Example density curves for the PERT probability distribution
Cumulative distribution function
Example cumulative distribution curves for the PERT probability distribution
Parameters
(real) (real)
Support
PDF
where
CDF
(the regularized incomplete beta function) with
Mean
Median
Mode
Variance
Skewness
Excess kurtosis
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
The mean of the distribution is therefore defined as the weighted average of the minimum, most likely and maximum values that the variable may take, with four times the weight applied to the most likely value.
This assumption about the mean was first proposed in Clark, 1962[1] for estimating the effect of uncertainty of task durations on the outcome of a project schedule being evaluated using the program evaluation and review technique, hence its name. The mathematics of the distribution resulted from the authors' desire to make the standard deviation equal to about 1/6 of the range.[2][3]
The PERT distribution is widely used in risk analysis[4] to represent the uncertainty of the value of some quantity where one is relying on subjective estimates, because the three parameters defining the distribution are intuitive to the estimator. The PERT distribution is featured in most simulation software tools.
^Clark CE (1962) The PERT model for the distribution of an activity. Operations Research 10, pp. 405406
^"PERT distribution". Vose Software. May 2, 2017. Retrieved July 16, 2017.
^Continuous Univariate Distributions - 2nd Ed (1995). Johnson K, Kotz S and Balakkrishnan N. (Section 25.4)
^Project Management Body of Knowledge: 5th Ed (2013). Project Management Institute Chapter 6
In probability and statistics, the PERTdistributions are a family of continuous probability distributions defined by the minimum (a), most likely (b)...
The program evaluation and review technique (PERT) is a statistical tool used in project management, which was designed to analyze and represent the tasks...
by a triangular distribution. See for example under corporate finance. The triangular distribution, along with the PERTdistribution, is also widely used...
pert, pērt, or PERT in Wiktionary, the free dictionary. Pert or PERT may refer to: USS Pert (1812) - see List of United States Navy ships: P USS Pert (PG-95)...
The arcsine distribution on [a,b], which is a special case of the Beta distribution if α = β = 1/2, a = 0, and b = 1. The PERTdistribution is a special...
Fox–Wright Psi function. Normal distribution Rectified Gaussian distribution Truncated distributionPERTdistribution "Lecture 4: Selection" (PDF). web...
regularized incomplete beta function. The PERTdistribution variation of the beta distribution is frequently used in PERT, critical path method (CPM) and other...
min) ~ PERT(min, max, m, λ) where PERT denotes a PERTdistribution used in PERT analysis, and m=most likely value. Traditionally λ = 4 in PERT analysis...
statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional...
elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. Intuitively...
project tasks. Program Evaluation and Review Technique, commonly abbreviated PERT, is a statistical tool, used in project management, that is designed to analyze...
Laplace distributions are extensions of the Laplace distribution and the asymmetric Laplace distribution to multiple variables. The marginal distributions of...
Bibcode:2006beev.book.....T. Minard, Charles Joseph. "Carte figurative des pertes successives en hommes de l'Armée Française dans la campagne de Russie 1812–1813"...
Light On Modern Digital Sex Work". Forbes. Retrieved January 9, 2019. X Pert, Lorgan (November 17, 2020). "Vertigo acquires erotic drama 'PVT Chat' for...
specific Gantt chart software. Program evaluation and review technique (PERT) Progress bar Event chain diagram Project Management Institute 2021, Glossary...
information about a project product Program evaluation and review technique (PERT) is a statistical tool, used in project management, designed to analyze and...
(5 August 1960). "ELLIS LISTS STARS OF 'HAPPY ENDING': Ruth Chatterton, Pert Kelton and Conrad Nagel to Head Cast at New Hope, Pa". The New York Times...
timing approach was based on the Program Evaluation and Review Technique (PERT), in 1966. More modern versions and algorithms appeared in the early 1980s...
use critical path method (CPM) or program evaluation and review technique (PERT) for planning and scheduling. These methods do not generate flow in the production...
psychiatric emergency response team (PERT) was placed. Fifty minutes after the first call, at least two non-PERT officers arrived on scene. In video footage...
it smoothly into place. According to Nugent, "Judy Garland's Dorothy is a pert and fresh-faced miss with the wonder-lit eyes of a believer in fairy tales...
The chart has a modern variation, Program Evaluation and Review Technique (PERT). Industrial Efficiency: Industrial efficiency can only be produced by the...
Marcus Aurelius, p. 116. Birley takes the phrase horror imperii from HA Pert. xiii. 1 and xv. 8. Birley, 'Hadrian to the Antonines', p. 156. HA Verus...
breakdown of fats in those undergoing pancreatic enzyme replacement therapy (PERT). It is a component in Sollpura (Liprotamase). Alpha toxin Pathology Lysosomal...
events and teams, mostly motorsports. Some of these sponsorships include the PERT (PETRONAS EON Rally Team), and also the PETRONAS Adventure Team, a 4X4 adventure...
Global Information
![{\displaystyle x\in [a,c]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/33e87be6d99d3460eb530a67669911d70eb61cf0)
![{\displaystyle \operatorname {E} [X]={\frac {a+4b+c}{6}}=\mu }](https://wikimedia.org/api/rest_v1/media/math/render/svg/a490721a339146a0e4af09cb41fc36a01733532b)
![{\displaystyle I_{\frac {1}{2}}^{[-1]}(\alpha ,\beta )(c-a)+a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/453abbfb186d102648164a83920255f54de58b90)
![{\displaystyle \operatorname {var} [X]={\frac {(\mu -a)(c-\mu )}{7}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0143d9de6f7d9772595cdc2ce60ad1354c32a0d3)
![{\displaystyle {\frac {6[(\alpha -\beta )^{2}(\alpha +\beta +1)-\alpha \beta (\alpha +\beta +2)]}{\alpha \beta (\alpha +\beta +2)(\alpha +\beta +3)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eea65a8d7c9e00ba6299b727eab679117776f41e)
