Tag: Simulation

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The "power" of finite mixture models

When I learn a new statistical technique, one of first things I do is to understand the limitations of the technique. This blog post shares some thoughts on modeling finite mixture models with the FMM procedure. What is a reasonable task for FMM? When are you asking too much? I

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Four essential functions for statistical programmers

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

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Generate a random sample from a mixture distribution

Sometimes a population of individuals is modeled as a combination of subpopulations. For example, if you want to model the heights of individuals, you might first model the heights of males and females separately. The height of the population can then be modeled as a combination of the male and

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Random number streams in SAS: How do they work?

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

Programming Tips
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How to generate random numbers in SAS

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

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Simulating the Coupon Collector's Problem

I recently blogged about how many times, on average, you must roll a die until you see all six faces. This question is a special case of the coupon collector's problem. My son noted that the expected value (the mean number of rolls) is not necessarily the best statistic to

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Simulate categorical data in SAS

As I was reviewing notes for my course "Data Simulation for Evaluating Statistical Methods in SAS," I realized that I haven't blogged about simulating categorical data in SAS. This article corrects that oversight. An Easy Way and a Harder Way SAS software makes it easy to sample from discrete "named"

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An improved simulation of card shuffling

Last week I presented the GSR algorithm, a statistical model of a riffle shuffle. In the model, a deck of n cards is split into two parts according to the binomial distribution. Each piece has roughly n/2 cards. Then cards are dropped from the two stacks according to the number

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A statistical model of card shuffling

I recently returned from a five-day conference in Las Vegas. On the way there, I finally had time to read a classic statistical paper: Bayer and Diaconis (1992) describes how many shuffles are needed to randomize a deck of cards. Their famous result that it takes seven shuffles to randomize

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How to sample from independent normal distributions

In my article on computing confidence intervals for rankings, I had to generate p random vectors that each contained N random numbers. Each vector was generated from normal distribution with different parameters. This post compares two different ways to generate p vectors that are sampled from independent normal distributions. Sampling

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Ranking with confidence: Part 2

In a previous post, I described how to compute means and standard errors for data that I want to rank. The example data (which are available for download) are mean daily delays for 20 US airlines in 2007. The previous post carried out steps 1 and 2 of the method

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Simulating a random walk

In my spare time, I enjoy browsing the StackOverflow discussion forum to see what questions people are asking about SAS, SAS/IML, and statistics. Last week, a statistics student asked for help with the following homework problem: I need to generate a one-dimensional random walk in which the step length and

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Scratch-off lottery games: How NOT to design them

Because of this week's story about a geostatistician, Mohan Srivastava, who figured out how predict winning tickets in a scratch-off lottery, I've been thinking about scratch-off games. He discovered how to predict winners when he began to "wonder how they make these [games]." Each ticket has a set of "lucky

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Divide and count: A test for spatial randomness

Last week I generated two kinds of random point patterns: one from the uniform distribution on a two-dimensional rectangle, the other by jittering a regular grid by a small amount. My show choir director liked the second method (jittering) better because of the way it looks on stage: there are

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Count the number of points in 2D bins

One of my New Year's resolutions is to learn a new area of statistics. I'm off to a good start, because I recently investigated an issue which started me thinking about spatial statistics—a branch of statistics that I have never formally studied. During the investigation, I asked myself: Given an

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Sampling from the multivariate normal distribution

SAS/IML software is often used for sampling and simulation studies. For simulating data from univariate distributions, the RANDSEED and RANDGEN subroutines suffice to sample from a wide range of distributions. (I use the terms "sampling from a distribution" and "simulating data from a distribution" interchangeably.) For multivariate simulations, the IMLMLIB

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Computing probabilities can be tricky. And if you are a statistician and you get them wrong, you feel pretty foolish. That's why I like to run a quick simulation just to make sure that the numbers that I think are correct are, in fact, correct. My last post of 2010

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Automating the Great Christmas Gift Exchange

In many families, siblings draw names so that each family member and spouse gives and receives exactly one present. This year there was a little bit of controversy when a family member noticed that once again she was assigned to give presents to me. This post includes my response to

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Sampling with replacement

Sampling with replacement is a useful technique for simulations and for resampling from data. Over at the SAS/IML Discussion Forum, there was a recent question about how to use SAS/IML software to sample with replacement from a set of events. I have previously blogged about efficient sampling, but this topic