The UncertainLMH and Pert distributions use similar parameters but produce more bell-shaped distributions. The distribution function. Use this to define a chance variable or uncertain quantity as having a triangular distribution. To define independent and identically distributed distributions over one or more indexes, list the indexes in the optional «over» parameter.
The analytic inverse cumulative probability, aka quantile function. Like all Analytica distribution functions, Triangular generates independent distributions across any dimensions occurring in the input parameters. If you want to generate the same triangular distribution independently over additional dimensions, use the optional «Over» parameter, e.
The triangular distribution is a continuous probability distribution with a probability density function shaped like a triangle. The name of the distribution comes from the fact that the probability density function is shaped like a triangle. It turns out that this distribution is extremely useful in the real world because we can often estimate the minimum value a , the maximum value b , and the most likely value c that a random variable will take on, so we can often model the behavior of random variables by using a triangular distribution with the knowledge of just these three values.
What is the mean expected sales for the restaurant? Under the assumption of Pert distributions, the 80th percentile for the duration of the entire project amounts to days. By sending this curve through the Send to Comparison functionality, we can compare both assumptions:.
Here, at the P80 level, we observe 6 additional days of contingency required under a Triangular. This is only 2. In other words, the final impact on the total project has not been as great as we would've expected, given the differences in the 80th percentiles of the 8 risks considered. How is it then possible that the impact on contingencies, Triangular or Pert, is reduced to only a difference of 2. The answer has to do with the combinatorial analysis of a Monte Carlo simulation and the theory of conditional probabilities.
That's because we're analysing a value that is already extreme, which is the 80th percentile. For this reason, when we compare at the level of an activity, seeing its differences in the tails between one alternative distribution and another; Pert and Triangular, we can observe significant differences. When we start to add more distributions where some depend in sequence on the others a project as a sequential series of dependent and simultaneous tasks , and we evaluate a non-central value such as an 80th percentile , the differences between one distribution and another tend to become less significant.
This is due to the compound or power effect that exists in the tails of the distributions. The Triangular will tend to have tails that are fatter than the Pert ones. The analyst should decide which distribution best describes the behaviour of the tail. We tend to prefer the shape of a Pert distribution, which assumes that the predominance of the results occurs in the most probable range, and then the tails are rounded.
Triangular distribution creates a mathematical discontinuity at its maximum point or mode, something that Pert distribution avoids. We can conclude that there's a certain impact of differentiation between the use of Pert and Triangular distributions if the analysis is done at the individual level of activity. As we add more risks and we see the image from a perspective of the sum of all the tasks in a project, the differences that may exist between one assumption and the other continue to appear.
However, these won't be as significant as when they were seen with greater specificity at the level of each activity. There will be some differences between the use of Pert and Triangular in a project. But in the end, the impact may not be as significant as it would be at the level of each of the activities, in the absence of correlations. If we were doing this analysis on the averages, there would be arithmetic consistency between the risk variations and the differences between Pert and Triangular distributions because our model has no correlations between risks yet.
If correlations were present, the results could be even more or less counterintuitive than they appear to be. Products Core Products. Planner The quick and easy tool to plan a project.
0コメント