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Analytics | Data Visualization | Programming Tips

Rick WicklinJuly 6, 2026 0

Pareto charts are used by quality engineers to visually display a set of causes that produce defects in a manufacturing process. The chart is based on the famous Pareto Principle (the 80/20 rule), which states that 20% of the causes often produce 80% of the defects. If you focus on

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Analytics | Learn SAS | Programming Tips

Rick WicklinJune 29, 2026 0

Confidence limits for counts in a multinomial distribution

A recent article discussed Pareto charts and how to create them in SAS. A Pareto chart is used in quality control to identify the most likely reasons that a manufacturing process produces defective items. Suppose there are k different reasons why a process can fail, and you intend to randomly

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Analytics | Learn SAS | Programming Tips

Rick WicklinJune 24, 2026 3

Sort the rows or columns of a matrix independently

When you have a data matrix, the rows represent observations and the columns represent variables. If you sort the matrix by one or more columns, the sorting occurs in a way that preserves the elements within rows. Although the rows of the sorted matrix are permuted by the sort, the

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Analytics | Learn SAS | Programming Tips

Rick WicklinJune 15, 2026 0

Create a confidence band for a normal Q-Q plot

This article shows how to compute a confidence band for a Q-Q plot in SAS. A previous article shows how to construct confidence bands for the CDF of continuous univariate data. The bands can be added to a plot of the empirical CDF (ECDF) for the data. One of the

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Analytics | Programming Tips

Rick WicklinJune 8, 2026 8

How to add confidence bands on the ECDF plot in SAS

A previous article shows how to construct an empirical cumulative distribution function (ECDF) for univariate data by using PROC UNIVARIATE or in the SAS IML language. The ECDF is a tool for visualizing the distribution of a sample and is helpful for estimating quantiles in the data. In statistics, we

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Analytics | Learn SAS | Programming Tips

Rick WicklinJune 1, 2026 1

How to visualize the variability in an ECDF

A previous article shows how to construct an empirical cumulative distribution function (ECDF) in SAS. The most common way is by using PROC UNIVARIATE, but you can also call the ECDF function in the SAS IML language. The ECDF is a tool for visualizing the distribution of a univariate sample

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Analytics | Learn SAS | Programming Tips

Rick WicklinMay 26, 2026 5

Create and graph the ECDF function in SAS

The empirical cumulative distribution function (ECDF) is an important tool in statistics. It is one of several plots you can use to visualize the shape of a data distribution. It is not used as often as the histogram, the kernel density estimate, and the box plot, but it is essential

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Advanced Analytics | Programming Tips

Rick WicklinMay 18, 2026 0

Compute the orthant probability for the 4-D multivariate normal distribution

This is the last article in a series about computing probabilities for the multivariate normal distribution. A previous article shows how to compute the probability of a standardized multivariate normal (MVN) distribution in an orthant for dimensions k=1, 2, and 3 by using the Childs-Sun formulas. The formulas are exact

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Analytics | Programming Tips

Rick WicklinMay 11, 2026 1

Compute multivariate normal orthant probabilities

In general, it is very difficult to compute a probability for a multivariate continuous distribution. For all continuous distributions, the probability requires solving a complicated multiple integral. For example, the probability for a bivariate normal distribution requires integrating the bivariate normal density over a two-dimensional (2-D) area. The probability for

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Analytics | Learn SAS | Programming Tips

Rick WicklinMay 4, 2026 1

On standardizing multivariate normal probabilities

A course in elementary statistics always introduces the "Z-score." A Z-score is the result of standardizing a normally distributed random variable. By subtracting the distribution's mean and dividing by its standard deviation, you transform a general normal random variable into a standardized variable that has zero mean and unit standard

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