I was at the Wikipedia site the other day, looking up properties of the Chi-square distribution. I noticed that the formula for the median of the chi-square distribution with d degrees of freedom is given as ≈ d(1-2/(9d))3. However, there is no mention of how well this formula approximates the
Last week I showed how to use the UNIQUE-LOC technique to iterate over categories in a SAS/IML program. The observant reader might have noticed that the algorithm, although general, could be made more efficient if the data are sorted by categories. The UNIQUEBY Technique Suppose that you want to compute
Being able to reshape data is a useful skill in data analysis. Most of the time you can use the TRANSPOSE procedure or the SAS DATA step to reshape your data. But the SAS/IML language can be handy, too. I only use PROC TRANSPOSE a few times per year, so
When you analyze data, you will occasionally have to deal with categorical variables. The typical situation is that you want to repeat an analysis or computation for each level (category) of a categorical variable. For example, you might want to analyze males separately from females. Unlike most other SAS procedures,
In SAS/IML 9.22 and beyond, you can call the R statistical programming language from within a SAS/IML program. The syntax is similar to the syntax for calling SAS from SAS/IML: You use a SUBMIT statement, but add the R option: SUBMIT / R. All statements in the program between the
"I think that my data are exponentially distributed, but how can I check?" I get asked that question a lot. Well, not specifically that question. Sometimes the question is about the normal, lognormal, or gamma distribution. A related question is "Which distribution does my data have," which was recently discussed
I was contacted by SAS Technical Support regarding a customer who was trying to use SAS/IML to compute quantiles of the folded normal distribution. I had heard of the distribution, but it is not built into SAS and I had never worked with it. Nevertheless, I set out to understand
In SAS/IML 9.22 and beyond, you can call any SAS procedure, DATA step, or macro from within a SAS/IML program. The syntax is simple: place a SUBMIT statement prior to the SAS statements and place an ENDSUBMIT statement after the SAS statements. This enables you to call any SAS procedure
Normal, Poisson, exponential—these and other "named" distributions are used daily by statisticians for modeling and analysis. There are four operations that are used often when you work with statistical distributions. In SAS software, the operations are available by using the following four functions, which are essential for every statistical programmer
I previously wrote about using SAS/IML for nonlinear optimization, and demonstrated optimization by maximizing a likelihood function. Many well-known optimization algorithms require derivative information during the optimization, including the conjugate gradient method (implemented in the NLPCG subroutine) and the Newton-Raphson method (implemented in the NLPNRA method). You should specify analytic
A popular use of SAS/IML software is to optimize functions of several variables. One statistical application of optimization is estimating parameters that optimize the maximum likelihood function. This post gives a simple example for maximum likelihood estimation (MLE): fitting a parametric density estimate to data. Which density curve fits the
When you misspell a word on your mobile device or in a word-processing program, the software might "autocorrect" your mistake. This can lead to some funny mistakes, such as the following: I hate Twitter's autocorrect, although changing "extreme couponing" to "extreme coupling" did make THAT tweet more interesting. [@AnnMariaStat] When
I previously wrote about an intriguing math puzzle that involves 5-digit numbers with certain properties. This post presents my solution in the SAS/IML language. It is easy to generate all 5-digit perfect squares, but the remainder of the problem involves looking at the digits of the squares. For this reason,
The other day I encountered a SAS Knowledge Base article that shows how to count the number of missing and nonmissing values for each variable in a data set. However, the code is a complicated macro that is difficult for a beginning SAS programmer to understand. (Well, it was hard
Polynomials are used often in data analysis. Low-order polynomials are used in regression to model the relationship between variables. Polynomials are used in numerical analysis for numerical integration and Taylor series approximations. It is therefore important to be able to evaluate polynomials in an efficient manner. My favorite evaluation technique
You can extend the capability of the SAS/IML language by writing modules. A module is a user-defined function. You can define a module by using the START and FINISH statements. Many people, including myself, define modules at the top of the SAS/IML program in which they are used. You can
Do you know someone who has a birthday in mid-September? Odds are that you do: the middle of September is when most US babies are born, according to data obtained from the National Center for Health Statistics (NCHS) Web site (see Table 1-16). There's an easy way to remember this
Looping is essential to statistical programming. Whether you need to iterate over parameters in an algorithm or indices in an array, a loop is often one of the first programming constructs that a beginning programmer learns. Today is the first anniversary of this blog, which is named The DO Loop,
I previously showed how to generate random numbers in SAS by using the RAND function in the DATA step or by using the RANDGEN subroutine in SAS/IML software. These functions generate a stream of random numbers. (In statistics, the random numbers are usually a sample from a distribution such as
You can generate a set of random numbers in SAS that are uniformly distributed by using the RAND function in the DATA step or by using the RANDGEN subroutine in SAS/IML software. (These same functions also generate random numbers from other common distributions such as binomial and normal.) The syntax
NOTE: SAS stopped shipping the SAS/IML Studio interface in 2018. It is no longer supported, so this article is no longer relevant. When I write SAS/IML programs, I usually do my development in the SAS/IML Studio environment. Why? There are many reasons, but the one that I will discuss today
I've previously described ways to solve systems of linear equations, A*b = c. While discussing the relative merits of the solving a system for a particular right hand side versus solving for the inverse matrix, I made the assertion that it is faster to solve a particular system than it
The SAS/IML language provides two functions for solving a nonsingular nxn linear system A*x = c: The INV function numerically computes the inverse matrix, A-1. You can use this to solve for x: Ainv = inv(A); x = Ainv*c;. The SOLVE function numerically computes the particular solution, x, for a
In the SAS/IML language, the index creation operator (:) is used to construct a sequence of integer values. For example, the expression 1:7 creates a row vector with seven elements: 1, 2, ..., 7. It is important to know the precedence of matrix operators. When I was in grade school,
I've previously discussed how to find the root of a univariate function. This article describes how to find the root (zero) of a function of several variables by using Newton's method. There have been many papers, books, and dissertations written on the topic of root-finding, so why am I blogging
In a previous blog post, I showed how to use the LOGISTIC procedure to construct a receiver operator characteristic (ROC) curve in SAS. That same day, Charlie H. blogged about how to use the DATA step to construct an ROC curve from basic principles. It has been a long time
One of the joys of statistics is that you can often use different methods to estimate the same quantity. Last week I described how to compute a parametric density estimate for univariate data, and use the parameters estimates to compute the area under the probability density function (PDF). This article
The area under a density estimate curve gives information about the probability that an event occurs. The simplest density estimate is a histogram, and last week I described a few ways to compute empirical estimates of probabilities from histograms and from the data themselves, including how to construct the empirical
Readers' comments indicate that my previous blog article about computing the area under an ROC curve was helpful. Great! There is another common application of numerical integration: finding the area under a density estimation curve. This article provides an overview of density estimation and computes an empirical cumulative density function.
This is Part 4 of my response to Charlie Huang's interesting article titled Top 10 most powerful functions for PROC SQL. As I did for eaerlier topics, I will examine one of the "powerful" SQL functions that Charlie mentions and show how to do the same computation in SAS/IML software.
