Consequently, this is the method I have chosen to use in this project. This is exactly what we need for ‘latin hypercube’ sampling. The two most general methods, in the sense that they can be made to return distributions with any possible functional form, are the acceptance-rejection method and the inverse transform method, the latter has the further advantage that it can easily be made to return values from equal-probability subdivisions of the range of our desired random variable. Other methods are more general and can produce random numbers conforming to many different distributions. Most of them are specific to particular distributions with, as you might expect, the normal having the most. We want to convert a random variable that is uniformly distributed on the range [0, 1), as supplied by VBA’s Rnd() function, into a random variable distributed according to any desired distribution. Ways of generating non-uniform random variables As we are trying to develop a tool that is of fairly general applicability, we need a method that will generate samples distributed according to any distribution we may choose. Out there ‘in the wild’ random variables occur in all shapes and sizes, not just the standard ones. Excel and many other applications natively provide a random function that returns values that are uniformly distributed on the range [0, 1). The object of the exercise is to generate an array of random numbers that are distributed according to a given frequency distribution.
#Latin hypercube sampling excel how to
Today’s post describes how to generate random numbers according to arbitrarily chosen probability distributions using the inverse transform method. It follows on from yesterday’s, where I gave an overview of the problem and how I propose to tackle it.
#Latin hypercube sampling excel series
This can be useful for identifying which parameters have the largest impact on response standard deviation and which parameters could be changed to reduce the response PNC.Welcome back! This is number two in a series of five blog posts that describe how to construct a Monte Carlo risk analysis application in Excel VBA. Pareto plots of the contributions of each parameter to the response are also created.
Histogram plots of the responses, along with summaries of their sample statistics, will be created in a Monte Carlo report after all trials are run. This probability is called the Probability of Non-Compliance or PNC. If the response has a defined Upper Specification Limit (USL) or Lower Specification Limit (LSL) then a confidence interval on the probability of the response falling outside of these limits will be computed using the binomial statistics. Monte Carlo Analysis is the gold standard to which all other techniques are judged, and if computational expense is not a problem, then it will always be the preferred method. By then applying sample statistics a substantial amount of information can be derived about the response distribution – its location, spread and shape. Monte Carlo analysis approximates the output distribution by randomly generating single values for each of the input parameters, plugging these values into the model, and computing a value for the response. If the input parameters of a mathematical function have statistical variation, then the output response will also have variation.
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