# exponential density function

## exponential density function

[‚ek·spə′nen·chəl den·səd·ē ‚fəŋk·shən]
(mathematics)
A probability density function obtained by integrating a function of the form exp (-| x-m |/σ), where m is the mean and σ the standard deviation.
References in periodicals archive ?
While many empirical studies employ the negative exponential density function to study such change, this paper studies urban form by examining the spatial pattern of development.
The most widely used method in describing these distributions is to employ zonal data in the estimation of the negative exponential density function. Despite the widespread use, zonal data and the density function provide only a limited picture of changes in urban form.
The paper also provides an alternative approach to the traditional exponential density function to explore transformations in urban form.
First, we explain the traditional negative exponential density function and then review several empirical studies that employ the function.
While the study areas may vary, the most commonly used method is to estimate the negative exponential density function. The negative exponential density function provides insight into the relationship between population and/or employment density and distance to the centre of the city.
Clark estimated the model for several cities and concluded that the negative exponential density function is the norm for urban population density patterns.
First, the study estimates the negative exponential density function using census tract data.
Despite the widespread use of the negative exponential density function, the growth and resultant urban form of contemporary urban areas brings into question the functions' applicability.
In addition to the problems associated with the negative exponential density function, there are several problems in using aggregate zonal data when estimating the function.
Second, many of the empirical studies employ the negative exponential density function in examining changes in urban form.
The negative exponential density function is a popular measure of urban spatial structure because calculations are not data intensive (as few as two points of data - city center and rural fringe - have been used to produce estimates of density gradients).
The most time consuming step in these particle based algorithms in presence of exponential density functions, is the evaluation of functions of following form,
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