This formula is based on the beta statistical distribution and weights the most likely time (m) four times more than either the optimistic time (a) or the pessimistic time (b).As the equation shows, the variance is the square of one-sixth of the difference between the two … The Beta distribution is one kind of probability distribution on probabilities which typically models an ancestry of probabilities. Normal distribution represents the behavior of most of the situations in the universe (That is why it’s called a “normal” distribution. So I'll interpret the question as asking when Beta(a,b) is approximately Normal, and why. If plotted against a chart, this beta distribution will result in an more uniform, bell shaped curve, called a normal distribution. Unlike the triangular distribution, the PERT distribution uses these parameters to create a smooth curve that fits well to the normal or lognormal distributions. The PERT distribution is a special case of the beta distribution that takes three parameters: a minimum, maximum, and most likely (mode). The Beta distribution has support [0,1] and the Normal distribution has support [math](-\infty, \infty)[/math], so they can't be the same distribution. The normal distribution is the most common type of distribution assumed in technical stock market analysis and in other types of statistical analyses. I guess!). This is a weighted average. Beta curve distribution is considered to be a versatile, resourceful way to describe outcomes for proportions or percentages. We expect that the player’s season-long batting average will be most likely around .27, but that it could reasonably range from .21 to .35. More weight is given to the most likely. The probability density functions are different in shape and the domain. It’s probably good to talk about why the Beta is so important now, since it doesn’t look very valuable at the moment. The large sum of (small) random variables often turns out to be normally distributed, contributing to its widespread application. The beta distribution, with its bounded domain, is explored as an alternative to the lognormal distribution in describing the uncertainty of permeability. If plotted against a chart, this beta distribution will result in an more uniform, bell shaped curve, called a normal distribution. Beta Distribution (PERT): (P + O + 4ML ) / 6 This is a weighted average. Understanding Normal Distribution . Beta Distribution (PERT): (P + O + 4ML ) / 6. The domain of the beta distribution is from 0 to 1, while the normal goes from negative infinite to positive infinity. – Cauchy Distribution (derived from the Normal Distribution) – Chi-squared Distribution (the Gamma Distribution with α=r/2 for r an integer) – Dirichlet (the multivariate generalization of the Beta Distribution) – F Distribution (extension of Chi-squared Distribution) More weight is given to the most likely. The domain of the beta distribution is \((0, 1)\), just like a probability, so we already know we’re on the right track- but the appropriateness of the beta for this task goes far beyond that. Priors. Since the Beta distribution represents a probability, its domain is bounded between 0 and 1.


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