## Tag: Spatial Data

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The area of the convex hull of random points

I recently blogged about how to compute the area of the convex hull of a set of planar points. This article discusses the expected value of the area of the convex hull for n random uniform points in the unit square. The article introduces an exact formula (due to Buchta,

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Is "La Quinta" Spanish for "Next to Denny's"?

“La Quinta” is Spanish for “next to Denny’s.”      -- Mitch Hedberg, comedian Mitch Hedberg's joke resonates with travelers who drive on the US interstate system because many highway exits feature both a La Quinta Inn™ and a Denny's® restaurant within a short distance of each other. But does a

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The empty-space distance plot

How far away is the nearest hospital? How far is the nearest restaurant? The nearest gas station? These are commonly asked questions whose answers depend on the location of the person asking the question. Recently I showed an algorithm that enables you to find the distance between a set of

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The distribution of nearest neighbor distances

Last week I showed how to compute nearest-neighbor distances for a set of numerical observations. Nearest-neighbor distances are used in many statistical computations, including the analysis of spatial point patterns. This article describes how the distribution of nearest-neighbor distances can help you determine whether spatial data are uniformly distributed or

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Create a map with PROC SGPLOT

Did you know that you can use the POLYGON statement in PROC SGPLOT to draw a map? The graph at the left shows the 48 contiguous states of the US, overlaid with markers that indicate the locations of major cities. The plot was created by using the POLYGON statement, which

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How to compute the distance between observations in SAS

In statistics, distances between observations are used to form clusters, to identify outliers, and to estimate distributions. Distances are used in spatial statistics and in other application areas. There are many ways to define the distance between observations. I have previously written an article that explains Mahalanobis distance, which is

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How to use spatial statistics to crack a scratch-off game

On Friday, I posted an article about using spatial statistics to detect whether a pattern of points is truly random. That day, one of my colleagues asked me whether there are any practical applications of detecting spatial randomness or non-randomness. "Oh, sure," I replied, and rattled off a list of

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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