The power method is a well-known iterative scheme to approximate the largest eigenvalue (in absolute value) of a symmetric matrix. It is useful in practice when you need only the largest eigenvalue and eigenvector of a large matrix. The method requires only matrix-vector multiplication and vector scaling. There is a
When I encounter a new function, I usually graph it to gain intuition about how the function transforms its inputs. Recently, I needed to use the Rayleigh quotient function, which is connected to the estimation of eigenvalues and eigenvectors for symmetric matrices. It has been several years since I last
The new school year had barely started when I got a call from a friend who is an elementary school principal. She told me that every morning she announces the names of students who are celebrating a birthday. "One student noticed that we've already had two days on which no
In probability and statistics, special numbers are used to compute probabilities by counting the number of ways certain events can occur. The most famous are combinations and permutations. Both are used to count the ways to arrange or select items from a set. If a set contains n elements: A
I've often wondered about the logic that the SGPLOT procedure in SAS uses to determine whether a set of graphical overlays will receive identical attributes or different attributes. (Recall that color, size, line style, and marker symbol are all examples of attributes.) I know that when you plot grouped data
In data analysis, sometimes we need to perform a preliminary task before we can analyze data. Often the task needs to be performed only once per session. For example, you might need to download or merge data prior to your analysis. Or you might need to define or load a
SAS supports more than 25 common probability distributions for the PDF, CDF, QUANTILE, and RAND functions. If you need a less-common distribution, you can implement new distributions by using Base SAS (specifically, PROC FCMP) or the SAS/IML language. On the SAS Support Communities, a SAS programmer asked how to implement
A previous article discusses Cohen's d statistic and how to compute it in SAS. For a two-sample independent design, Cohen's d estimates the standardized mean difference (SMD). Because Cohen's d is a biased statistic, the previous article also computes Hedges' g, which is an unbiased estimate of the SMD. Lastly,
What is Cohen's d statistic and how is it used? How can you compute it in SAS? This article gives some history behind Cohen's d statistic. It shows how to compute the statistic in SAS for the difference in means between two independent samples. It shows how to estimate a
SAS provides procedures to fit common probability distributions to sample data. You can use PROC UNIVARIATE in Base SAS or PROC SEVERITY in SAS/ETS software to estimate the distribution parameters for approximately 20 common distributions, including normal, lognormal, beta, gamma, and Weibull. Since there are infinitely many distributions, you may
