Rick Wicklin, PhD, is a distinguished researcher in computational statistics at SAS and is a principal developer of SAS/IML software. His areas of expertise include computational statistics, simulation, statistical graphics, and modern methods in statistical data analysis. Rick is author of the books Statistical Programming with SAS/IML Software and Simulating Data with SAS.
In several previous articles, I've shown how to use SAS to fit models to data by using maximum likelihood estimation (MLE). However, I have not previously shown how to obtain standard errors for the estimates. This article combines two previous articles to show how to obtain MLE estimates and the
A previous article shows how to use Monte Carlo simulation to approximate the sampling distribution of the sample mean and sample median. When x ~ N(0,1) are normal data, the sample mean is also normal, and there are simple formulas for the expected value and the standard error of the
An elementary course in statistics often includes a discussion of the sampling distribution of a statistic. The canonical example is the sampling distribution of the sample mean. For samples of size n that are drawn from a normally distribution (X ~ N(μ, σ)), the sample mean is normally distributed as
A previous article discusses the birthday problem and its generalizations. The classic birthday problem asks, "In a room that contains N people, what is the probability that two or more people share a birthday?" The probability is much higher than you might think. For example, in a room that contains
The birthday-matching problem (also called the birthday paradox or simply the birthday problem), is a classic problem in probability. Simply stated, the birthday-matching problem asks, "If there are N people in a room, what is the chance that two of them have the same birthday?" The problem is sometimes called
Recently I wrote about numerical analysis problem: the accurate computation of log(1+x) when x is close to 0. A naive computation of log(1+x) loses accuracy if you call the LOG function, which is why the SAS language provides the built-in LOG1PX for this computation. In addition, I showed that you
SAS supports a special function for the accurate evaluation of log(1+x) when x is near 0. The LOG1PX function is useful because a naive computation of log(1+x) loses accuracy when x is near 0. This article demonstrates two general approximation techniques that are often used in numerical analysis: the Taylor
The documentation for Python's SciPy package provides a table that concisely summarizes functions that are associated with continuous probability distributions. This article provides a similar table for SAS functions. For more information on the CDF, PDF, quantile, and random-variate functions, see "Four essential functions for statistical programmers." SAS functions for
A previous article shows ways to perform efficient BY-group processing in the SAS IML language. BY-group processing is a SAS-ism for what other languages call group processing or subgroup processing. The main idea is that the data set contains several discrete variables such as sex, race, education level, and so
One thing I have learned about rank-based statistics over the years is "Be careful of tied values!" On multiple occasions, I have been asked, "Why doesn't the SAS result for [NAME] statistic agree with my hand calculation?" The answer is sometimes because of the way that tied values are handled.
