geometric distribution

{
  "id": "MLC-T-ENV-012263",
  "term": "geometric distribution",
  "field": "Environment",
  "definition": "1. A discrete, statistical distribution which is described by the probability density function: p(k) = p (1-p)^(k-1). It is the discreet analog of the exponential distribution.\n\n2. Geometric distributions model (some) discrete random variables. Typically, a geometric random variable is the number of trials required to obtain the first failure, for example, the number of tosses of a coin until the first \"tail\" is obtained, or a process where components from a production line are tested, in turn, until the first defective item is found. A discrete random variable X is said to follow a geometric distribution with parameter p, written X ~ Ge(p), if it has probability distribution where x = 1, 2, 3, ... p = success probability; 0 < p < 1 The trials must meet the following requirements: a) the total number of trials is potentially infinite; b) there are just two outcomes of each trial; success and failure; c) the outcomes of all the trials are statistically independent; d) all the trials have the same probability of success. The geometric distribution has expected value E(X)= 1/(1-p) and variance V(X)=p/{(1-p)²}. The geometric distribution is related to the binomial distribution in that both are based on independent trials in which the probability of success is constant and equal to p. However, a geometric random variable is the number of trials until the first failure, whereas a binomial random variable is the number of successes in n trials. [STEPS 1997]",
  "references": [
    "National Cancer Institute Thesaurus",
    "Thesaurus of Terms Used in Microbial Risk Assessment"
  ],
  "url": "https://mlchart.com/terminology/environment/geometric-distribution/"
}