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In probability and statistics, the PERT distributions are a family of continuous probability distributions defined by the minimum (a), most likely (b) and maximum (c) values that a variable can take. It is a transformation of the four-parameter beta distribution with an additional assumption that its expected value is
Based on the assumption that a PERT distribution governs the data, several estimates are possible. These values are used to calculate an E value for the estimate and a standard deviation (SD) as L-estimators, where: E = (a + 4m + b) / 6 SD = (b − a) / 6
PERT provides for potentially reduced project duration due to better understanding of dependencies leading to improved overlapping of activities and tasks where feasible. The large amount of project data can be organized and presented in diagram for use in decision making. PERT can provide a probability of completing before a given time.
Program Evaluation and Review Technique, commonly abbreviated PERT, is a statistical tool, used in project management to analyze and represent the tasks involved in completing a given project. PERT network chart for a seven-month project with five milestones (10 through 50) and six activities (A through F).
The Dirac delta function, although not strictly a probability distribution, is a limiting form of many continuous probability functions. It represents a discrete probability distribution concentrated at 0 — a degenerate distribution — it is a Distribution (mathematics) in the generalized function sense; but the notation treats it as if it ...
The "68–95–99.7 rule" is often used to quickly get a rough probability estimate of something, given its standard deviation, if the population is assumed to be normal. It is also used as a simple test for outliers if the population is assumed normal, and as a normality test if the population is potentially not normal.
This distribution for a = 0, b = 1 and c = 0.5—the mode (i.e., the peak) is exactly in the middle of the interval—corresponds to the distribution of the mean of two standard uniform variables, that is, the distribution of X = (X 1 + X 2) / 2, where X 1, X 2 are two independent random variables with standard uniform distribution in [0, 1]. [1]
The Johnson's S U-distribution is a four-parameter family of probability distributions first investigated by N. L. Johnson in 1949. [1] [2] Johnson proposed it as a transformation of the normal distribution: [1] = + ()