Settlement Populations and the Lognormal Distribution

Aitchison, J. and Brown, J.A.C. (1957) The Lognormal Distribution. Cambridge: Cambridge University Press.

Beckmann, M.J. (1958) City Hierarchies and the Distribution of City Size . Economic Development and Cultural Change, Vol. 6, No. 3, 243-248.

Beckmann, M.J. (1968) Location Theory. New York: Random House.

Berry, B.J.L. (1961) City Size Distributions and Economic Development . Economic Development and Cultural Change, Vol. 9, No. 4, 573-587.

Berry, B.J.L. (1964) Cities as Systems within Systems of Cities. Papers of the Regional Science Association, Vol. 13, 147-163.

Berry, B.J.L. (1971) City Size and Economic Development: Conceptual Synthesis and Policy Problems, with Special Reference to South and Southeast Asia. Urbanization and National Development, edited by L. Jakobson and V. Prakash. Beverley Hills, California: Sage Publications.

Christaller, W. (1966) Central Places in Southern Germany. Translated by C. Baskin. Englewood Cliffs, N. J.: Prentice-Hall.

Curry, L. (1964) The Random Spatial Economy: An Exploration in Settlement Theory. Annals of the Association of American Geographers , Vol. 54, No. 1,138-146.

Deutsche Arbeitsfront (1939) Zwei Ausgleigungsmethoden für statistische Verteilungen. Arbeitswissenschaftliches Institut der Deutschen Arbeitsfront, Vol. 2, 205-226.

Fano, P. (1969) Organization, City-Size Distributions and Central Places. Papers of the Regional Science Association, Vol. 22, 29-38.

Feller, W. (1960) An Introduction to Probability Theory and its Applications , Vol. 1. New York: John Wiley.

Gibrat, R. (1931) Les Inégalites Économiques. Paris: Recueil Sirey.

Haggett, P. (1965) Locational Analysis in Human Geography. London: Edward Arnold.

Johnson, J.H. (1967) Urban Geography. Oxford: Pergammon Press.

Kalecki, M. (1945) On the Gibrat Distribution. Econometrica , Vol. 13, No. 1, 161-170.

Kapteyn, J.C. (1903) Skew Frequency Curves in Biology and Statistics. Groningen : Noordhoof.

Losch, A. (1954) The Economics of Location. Translated by W. H. Woglom and W. F. Stolper. New Haven: Yale University Press.

Lotka, A. (1925) Elements of Physical Biology. Baltimore: Williams and Wilkins.

Mandelbrot, B. (1965) A Class of Long-Tailed Probability Distributions and the Empirical Distribution of City Size. Mathematical Explorations in Behavioral Science, edited by F. Massarik and P. Ratoosh. Homewood, Ill.: Richard D. Irwin.

McAlister, D. (1879) The Law of the Geometric Mean. Proceedings of the Royal Society of London, Vol. 29, 367-376.

Parr, J.B. (1970) Models of City Size in an Urban System. Papers of the Regional Science Association, Vol. 25, 221-253.

Parr, J.B. (1973) Structure and Size in the Urban System of Lösch . Economic Geography, Vol. 49, No. 3, 185-212.

Prost, M.A. (1965) La Hiérarchie des Villes en Fonction de leurs Activités de Commerce et de Service. Paris: Gauthier-Villars.

Quandt, R.E. (1964) Statistical Discrimination among Alternative Hypotheses and some Economic Regularities. Journal of Regional Science , Vol. 5, No. 2, 1-23.

Simon, H. (1955) On a Class of Skew Distribution Functions. Biometrika, Vol. 42, No. 3, 425-440.

Simon, H. (1968) On Judging the Plausibility of Theories. Logic, Methodology, and Philosophy of Science, Vol. 3, edited by B. Van Rootselaar and J. F. Staal. Amsterdam: North-Holland Publishing Company.

Stanback, T.M. and Knight, R.V. (1970) The Metropolitan Economy: The Process of Employment Expansion. New York: Columbia University Press.

Steindl, J. (1965) Random Processes and the Growth of Firms. New York: Hafner.

Stewart, C.T. (1958) The Size and Spacing of Cities. Geographical Review, Vol. 48, No. 2, 222-245.

Tachi, M. (1962) Shuto o Chusin toshite mita Jinko Shuchu ni kansuru 'Hosoko' [The 'Laws' Concerning the Tendency toward the Concentration of Population, especially in Metropolitan Areas]. Mimeographed report, Institute for Urban Affairs, Tokyo Urban Research Association.

Thomas, E.N. (1967) Additional Comments on Population Size Relationships for Sets of Cities. Quantitative Geography, edited by W. H. Garrison and D. F. Marble, Northwestern University Studies in Geography, No. 13.

U.S. Department of Commerce, Bureau of the Census (1968) Metropolitan Area Definition: A Re-evaluation of Concept and Statistical Practice. Bureau of the Census Working Paper No. 28 . Washington, D.C.

U.S. Department of the Interior, Census Office ( 1883) Population of the United States at the Tenth Census. Washington, D.C.

Ward, B. (1962) Greek Regional Development. Research Monograph Series No. 4. Athens: Center of Economic Research.

Zipf, G.K. (1949) Human Behavior and the Principle of Least Effort . Cambridge: Addison-Wesley.