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Analytics | Learn SAS

Rick WicklinDecember 1, 2021 2

Beware of repeated values in loess models

Did you know that the loess regression algorithm is not well-defined when you have repeated values among the explanatory variables, and you request a very small smoothing parameter? This is because loess regression at the point x0 is based on using the k nearest neighbors to x0. If x0 has

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Analytics | Data Visualization

Rick WicklinNovember 8, 2021 0

The normal approximation and random samples of the binomial distribution

Recall that the binomial distribution is the distribution of the number of successes in a set of independent Bernoulli trials, each having the same probability of success. Most introductory statistics textbooks discuss the approximation of the binomial distribution by the normal distribution. The graph to the right shows that the

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Analytics | Learn SAS

Rick WicklinNovember 1, 2021 1

Fit a mixture of Weibull distributions in SAS

A previous article discusses how to use SAS regression procedures to fit a two-parameter Weibull distribution in SAS. The article shows how to convert the regression output into the more familiar scale and shape parameters for the Weibull probability distribution, which are fit by using PROC UNIVARIATE. Although PROC UNIVARIATE

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Analytics | Learn SAS

Rick WicklinOctober 27, 2021 13

Interpret estimates for a Weibull regression model in SAS

It can be frustrating when the same probability distribution has two different parameterizations, but such is the life of a statistical programmer. I previously wrote an article about the gamma distribution, which has two common parameterizations: one that uses a scale parameter (β) and another that uses a rate parameter

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Analytics | Learn SAS

Rick WicklinOctober 20, 2021 0

An introduction to genetic algorithms in SAS

A genetic algorithm (GA) is a heuristic optimization technique. The method tries to mimic natural selection and evolution by starting with a population of random candidates. Candidates are evaluated for "fitness" by plugging them into the objective function. The characteristics of the better candidates are combined to create a new

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Analytics | Programming Tips

Rick WicklinOctober 18, 2021 2

Crossover and mutation: An introduction to two operations in genetic algorithms

This article uses an example to introduce to genetic algorithms (GAs) for optimization. It discusses two operators (mutation and crossover) that are important in implementing a genetic algorithm. It discusses choices that you must make when you implement these operations. Some programmers love using genetic algorithms. Genetic algorithms are heuristic

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Analytics | Programming Tips

Rick WicklinOctober 13, 2021 1

Penalties versus constraints in optimization problems

Sometimes we can learn as much from our mistakes as we do from our successes. Recently, I needed to solve an optimization problem for which the solution vector was a binary vector subject to a constraint. I was in a hurry. Without thinking much about what I was doing, I

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Analytics | Learn SAS

Rick WicklinOctober 4, 2021 2

Choose samples with specified statistical properties

A reader asked whether it is possible to find a bootstrap sample that has some desirable properties. I am using the term "bootstrap sample" to refer to the result of randomly resampling with replacement from a data set. Specifically, he wanted to find a bootstrap sample that has a specific

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Analytics | Learn SAS | Programming Tips

Rick WicklinSeptember 22, 2021 0

Use simulations to evaluate the accuracy of asymptotic results

The field of probability and statistics is full of asymptotic results. The Law of Large Numbers and the Central Limit Theorem are two famous examples. An asymptotic result can be both a blessing and a curse. For example, consider a result that says that the distribution of some statistic converges

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Analytics | Learn SAS | Programming Tips

Rick WicklinSeptember 15, 2021 1

The partition problem: An optimization approach

I previously wrote about one way to solve the partition problem in SAS. In the partition problem, you divide (or partition) a set of N items into two groups of size k and N-k such that the sum of the items' weights is the same in each group. For example,

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