Posts Tagged ‘ Numerical Analysis ’

Optimizing a function of an integral

March 12, 2014
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Optimizing a function of an integral

Last week I showed how to find parameters that maximize the integral of a certain probability density function (PDF). Because the function was a PDF, I could evaluate the integral by calling the CDF function in SAS. (Recall that the cumulative distribution function (CDF) is the integral of a PDF.)
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Optimizing a function that evaluates an integral

March 5, 2014
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Optimizing a function that evaluates an integral

SAS programmers use the SAS/IML language for many different tasks. One important task is computing an integral. Another is optimizing functions, such as maximizing a likelihood function to find parameters that best fit a set of data. Last week I saw an interesting problem that combines these two important tasks.
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Define functions with default parameter values in SAS/IML

February 10, 2014
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Define functions with default parameter values in SAS/IML

One of my favorite new features of SAS/IML 12.1 enables you to define functions that contain default values for parameters. This is extremely useful when you want to write a function that has optional arguments. Example: Centering a data vector It is simple to specify a SAS/IML module with a
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A simple way to find the root of a function of one variable

February 5, 2014
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A simple way to find the root of a function of one variable

Finding the root (or zero) of a function is an important computational task because it enables you to solve nonlinear equations. I have previously blogged about using Newton's method to find a root for a function of several variables. I have also blogged about how to use the bisection method
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How to compute the incomplete beta function in SAS

November 13, 2013
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How to compute the incomplete beta function in SAS

While sorting through an old pile of papers, I discovered notes from a 2012 SAS conference that I had attended. Next to the abstract for one presentation, I had scrawled a note to myself that read "BLOG about the incomplete beta function!" Okay, Rick, whatever you say! In statistics, the
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Using finite differences to estimate the maximum of a time series

July 28, 2013
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Using finite differences to estimate the maximum of a time series

Finding the maximum value of a function is an important task in statistics. There are three approaches to finding a maxima: When the function is available as an analytic expression, you can use an optimization algorithm to find the maxima. For example, in the SAS/IML language, you can use any
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How to choose parameters so that a distribution has a specified mean and variance

July 26, 2013
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How to choose parameters so that a distribution has a specified mean and variance

The truncated normal distribution TN(μ, σ, a, b) is the distribution of a normal random variable with mean μ and standard deviation σ that is truncated on the interval . I previously blogged about how to implement the truncated normal distribution in SAS. A friend wanted to simulate data
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Duplicate values in a stream of random numbers

July 3, 2013
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Duplicate values in a stream of random numbers

As I wrote in my previous post, a SAS customer noticed that he was getting some duplicate values when he used the RAND function to generate a large number of random uniform values on the interval . He wanted to know if this result indicates a bug in the RAND
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