This paper suggests a general framework for several frequently used information statistics. The basis for the analysis is a set of regions each of which contains a number of cells. The objective is to evaluate the number of microstates associated with a distribution of distinguishable individuals amongst these cells. Several existing measures are derived, and a more general measure is suggested which incorporates knowledge about the sizes of the regions and the types of individuals. In each case an example is given of the application of the measure that uses Jaynes's principle of maximum entropy.
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References
1.
BattyM, 1976“Entropy in spatial aggregation”Geographical Analysis81–21.
2.
DowsonD CWraggA, 1973“Maximum-entropy distributions having prescribed first and second moments”IEEE Transactions on Information TheoryIT-19689–693.
3.
EvansR A, 1969“The principle of minimum information”IEEE Transactions on ReliabilityR-1887–90.
4.
Georgescu-RoegenN, 1971The Entropy Law and the Economic Process (Harvard University Press, Cambridge, Mass).
5.
HobsonA, 1969“A new theorem of information theory”Journal of Statistical Physics1383–391.
6.
HobsonAChengB K, 1973“A comparison of the Kullback and Shannon information measures”Journal of Statistical Physics7301–310.
7.
JaynesE T, 1957“Information theory and statistical mechanics”Physical Review106171–190.
8.
JaynesE T, 1968“Prior probabilities”IEEE Transactions on Systems Science and CyberneticsSSC-4227–248.
9.
KullbackS, 1968Information Theory and Statistics (Dover, New York).
10.
RenyiA, 1970Probability Theory (North-Holland, Amsterdam).
11.
SeniorH L, 1973“Approaches to residential location modelling 1: Urban ecological and spatial interaction models”Environment and Planning5165–197.
12.
ShannonC E, 1948“A mathematical theory of communication”Bell System Technical Journal27379–423, 623–656.
13.
SnickarsFWeibullJ W, 1977“A minimum information principle, theory and practice”Regional Science and Urban Economics7137–168.
14.
TribusM, 1969Rational Descriptions, Decisions and Designs (Pergamon Press, New York).
15.
WalshJ A, 1978“An analysis of intraurban residential ownership patterns”Environment and Planning A1017–28.
16.
WalshJ AO'KellyM E, 1979“An information theoretic approach to measurement of spatial inequality”Economic and Social Review10267–286.
17.
WalshJ AWebberM J, 1977“Information theory: Some concepts and measures”Environment and Planning A9395–417.
18.
WebberM J, 1975“Entropy-maximising location models for nonindependent events”Environment and Planning A799–108.
19.
WebberM J, 1979Information Theory and Urban Spatial Structure (Croom Helm, London).
20.
WilsonA G, 1967“Statistical theory of spatial trip distribution models”Transportation Research1253–269.
21.
WilsonA G, 1970Entropy in Urban and Regional Modelling (Pion, London).
22.
WilsonA G, 1974Urban and Regional Models in Geography and Planning (John Wiley, Chichester, Sussex).
