The trip-distribution problem is discrete in formulation and combinatorial in nature. This truism has been ignored, as well as obscured, by the total attention focused on the use of the asymptotic methods of the gravity model for the maximum-entropy estimation of interzonal trips. These estimates appear to be reasonably reliable in indicating the regions—not the exact states—of highest probability. The Darwin–Fowler derivation of the gravity model demonstrates that the asymptotic solution is exactly equal to the average of all feasible microstates. Calibration of the model can be based on this proposition. An approach to testing the principle that all microstates are equally probable is outlined.
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References
1.
ArtinE, 1964The Gamma Function (Holt, Rinehart and Winston, New York)
2.
BakerR J, 1977“Exact distributions derived from two-way tables”Applied Statistics26199–206
3.
ChapmanG C, 1977Human and Environmental Systems: A Geographer's Appraisal (Academic Press, London)
4.
DinkelJ JKochenbergG AWongS-N, 1977“Entropy maximization and geometric programming”Environment and Planning A9419–427
5.
DuffinR JZenerC, 1970“Geometric programming and the Darwin–Fowler method in statistical mechanics”Journal of Physical Chemistry742419–2423
6.
EvansA W, 1971“The calibration of trip distribution models with exponential or similar cost functions”Transportation Research515–38
7.
FavellaL F, 1968“On the connection between quantum-mechanical Green's functions and the Darwin–Fowler method in statistical mechanics”Nuovo Cimento58B107–123
8.
GailMMantelN, 1977“Counting the number of r × c contingency tables with fixed margins”Journal of the American Statistical Association72859–862
9.
Georgescu-RoegenN, 1971The Entropy Law and the Economic Process (Harvard University Press, Cambridge, Mass)
10.
GoodI JCrookJ F, 1977“The enumeration of arrays and a generalization related to contingency tables”Discrete Mathematics1923–45
11.
GreenbergH, 1971Integer Programming (Academic Press, New York)
12.
JurkatW BRyserH J, 1967“Term ranks and permanents of nonnegative matrices”Journal of Algebra5342–357
13.
NijenhuisAWilfH S, 1975Combinatorial Algorithms (Academic Press, New York)
14.
NijkampP, 1975“Reflections on gravity and entropy models”Regional Science and Urban Economics5203–225
15.
RényiA, 1970Probability Theory (North-Holland, Amsterdam)
16.
SnickarsFWeibullJ W, 1977“A minimum information principle: Theory and practice”Regional Science and Urban Economics7137–168
17.
ThomasR W, 1976“The role of Bose–Einstein statistics in point pattern analysis”Geographical Analysis9113–136
18.
ThomasR W, 1977“An interpretation of the journey-to-work on Merseyside using entropy-maximizing methods”Environment and Planning A9817–834
19.
WilsonA G, 1970Entropy in Urban and Regional Modelling (Pion, London)
