Gamma Distribution

{
  "id": "MLC-T-ENV-012010",
  "term": "Gamma Distribution",
  "field": "Environment",
  "definition": "1. A unimodal statistical distribution (relative proportion of responders as a function of some measure) that is restricted to effects greater than or equal to zero that can describe a wide variety of shapes, e.g., flat, peaked, asymmetrical.\n\n2. The general formula for the probability density function of the gamma distribution is [See PDF page 134 for formula http://water.epa.gov/scitech/swguidance/standards/upload/2007_10_01_criteria_humanhealth_microbial_thesaurus_microbial-thesaurus.pdf] Where γ is the shape parameter, µ is the location parameter, β is the scale parameter, and Γ is the gamma function which has the formula [See PDF page 134 for formula http://water.epa.gov/scitech/swguidance/standards/upload/2007_10_01_criteria_humanhealth_microbial_thesaurus_microbial-thesaurus.pdf] The case where µ = 0 and β = 1 is called the standard gamma distribution. The equation for the standard gamma distribution reduces to [See PDF page 134 for formula http://water.epa.gov/scitech/swguidance/standards/upload/2007_10_01_criteria_humanhealth_microbial_thesaurus_microbial-thesaurus.pdf] The gamma is a flexible life distribution model that may offer a good fit to some sets of failure data. It is not, however, widely used as a life distribution model for common failure mechanisms. A common use of the gamma model occurs in Bayesian reliability applications.\n\n3. A two-parameter family of continuous probability distributions, with a scale parameter theta and a shape parameter k.\n\n4. The general formula for the probability density function of the gamma distribution is where γ is the shape parameter, µ is the location parameter, β is the scale parameter, and Γ is the gamma function which has the formula The case where µ = 0 and β = 1 is called the standard gamma distribution. The equation for the standard gamma distribution reduces to. (etc) The gamma is a flexible life distribution model that may offer a good fit to some sets of failure data. It is not, however, widely used as a life distribution model for common failure mechanisms. A common use of the gamma model occurs in Bayesian reliability applications. [NIST/SEMATECH 2005a]\n\n5. The gamma is a flexible life distribution model that may offer a good fit to some sets of failure data. It is not, however, widely used as a life distribution model for common failure mechanisms. A common use of the gamma model occurs in Bayesian reliability applications. [NIST/SEMATECH 2005a]",
  "subject": "Science and research",
  "references": [
    "Benchmark Dose Software (BMDS) Glossary of Terms",
    "NIST/SEMATECH 2005a",
    "National Cancer Institute Thesaurus",
    "See MRA Thesaurus",
    "Thesaurus of Terms Used in Microbial Risk Assessment"
  ],
  "url": "https://mlchart.com/terminology/environment/gamma-distribution/"
}