29. Lognormal Distribution

  1. Catherine Forbes1,
  2. Merran Evans1,
  3. Nicholas Hastings2 and
  4. Brian Peacock3

Published Online: 16 DEC 2010

DOI: 10.1002/9780470627242.ch29

Statistical Distributions, Fourth Edition

Statistical Distributions, Fourth Edition

How to Cite

Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2010) Lognormal Distribution, in Statistical Distributions, Fourth Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470627242.ch29

Author Information

  1. 1

    Monash University, Victoria, Australia

  2. 2

    Albany Interactive, Victoria, Australia

  3. 3

    Brian Peacock Ergonomics, SIM University, Singapore

Publication History

  1. Published Online: 16 DEC 2010
  2. Published Print: 29 NOV 2010

ISBN Information

Print ISBN: 9780470390634

Online ISBN: 9780470627242



  • hazard function;
  • lognormal distribution;
  • parameter estimation;
  • probability density function;
  • random number;
  • variate


The lognormal distribution is applicable to random variables that are constrained by zero but have a few very large values. The resulting distribution is asymmetrical and positively skewed. Examples for lognormal distribution include the following: the weight of adults, the concentration of minerals in deposits, duration of time off due to sickness, distribution of wealth and machine down times. The application of a logarithmic transformation to the data can allow the data to be approximated by the symmetrical normal distribution, although the absence of negative values may limit the validity of this procedure. This chapter illustrates probability density function, distribution function and Hazard function for the lognormal variate. It discusses variate relationships, parameter estimation and random number generation for the lognormal variate.

Controlled Vocabulary Terms

control variate; hazard function; log-normal distribution; normal distribution; probability density function; random variables