Poisson Distribution

{
  "id": "MLC-T-ENV-021381",
  "term": "Poisson Distribution",
  "field": "Environment",
  "definition": "1. The Poisson distribution is used to model the number of events occurring within a given time interval. The formula for the Poisson probability mass function is [See PDF page 148 for formula http://water.epa.gov/scitech/swguidance/standards/upload/2007_10_01_criteria_humanhealth_microbial_thesaurus_microbial-thesaurus.pdf] for x=0,1,2, ... Λ is the shape parameter which indicates the average number of events in the given time interval.\n\n2. An important theoretical distribution used to model discrete events, especially the count of defects in an area. The Poisson distribution depends on one parameter, lambda, which represents the average defect density per observation area (or volume, time interval, etc.). The Poisson distribution assumes that the counts of defects in two non-overlapping observation units are independent. Further, the Poisson distribution assumes the distribution of defect counts depend only on the area in which they are to be observed. Unlike the binomial distribution, the Poisson distribution in principle sets no limit to the number of defects that can be observed in any area. Of particular interest the semi-conductor industry, the Poisson probability of observing zero defects in a region of area A, exp{-lambda A}, is useful for yield modeling.\n\n3. A distribution function used to describe the occurrence of rare events or to describe the sampling distribution of isolated counts in a continuum of time or space. This special probability distribution can apply to the number of discrete independent random events occurring in a given interval when knowing their average rate of occurrence over a very long interval.\n\n4. A Poisson distribution is a probability distribution that characterizes discrete events occurring independently of one another in time.\n\n5. Poisson distributions model (some) discrete random variables (i.e., variables that may take on only a countable number of distinct values, such as 0, 1, 2, 3, 4, ....). Typically, a Poisson random variable is a count of the number of events that occur in a certain time interval or spatial area (statistics). [FAO/WHO 2003b, STEPS 1997]\n\n6. The Poisson distribution is used to model the number of events occurring within a given time interval. .. Λ is the shape parameter which indicates the average number of events in the given time interval. [NIST/SEMATECH 2005a]\n\n7. An important theoretical distribution used to model discrete events, especially the count of defects in an area. The Poisson distribution depends on one parameter, lambda, which represents the average defect density per observation area (or volume, time interval, etc.). The Poisson distribution assumes that the counts of defects in two non-overlapping observation units are independent. Further, the Poisson distribution assumes the distribution of defect counts depend only on the area in which they are to be observed. Unlike the binomial distribution, the Poisson distribution in principle sets no limit to the number of defects that can be observed in any area. Of particular interest the semi-conductor industry, the Poisson probability of observing zero defects in a region of area A, exp{-lambda A}, is useful for yield modeling. [NIST/SEMATECH 2005b]\n\n8. Distribution describing the number of times an event occurs in a unit of time or space. Usually a sample of time or space is taken and the number of events recorded. [Choosing and Using Statistics: A Biologist's Guide]",
  "subject": "Health and safety",
  "references": [
    "NIST/SEMATECH 2005a",
    "NIST/SEMATECH 2005b",
    "National Cancer Institute Thesaurus",
    "USGS Earthquake Glossary",
    "Thesaurus of Terms Used in Microbial Risk Assessment",
    "Adapted from Thesaurus of Terms Used in Microbial Risk Assessment",
    "Environmental Sampling and Analytical Methods (ESAM) Program Glossary"
  ],
  "url": "https://mlchart.com/terminology/environment/poisson-distribution/"
}