STATISTICAL ANALYSIS OF MAPPED SPATIAL POINT PATTERNS
STATISTICAL ANALYSIS OF MAPPED SPATIAL POINT PATTERNS
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Date
1988-05
Authors
DOGUWA, SANI IBRAHIM
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Abstract
The object of this study is to examine the various methods which deal
with tests of randomness for univariate mapped point patterns. Some of
these methods are extended to multitype patterns. Particular attention is
paid to the bounded nature of the pattern being studied, and the
complications that thereby arise in the implementation of the various
methods.
Edge corrections are reported for the mean and variance of the average
distance between a sampling point and the nearest object, X, for the case
of a regular grid of sampling points. Using these corrections the
point-object analogue of the Clark-Evans statistic is found to be a
powerful detector of departures from randomness in the clustered direction.
A new edge-corrected estimator is proposed for the second moment
cumulative function K(t), introduced by Ripley for the study of spatial
point processes. This new estimator is compared by simulation methods with
existing edge-corrected estimators in the context of L(t) function which is
used to study point patterns. The result of the simulation study suggests
that the new estimator provides almost unbiased estimate of L(t) and has a
smaller mean squared error than its predecessors.
A new method is proposed for estimating G(w) and F(x), the
distribution functions of the object-to-object and point-to-object nearest
neighbour distances respectively. The new method makes more complete use
of the information available and has a smaller mean squared error than the
existing alternatives. The method appears equally effective with random,
clustered and regular patterns.
Programs for statistical analysis were written in FORTRAN and run on a
DEC system - 1.0/99 computer of the University of Essex. The graphs were
plotted on the versatec-plotter of the University using SIMPLE PLOT MARK2
Description
A thesis submitted to satisfy the requirements of the degree of Doctor of
Philosophy (Ph.D) in the Department of Mathematics, University of Essex.
Keywords
STATISTICAL ANALYSIS,, MAPPED SPATIAL POINT PATTERNS,