, Monterrey, Nuevo León, México.
  • Google Scholar

  •  Received: 05 February 2024
  •  Accepted: 31 May 2024
  •  Published: 30 June 2024


This academic article aims to present the lognormal distribution clearly, accompanied by an example applied to sexual behavior, facilitating understanding among social researchers. This distribution, characterized by positive skewness, thin shoulders, and heavy tails, serves as a robust probability model for various social and behavioral variables. It is developed from its two-parameter format, a location parameter (μ) and a squared scale parameter (σ²). The paper begins with a historical note on the relationship of the lognormal distribution to the normal distribution. The density, cumulative, and characteristic functions of the distribution are shown. Although it has an analytical expression for the nth order moment, it is not determined by its moments, lacking a moment generating function. Following the presentation of these functions, measures of central tendency, variability, and shape are discussed. The estimators of μ and σ² using the methods of moments and maximum likelihood are then introduced. Some of their mathematical properties and the calculation of dispersion intervals for 68.3, 95.4 and 99.7% of the data are presented. All this material is applied to two examples of probability calculation, descriptive measures, and parameter estimation related to sexual behavior. Finally, suggestions are provided for the practical application of the lognormal distribution.


Key words: Probability distribution, continuous variable, parameter estimation, arithmetic descriptive measures, geometric descriptive measures.