PointEstimateMethod.jl

This repository implements the well known Point Estimate Method (PEM) to represent a distribution with a number of points that preserve the moments of the original distribution.

The methodology implements the Miller and Rice methodology as described at:

• H.P.Hong, An efficient point estimate method for probabilistic analysis, Reliability Engineering and System Safety, 1998, https://doi.org/10.1016/S0951-8320(97)00071-9
• Miller, Allen C., and Thomas R. Rice. “Discrete Approximations of Probability Distributions.” Management Science 29, no. 3 (1983): 352–62. http://www.jstor.org/stable/2631060.

Example of usage is as follow:

using Distributions
using PointEstimateMethod

distribution = Normal()  # distribution to consider
N_pem = 3  # number of point estimate models to use

pem_output = pem(distribution, N_pem)

pem_output.x  # locations of the points
pem_output.p  # probability of each point

The pem function automatically calculates the moments of the distribution with the method Distributions.moment(::UnivariateDistribution, ::Int), by default; custom function can also be specified using the optional keyword central_moment_fun; see the docstring of the pem function.

When the function is not available, the proposed distribution is sampled using the rand function and then the sampled vector is used to calculate the moments. For more details, see the docstring of the pem function.

Examples are provided in the notebooks folder.