为精确表述公共交通资源的分布特征，进而准确衡量公共交通服务的公平性，以公交可达性作为公共交通资源度量指标，考虑可达性数据统计特性，选取对数正态（Logarithmic Normal, Lognormal）、对数Logistic（Fisk）、伽玛（Gamma）、韦伯（Weibull）、Singh-Maddala（SM）、Dagum、第二类Beta（Beta of the Second Kind, B2）和广义第二类Beta（Generalized Beta of the Second Kind, GB2）8种分布函数对公交可达性数据进行拟合，并检验各分布函数的拟合效果，从而寻找对公交可达性数据拟合效果最佳的分布函数。计算结果显示，各分布函数拟合效果从优至劣排序为：GB2 > B2 > Dagum>SM>Fisk>Lognormal>Weibull>Gamma，即四参数分布函数的拟合效果优于三参数分布函数，三参数分布函数的拟合效果优于两参数分布函数。研究表明：四参数GB2分布函数对公交可达性数据的拟合效果最佳，可更准确地体现出公共交通资源的分配情况。
In order to accurately express the distribution characteristics of public transportation resources, and then accurately measure the equity of public transportation services, the accessibility of public transportation was taken as the index to measure public transportation resources, and the statistical characteristics of accessibility data were considered. Eight distribution functions which were Lognormal(Logarithmic Normal), Fisk, Gamma, Weibull, SM(Singh-Maddala), Dagum, B2(Beta of the Second Kind) and GB2(Generalized Beta of the Second Kind) were selected to fit the data of public transportation accessibility. The fitting effect of each distribution function was tested to find the distribution function with the best fitting effect of public transportation accessibility data. The results show that the fitting effect of each distribution function is ranked as follows: GB2 > B2 > Dagum > SM > Fisk > Lognormal>Weibull>Gamma, which means the fitting effect of four-parameter distribution function is better than that of three-parameter distribution function, and the fitting effect of three-parameter distribution function is better than that of two-parameter distribution function. The research shows that the four-parameter GB2 distribution function has the best fitting effect on public transportation accessibility, and it could reflect the allocation of public transportation resources more accurately.
[1] Delbosc A, Currie G. Using Lorenz curves to assess public transportation equity[J]. Journal of Transport Geography, 2011, 19(6): 1252-1259.
[2] Welch T F, Mishra S. A measure of equity for public transit connectivity[J]. Journal of Transport Geography, 2013, 33: 29-41.
[3] Ricciardi A M, Xia J, Currie G. Exploring public transportation equity between separate disadvantaged cohorts: A case study in Perth, Australia[J]. Journal of Transport Geography, 2015, 43: 111-122.
[4] Carleton P R, Porter J D. A comparative analysis of the challenges in measuring transit equity: definitions, interpretations, and limitations[J]. Journal of Transport Geography, 2018, 72: 64-75.
[5] Ben-Elia E, Benenson I. A spatially-explicit method for analyzing the equity of transit commuters' accessibility[J]. Transportation Research Part A: Policy and Practice, 2019, 120: 31-42.
[6] Frosini B V. Approximation and decomposition of Gini, Pietra-Ricci and Theil inequality measures[J]. Empirical Economics, 2012, 43: 175-197.
[7] 陈建东，程树磊，蒲明．如何准确地拟合居民的收入分布[J]．北京工商大学学报（社会科学版），2017，32（2）：10-20．
[8] Giorgi G M, Nadarajah S. Bonferroni and Gini indices for various parametric families of distributions[J]. Metron, 2010, 68: 23-46.
[9] Chotikapanich D, Griffiths W, Karunarathne W, et al. Calculating poverty measures from the generalised beta income distribution[J]. Economic Record, 2013, 89(S1): 48-66.
[10] 吴玲玲，黄正东．基于多样性的大城市公共交通服务水平研究[J]．交通运输系统工程与信息，2019，19（1）：222-227．
[11] McDonald J B, Sorensen J, Turley P A. Skewness and kurtosis properties of income distribution models[J]. Review of Income and Wealth, 2013, 59(2): 360-374.
[12] 陈建东，罗涛，赵艾凤．收入分布函数在收入不平等研究领域的应用[J]．统计研究，2013，30（9）：79-86．
[13] Sarabia J M, Jordá V. Explicit expressions of the Pietra index for the generalized function for the size distribution of income[J]. Physica A: Statistical Mechanics and its Applications, 2014, 416: 582-595.
[14] Chen Y T. A Unified approach to estimating and testing income distributions with grouped data[J]. Journal of Business & Economic Statistics, 2018, 36(3): 438-455.
[15] Perez C G, Alaiz M P. Using the Dagum model to explain changes in personal income distribution[J]. Applied Economics, 2011, 43(28): 4377-4386.
[16] Graf M, Nedyalkova D. Modeling of Income and Indicators of Poverty and Social Exclusion Using the Generalized Beta Distribution of the Second Kind[J]. Review of Income and Wealth, 2013, 60(4): 821-842.
[17] Chotikapanich D, Griffiths W E, Hajargasht G, et al. Using the GB2 Income Distribution[J]. Econometrics, 2018, 6(2): 21.
[18] Currie G. Quantifying spatial gaps in public transportation supply based on social needs[J]. Journal of Transport Geography, 2010, 18(1): 31-41.
[19] Murray A T. Strategic analysis of public transportation coverage[J]. Socio-Economic Planning Sciences, 2001, 35(3): 175-188.
[20] Gutiérrez J, García-Palomares J C. Distance-measure impacts on the calculation of transport service areas using GIS[J]. Environment and Planning B: Planning and Design, 2008, 35(3): 480-503.
[21] Soest D V, Tight M R, Rogers C D. Exploring the distances people walk to access public transportation[J]. Transport reviews, 2020, 40(2): 160-182.
[22] 杜光远，谭桂菲．基于路径规划数据的公共交通站点覆盖水平评价方法[J]．交通运输研究，2020，6（2）：68-75，82．
[23] Xia J, Nesbitt J, Daley R, et al. A multi-dimensional view of transport-related social exclusion: A comparative study of Greater Perth and Sydney[J]. Transportation Research Part A: Policy and Practice, 2016, 94: 205-221.
[24] Camporeale R, Caggiani L, Fonzone A, et al. Quantifying the impacts of horizontal and vertical equity in transit route planning[J]. Transportation Planning and Technology, 2017, 40(1): 28-44.
[25] 张萌旭，陈建东，蒲明．城镇居民收入分布函数的研究[J]．数量经济技术经济研究，2013，30（4）：57-71．
[26] Bandourian R, Mcdonald J, Turley R. A Comparison of parametric models of income distribution across countries and over time[R]. Provo: Department of Economics, Brigham Young University, 2002.
[27] Reed W J, Wu F. New four-and five-parameter models for income distributions[M]// Modeling Income Distributions and Lorenz Curves. New York: Springer, 2008: 211-223.
[28] 林立，陈政清，洪华生，等．基于广义统一概率图的东南沿海风速概率分布研究[J]．湖南大学学报（自然科学版），2019，46（11）：181-188．
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