Uniform distribution

{
  "id": "MLC-T-ENV-029104",
  "term": "Uniform distribution",
  "field": "Environment",
  "definition": "1. The general formula for the probability density function of the uniform distribution is f(x) = 1/(B-A) for A ≤ x ≤ B where A is the location parameter and (B - A) is the scale parameter. The case where A = 0 and B = 1 is called the standard uniform distribution. The equation for the standard uniform distribution is f(x) = 1 for 0 ≤ x ≤ 1 The uniform distribution defines equal probability over a given range for a continuous distribution. For this reason, it is important as a reference distribution.\n\n2. Uniform distributions model (some) continuous random variables and (some) discrete random variables. The values of a uniform random variable are uniformly distributed over an interval. For example, if buses arrive at a given bus stop every 15 minutes, and you arrive at the bus stop at a random time, the time you wait for the next bus to arrive could be described by a uniform distribution over the interval from 0 to 15. A discrete random variable X is said to follow a Uniform distribution with parameters a and b, written X ~ Un(a,b), if it has probability distribution P(X=x) = 1/(b-a) where x = 1, 2, 3, ......., n. A discrete uniform distribution has equal probability at each of its n values. A continuous random variable X is said to follow a Uniform distribution with parameters a and b, written X ~ Un(a,b), if its probability density function is constant within a finite interval [a,b], and zero outside this interval (with a less than or equal to b). The uniform distribution has expected value E(X)=(a+b)/2 and variance {(b-a)²}/12.\n\n3. A continuous statistical distribution whose variable of interest has a single probability of occurrence over all possible values.",
  "subject": "Measurements",
  "references": [
    "NIST/SEMATECH 2005a; Thesaurus of Terms Used in Microbial Risk Assessment",
    "STEPS 1997; Thesaurus of Terms Used in Microbial Risk Assessment",
    "National Cancer Institute Thesaurus"
  ],
  "url": "https://mlchart.com/terminology/environment/uniform-distribution/"
}