MODIFIED POISSON PROBABILITY LAW FOR POINT PATTERN MORE REGULAR THAN RANDOM1
Michael F. Dacey · Annals of the Association of American Geographers · 1964
MAPPING, and using map evidence, for incisive, descriptive statements about spatial distributions is a fundamental operation in geographic research. In terms of their abstract properties, map distributions exist in one of the three lowest geometric dimensions -the use of points, lines, and areas to represent a distribution. Map analysis is the description of the density and pattern of this geometry. The map itself may serve as the descriptive statement, or the many subtleties of map distributions may be summarized into symbols, words, or numbers. Highly regular or obviously systematic patterns are found infrequently in geographic investigations. Usually, the patterns display no obvious order or system. In interpreting such patterns, there is a temptation to dismiss analysis with the statement that the distribution is irregular or, possibly, to say that it is a distribution. To say that a distribution is irregular neither effectively describes it nor suggests cause. To say that a distribution is random, in a nontechnical sense, is to say that the pattern has no discernible order and that cause is undeterminable. In the terminology of mathematical statistics, the term random has a precise meaning which refers to the process generating a pattern and the pattern is the realization of a theoretical process. A process is synonymous with pure chance because each event has an equal probability of occurrence. In terms of a map pattern, pure chance means that each map location has an equal probability of receiving a symbol. Since it is highly unlikely that geographic distributions, particularly locational patterns involving human decisions, are the result of equally probable events, it is expected that most map patterns reflect some system or order. It is for this reason that map patterns are examined for evidence of a spatial process. The search for