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The triangular distribution, along with the PERT distribution, is also widely used in project management (as an input into PERT and hence critical path method (CPM)) to model events which take place within an interval defined by a minimum and maximum value.
The PERT distribution has a smoother shape than the triangular distribution. The triangular distribution has a mean equal to the average of the three parameters: = + + which (unlike PERT) places equal emphasis on the extreme values which are usually less-well known than the most likely value, and is therefore less reliable. The triangular ...
While the distribution used for the approximation might be a normal distribution, this is not always so. For example, a triangular distribution might be used, depending on the application. In three-point estimation, three figures are produced initially for every distribution that is required, based on prior experience or best-guesses:
The reciprocal distribution; The triangular distribution on [a, b], a special case of which is the distribution of the sum of two independent uniformly distributed random variables (the convolution of two uniform distributions). The trapezoidal distribution; The truncated normal distribution on [a, b]. The U-quadratic distribution on [a, b].
A discrete probability distribution is applicable to the scenarios where the set of possible outcomes is discrete (e.g. a coin toss, a roll of a die) and the probabilities are encoded by a discrete list of the probabilities of the outcomes; in this case the discrete probability distribution is known as probability mass function.
PERT distribution; Phase-type distribution; Poly-Weibull distribution; Polynomial Wigner–Ville distribution; ... Triangular distribution; Truncated normal distribution;
PERT network chart for a seven-month project with five milestones (10 through 50) and six activities (A through F). The program evaluation and review technique ( PERT ) is a statistical tool used in project management , which was designed to analyze and represent the tasks involved in completing a given project .
If the uniform distributions have the same width w, the result is a triangular distribution, symmetric about its mean, on the support [a+c,a+c+2w]. The sum of two independent, equally distributed, uniform distributions U 1 (a,b)+U 2 (a,b) yields a symmetric triangular distribution on the support [2a,2b].