Lognormal Distribution

{
  "id": "MLC-T-ENV-016015",
  "term": "Lognormal Distribution",
  "field": "Environment",
  "definition": "1. A variable X is lognormally distributed if Y = LN(X) is normally distributed with \"LN\" denoting the natural logarithm. The general formula for the probability density function of the lognormal distribution is [See PDF page 138 for formula http://water.epa.gov/scitech/swguidance/standards/upload/2007_10_01_criteria_humanhealth_microbial_thesaurus_microbial-thesaurus.pdf] where σ is the shape parameter, Θ is the location parameter and m is the scale parameter. The case where Θ = 0 and m = 1 is called the standard lognormal distribution. The case where Θ equals zero is called the 2-parameter lognormal distribution. The equation for the standard lognormal distribution is [See PDF page 138 for formula http://water.epa.gov/scitech/swguidance/standards/upload/2007_10_01_criteria_humanhealth_microbial_thesaurus_microbial-thesaurus.pdf]\n\n2. If a variable y is such that x = log y, it is said to have a lognormal distribution; this is a skew distribution. [CancerWeb 2005]\n\n3. If a variable Y is such that X = log Y is normally distributed, it is said to have lognormal distribution. This is a skew distribution. [Last 1983]\n\n4. A variable X is lognormally distributed if Y = LN(X) is normally distributed with \"LN\" denoting the natural logarithm. The general formula for the probability density function of the lognormal distribution is ... where σ is the shape parameter, Θ is the location parameter and m is the scale parameter. The case where Θ = 0 and m = 1 is called the standard lognormal distribution. The case where Θ equals zero is called the 2-parameter lognormal distribution. The equation for the standard lognormal distribution is ...] [NIST/SEMATECH 2005a]\n\n5. Distribution of frequencies that is symmetric (i.e. bell shaped) when plotted on a logarithmic abscissa.\n\n6. An important probability distribution when analyzing environmental data where normality cannot be assumed. Bounded on the left by 0, has a fatter right-tail than the normal distribution, and has a right-skewed shape. [EPA/240/B-06/003]\n\n7. An important probability distribution when analyzing environmental data where normality cannot be assumed. Bounded on the left by 0, has a fatter right-tail than the normal distribution, and has a right-skewed shape.",
  "subject": "Science and research",
  "references": [
    "NIST/SEMATECH 2005a",
    "Thesaurus of Terms Used in Microbial Risk Assessment",
    "Adapted from Thesaurus of Terms Used in Microbial Risk Assessment",
    "Basic Concepts in Environmental Sciences",
    "Environmental Sampling and Analytical Methods (ESAM) Program Glossary",
    "EPA/240/B-06/003"
  ],
  "url": "https://mlchart.com/terminology/environment/lognormal-distribution/"
}