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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.
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: a = the best-case estimate; m = the most likely estimate; b = the worst-case estimate
Triangular function; Central limit theorem — The triangle distribution often occurs as a result of adding two uniform random variables together. In other words, the triangle distribution is often (not always) the result of the first iteration of the central limit theorem summing process (i.e. =). In this sense, the triangle distribution can ...
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].
Exemplary triangular function. A triangular function (also known as a triangle function, hat function, or tent function) is a function whose graph takes the shape of a triangle. Often this is an isosceles triangle of height 1 and base 2 in which case it is referred to as the triangular function.
PERT and CPM are complementary tools, because "CPM employs one time estimation and one cost estimation for each activity; PERT may utilize three time estimates (optimistic, expected, and pessimistic) and no costs for each activity. Although these are distinct differences, the term PERT is applied increasingly to all critical path scheduling." [3]
The difference between the geometric mean and the mean is larger for small values of α in relation to β than when exchanging the magnitudes of β and α. N. L.Johnson and S. Kotz [1] suggest the logarithmic approximation to the digamma function ψ(α) ≈ ln(α − 1/2) which results in the following approximation to the geometric mean:
Johnson's -distribution has been used successfully to model asset returns for portfolio management. [3] This comes as a superior alternative to using the Normal distribution to model asset returns.