Posts Tagged ‘ Numerical Analysis ’

Compute the rank of a matrix in SAS

April 8, 2015
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Compute the rank of a matrix in SAS

A common question from statistical programmers is how to compute the rank of a matrix in SAS. Recall that the rank of a matrix is defined as the number of linearly independent columns in the matrix. (Equivalently, the number of linearly independent rows.) This article describes how to compute the

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Create a custom PDF and CDF in SAS

March 6, 2015
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Create a custom PDF and CDF in SAS

In my previous post, I showed how to approximate a cumulative density function (CDF) by evaluating only the probability density function. The technique uses the trapezoidal rule of integration to approximate the CDF from the PDF. For common probability distributions, you can use the CDF function in Base SAS to

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Optimizing a function of an integral

March 12, 2014
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Optimizing a function of an integral

This post was kindly contributed by The DO Loop - go there to comment and to read the full post. 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...
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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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