chi-squared distribution

{
  "id": "MLC-T-ENV-004874",
  "term": "chi-squared distribution",
  "field": "Environment",
  "definition": "1. The chi-square distribution results when υ independent variables with standard normal distributions are squared and summed. The formula for the probability density function of the chi-square distribution is [See PDF page 127 for formula http://water.epa.gov/scitech/swguidance/standards/upload/2007_10_01_criteria_humanhealth_microbial_thesaurus_microbial-thesaurus.pdf] Where υ is the shape parameter and Γ is the gamma function. The formula for the gamma function is [See PDF page 127 for formula http://water.epa.gov/scitech/swguidance/standards/upload/2007_10_01_criteria_humanhealth_microbial_thesaurus_microbial-thesaurus.pdf] In a testing context, the chi-square distribution is treated as a \"standardized distribution\" (i.e., no location or scale parameters). However, in a distributional modeling context (as with other probability distributions), the chi-square distribution itself can be transformed with a location parameter, µ, and a scale parameter, σ.\n\n2. A mathematical distribution whose shape is determined by its one parameter, the degree(s) of freedom (df). This distribution is often used in inferential statistics in tests of significance.\n\n3. The chi-square distribution results when υ independent variables with standard normal distributions are squared and summed.... In a testing context, the chi-square distribution is treated as a \"standardized distribution\" (i.e., no location or scale parameters). However, in a distributional modeling context (as with other probability distributions), the chi-square distribution itself can be transformed with a location parameter, µ, and a scale parameter, σ.[NIST/SEMATECH 2005a]\n\n4. A distribution in which a variable is distributed like the sum of the squares of any given independent random variable, each of which has a normal distribution with mean of zero and variance of one. [CancerWeb 2005]",
  "subject": "Health and safety",
  "references": [
    "NIST/SEMATECH 2005a",
    "National Cancer Institute Thesaurus",
    "Adapted from Thesaurus of Terms Used in Microbial Risk Assessment",
    "Thesaurus of Terms Used in Microbial Risk Assessment"
  ],
  "url": "https://mlchart.com/terminology/environment/chi-squared-distribution/"
}