Cumulative Distribution Function

{
  "id": "MLC-T-ENV-007074",
  "term": "Cumulative Distribution Function",
  "field": "Environment",
  "definition": "1. Cumulative distribution functions are particularly useful for describing the likelihood that a variable will fall within different ranges of x. F(x) (i.e., the value of y at x in a CDF plot) is the probability that a variable will have a value less than or equal to x.\n\n2. The CDF is alternatively referred to in the literature as the distribution function, cumulative frequency function, or the cumulative probability function. The cumulative distribution function, F(x), expresses the probability the random variable X assumes a value less than or equal to some value x, F(x) = Prob (X # x). For continuous random variables, the cumulative distribution function is obtained from the probability density function by integration, or by summation in the case of discrete random variables.\n\n3. The risk of a common toxic effect associated with concurrent exposure by all relevant pathways and routes of exposure to a group of chemicals that share a common mechanism of toxicity.\n\n4. All random variables (discrete and continuous) have a cumulative distribution function. It is a function giving the probability that the random variable X is less than or equal to x, for every value x. Formally, the cumulative distribution function F(x) is defined to be: F(x) = P(X ≤ x) for -∞ < x < ∞\n\n5. A graph that shows the cumulative probability of occurrence for a random independent variable. The cumulative probability is typically given as the y-axis, ranging from 0 to 1.0. Each value c of the function is the probability that a random observation x will be less than or equal to c. Mathematically, the function that defines the CDF is obtained from the PDF by integration (in the case of a continuous random variable) or by summation (for discrete random variables).\n\n6. The risk of a common toxic effect associated with concurrent exposure by all relevant pathways and routes of exposure to a group of chemicals that share a common mechanism of toxicity. [EPA 2005e]\n\n7. The CDF is alternatively referred to in the literature as the distribution function, cumulative frequency function, or the cumulative probability function. The cumulative distribution function, F(x), expresses the probability the random variable X assumes a value less than or equal to some value x, F(x) = Prob (X # x). For continuous random variables, the cumulative distribution function is obtained from the probability density function by integration, or by summation in the case of discrete random variables. [EPA 2004]\n\n8. Cumulative distribution functions are particularly useful for describing the likelihood that a variable will fall within different ranges of x. F(x) (i.e., the value of y at x in a CDF plot) is the probability that a variable will have a value less than or equal to x. [EPA 1998a]\n\n9. For a discrete random variable, the cumulative distribution function is found by summing up the probabilities. For a continuous random variable, the cumulative distribution function is the integral of its probability density function. [STEPS 1997]",
  "abbreviation": "CDF",
  "subject": "Health and safety",
  "references": [
    "Waste and Cleanup Risk Assessment Glossary; EPA 1998a",
    "EPA 2004",
    "EPA 2005e",
    "Thesaurus of Terms Used in Microbial Risk Assessment",
    "EPA Definitions of Terms Relevant to PRA and References for Further Reading at http://www.epa.gov/oswer/riskassessment/rags3adt/pdf/appendixe.pdf"
  ],
  "url": "https://mlchart.com/terminology/environment/cumulative-distribution-function/"
}