Some Extensions of Mills's Method for Urban Population Density Gradient Estimation

This paper extends Milk's method for estimating urban population density gradients to general noncircular and asymmetrical urban forms, using Gauss-Legendre quadrature embedded in a Newton-Raphson root finding algorithm. We also examine the sensitivity of the Mills method to measurement errors in the assumptions. Several issues arising from the comparison of analytical, Mills type estimation procedures with statistical procedures are explored, particularly in light of recent work that questions the negative exponential formulation of urban density gradients. We note in particular the influence of secondary population centers as a source of estimation bias.     

A Mathematical Model of the Density Distribution of Moscow's Population

A student research project at Moscow University tests Colin Clark's formula for the distribution of the density of a single-center city by applying it to population data of Moscow for 1963, 1964, and 1965. The students obtain repression lines and equations for the population density of Moscow and draw the density field by means of isolines. The results suggest population movement from the central district to outlying areas where intensive housing construction is under way.     

A Structural Approach to the Form of the Population Density Function

The central objective of this paper is to explore a comprehensive structural modeling approach that extracts analytical density functions answering questions raised by recent empirical studies.     

The Density of Population of a City and the Density of Probability of a Random Magnitude

A continuation of a paper translated in Soviet Geography, April 1966, establishes a systematic relationship between the concept of a city's population density and the general theoretical probability concept of the probability density function of a two-dimensional random magnitude, and extends the discussion of population-density models beyond the category of single-center cities to a variety of non-single-center formations.     

Association between Population Density and The Market Areas of Towns

This paper examines the relationship between population density and town spacing in four kinds of environment. These are: (1) linear curves of demand, transport and production costs and an even population distribution; (2) nonlinear transport cost curves over space; (3) variable population density within hinterlands; and (4) variation of transport costs with population density. Previously, it has been shown that the criterion of free entry does not uniquely determine town spacing. The implications of four stronger criteria are therefore examined in this paper. These location criteria are: (a) the number of towns is maximized; (b) the number of towns in minimized, subject to all consumers' being served; (c) the towns are all owned by one profit-maximizing monopolist; and (d) the average of some consumer utility function is maximized. In cases (a), (c), and (d) spacing decreases with density; in (b) spacing is an increasing function of density. Actual data are presented on the spacing of towns in Iowa and shopping centers in Chicago which indicate that spacing and population density are not associated. These results are consistent with the notion that entry is free but are not consistent with the stronger constraints employed in this paper.     

Uniform Probability Density Analysis and Population History in the Northern Rio Grande

One of the basic challenges facing archaeology is translating surface evidence into population estimates with sufficient chronological resolution for demographic analysis. The problem is especially acute when one is working with sites inhabited across multiple chronological periods and the production curves for pottery types are unknown. In this paper, I present a Bayesian statistical method which I call uniform probability density analysis that is tailored to this situation. This method combines uniform distributions derived from the local pottery chronology with pottery assemblage data to reconstruct the population history of individual settlements. I also illustrate applications of this method at the site and regional level using data from Cuyamungue and the surrounding Tewa Basin/VEP II New Mexico project area. The results allow one to identify a period of significant population movement corresponding to the period of Tewa ethnogenesis in the thirteenth century CE.     

Reconstructing Population Density Surfaces from Areal Data: A Comparison of Tobler's Pycnophylactic Interpolation Method and Area-to-Point Kriging

We compare Tobler's pycnophylactic interpolation method with the geostatistical approach of area-to-point kriging for distributing population data collected by areal unit in 18 census tracts in Ann Arbor for 1970 to reconstruct a population density surface. In both methods, (1) the areal data are reproduced when the predicted population density is upscaled; (2) physical boundary conditions are accounted for, if they exist; and (3) inequality constraints, such as the requirement of non-negative point predictions, are satisfied. The results show that when a certain variogram model, that is, the de Wijsian model corresponding to the free-space Green's function of Laplace's equation, is used in the geostatistical approach under the same boundary condition and constraints with Tobler's approach, the predicted population density surfaces are almost identical (up to numerical errors and discretization discrepancies). The implications of these findings are twofold: (1) multiple attribute surfaces can be constructed from areal data using the geostatistical approach, depending on the particular point variogram model adopted—that variogram model need not be the one associated with Tobler's solution and (2) it is the analyst's responsibility to justify whether the smoothness criterion employed in Tobler's approach is relevant to the particular application at hand. A notable advantage of the geostatistical approach over Tobler's is that it allows reporting the uncertainty or reliability of the interpolated values, with critical implications for uncertainty propagation in spatial analysis operations.     

Cost Efficiency,Urban Patterns and Population Density When Providing Public Infrastructure: A Stochastic Frontier Approach

Relying on stochastic frontier analysis we propose a methodology to study the technological characteristics and cost efficiency levels related to the provision of public infrastructure for basic utilities. The methodology assumes a cost minimizing behaviour on the part of public officials when planning the construction of local infrastructure, which is represented by way of a flexible translog cost function. Introducing relevant definitions of scale economies, associated with larger numbers of inhabitants and dwellings, as well as economies of density, brought about by reductions in urban dispersion, we analytically determine the optimal population densities for which average cost is minimized. We illustrate our model with the water cycle sector, including water distribution, sewage collection and cleansing of wastewater, and considering data at the municipality level for the Spanish region of Castilla y León. The obtained results indicate potential cost savings in the form of decreasing average costs, as relevant scale and density economies are present, along with large inefficiency levels. Relevant policy guidelines favouring larger and denser urban sizes are drawn, as the observed cost excess is the result of a general suboptimal urban size in terms of population density, and the negative effects of dispersed settlement patterns.     

Spatial Analysis of Employment and Population Density: The Case of the Agglomeration of Dijon 1999

The aim of this paper is to analyze the intraurban spatial distributions of population and employment in the agglomeration of Dijon (regional capital of Burgundy, France). We study whether this agglomeration has followed the general tendency of job decentralization observed in most urban areas or whether it is still characterized by a monocentric pattern. To that purpose, we use a sample of 136 observations at the communal and at the IRIS (infraurban statistical area) levels with 1999 census data and the employment database SIRENE (INSEE). First, we study the spatial pattern of total employment and employment density using exploratory spatial data analysis. Apart from the CBD, few IRIS are found to be statistically significant, a result contrasting with those found using standard methods of subcenter identification with employment cut‐offs. Next, in order to examine the spatial distribution of residential population density, we estimate and compare different specifications: exponential negative, spline‐exponential, and multicentric density functions. Moreover, spatial autocorrelation, spatial heterogeneity, and outliers are controlled for by using the appropriate maximum likelihood, generalized method of moments, and Bayesian spatial econometric techniques. Our results highlight again the monocentric character of the agglomeration of Dijon.     

A Generalization of the Utility Theory Approach To the Problem of Spatial Interaction

The derivation of the gravity model from utility theory is reformulated and generalized in order to show (1) how both the number of trips to individual destinations and the total travel budget may be determined simultaneously, and (2) how the effect of both distance and destination quality on trip distribution and total budget may be analyzed. Results are compared with the revealed space preference approach and are found to be superior in dealing theoretically with trip frequency and the effects of spatial context. For empirical applications, however, the revealed preference approach is advantageous.