The concept of density lacks the ability to explain the diversity of physical elements of urban form such as building lot sizes. Thus, urban planners tend to discuss the validity of density values without taking into consideration the variation of building lot sizes due to the limited data available on building lot shapes. Our objective is to discuss the potential of building density and road network density in order to estimate the size distribution of building lots at the district scale in downtown Tokyo. The study finds that (1) building lot sizes approximately follow the lognormal distribution whose parameters, mean, and variance are formulated by gross building density, the coefficient of variation of building lots, road network density, and average road width by removing large building lots and (2) the value of the coefficient of variation is approximately equal to one. As a practical problem, we discuss how to determine the maximum building density by considering the variation of building lot sizes. It was found that the maximum building density can be determined based on a stochastic approach. These findings are expected to provide urban planners with a theoretical basis for discussing the validity of density values.

中文翻译：

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建筑物的大小分布以及建筑物和道路网络的密度：基于吉布拉特定律的理论推导和东京市区的实证研究

密度的概念缺乏解释城市形式的物理要素（例如建筑规模）的多样性的能力。因此，城市规划者倾向于讨论密度值的有效性，而不考虑由于建筑地块形状的有限数据而导致的建筑地块大小的变化。我们的目的是讨论建筑物密度和道路网络密度的潜力，以便估算东京市区区域规模内建筑物规模的分布。研究发现（1）建筑物的大小大致遵循对数正态分布，其参数，均值和方差由建筑物的总密度，建筑物的变异系数，路网密度，（2）变异系数的值大约等于1。作为一个实际问题，我们讨论了如何通过考虑建筑物地块大小的变化来确定最大建筑物密度。已经发现，可以基于随机方法来确定最大建筑物密度。这些发现有望为城市规划者提供讨论密度值有效性的理论依据。