Zipf Law Analysis of Urban Scale in China

Transcription

1 Asan Journal of Socal Scence Studes; Vol. 1, No. 1; 2016 ISSN Publshed by July Press Zpf Law Analyss of Urban Scale n Chna Wen Zqn 1 1 Graduate School of educaton, Jnan Unversty, Guangzhou, Chna Correspondence: L Yang, School of economcs, Jnan Unversty, Guangzhou, Chna. Tel: E-mal: kobe0823yang1022@163.com Receved: February 1, 2016 Accepted: February 5, 2016 Onlne Publshed: February 29, 2016 do: /ajsss.v11.21 URL: Abstract In ths paper, by usng Chna's urban populaton data from 1990 to 2010 and double logarthmc regresson model to test Chna s urban scale and urban rank through Zpf law, we found that Chna s urban scale dstrbuton s relatvely balanced, vrtually conformng to Zpf's law. Researchng and analyzng urban scale dstrbuton of Chna s every provnce s, we also found that the urban scale dstrbutons of Chna s all provnces are relatvely complcated and they are not even close to 1. The ncrease of Zpf ndex means that urban scale dstrbuton s transtng from prmacy degree dstrbuton to deal Zpf dstrbuton. Further analyzng and categorzng every provnce s Zpf ndex, we can conclude that Chna s urban scale dstrbuton can be categorzed four manly: acheved deal Zpf law; approachng to deal Zpf dstrbuton; The transton state from the prmacy degree dstrbuton to the Zpf law dstrbuton; typcal prmacy degree dstrbuton. Keywords: Zpf law, urban dstrbuton, urban scale 1. Introducton In the research of cty sze dstrbuton, the urban scale and the urban level have good characterstcs. The earlest research on urban scale and order s from Auerbach (1913) and Snger (1936). They beleve that the scale of the cty and the sequence can be characterzed by Pareto dstrbuton, and there s a mathematcal relatonshp of: y A x a.zpf (1949) beleves that the scale of the cty can not only be expressed by the Pareto dstrbuton, and when 1,t found R S A, Zpf ndex, the relatonshp between the sze of the cty and the order of the cty s called the Zpf rule. Snce 1950s, a large number of emprcal studes have been carred out on the Zpf law. Berry (1961) by the 38 countres on the urban populaton data for emprcal testng, the cty sze dstrbuton s dvded nto three categores:frstly, ncludng 13 countres, n full complance wth the sze of the cty and the sequence dstrbuton, that s, the cty sze dstrbuton of the Zpf rule. Secondly, ncludng 15 countres, ncludng the frst cty to control the scale of urban structure characterstcs; thrdly, there are 10 countres balance between the above characterstcs. Madden (Madden) usng the Unted States cty populaton data from 1790 to 1950, the use of a logarthmc model to test the stablty of the Zpf rule. The concluson shows that the urban structure system changes very quckly n the scale, and the cty's rank s also found changng, but the cty sze dstrbuton tself s stable n a long tme. Soo (2004) usng 75 natonal urban populaton data, usng the method of least squares fttng and maxmum lkelhood estmaton to compare the Zpf ndex of several countres n the world. The results show that the dstrbuton of the countres n the world s bascally n accordance wth the Zpf law, and the law s stable. The domestc scholar Xu Xueqang (1993) tracked the urban scale dstrbuton of the top 1953 n Chna n the , and predcted the stuaton n Through the Zpf rule test of the cty sze dstrbuton n Chna, the characterstcs and the changng trend of the cty sze dstrbuton n Chna are analyzed. The study s dvded nto four parts. Frst part s a lterature revew; the second part s the part of emprcal research, manly on the model set and research data do a bref descrpton; 53

2 the thrd part of the emprcal results were analyzed; the fourth part s a bref concluson of the research. 2. Model and Data 2.1 Model Settngs We manly uses the followng model to test the sze dstrbuton of ctes n Chna: ln R ln A ln S (1) Where R s the cty level,, S s the sze of the cty, s the Zpf ndex,the Pareto value,but also need to estmate the data equaton. The man purpose of the study s to study the sze and change trend of the Zpf ndex of urban sze dstrbuton n Chna. In the cty sze dstrbuton, the Zpf ndex ( value) shows the aggregaton of the cty sze dstrbuton. The natural logarthm of cty scale and regstraton s calculated, and the regresson of these data s obtaned. The sgnfcant log lnear model s the order - scale rule. If the slope of the regresson s-1 ( 1 ),then the cty sze of the Zpf rule can be verfed. If 1,shows that the cty's populaton s relatvely scattered, small and medum-szed cty scale development s good, the hgh level of urban sze s not promnent; f 1,proved that the scale of the dstrbuton s concentrated, small and medum-szed urban populaton sze s poor, the sze of large urban populaton growth, urban sze dstrbuton of the frst degree s hgher. In Zpf's ndex to study the trend of changes, n becomes large,show that the cty sze dstrbuton tends to be concentrated strength s greater than that of the dsperson of power ;f s smaller, ndcatng that makes the cty scale dstrbuton tends to dsperse the strength s greater than the concentraton of power. Gabax and Ioanndes (1975) proposed usng Hll method to replace the least squares method to calculate the dstrbuton of urban sze Zpf ndex. The Hll method s essentally a maxmum lkelhood estmaton method n the case of the model. If the sample sze s n, the expresson of the sze of the cty s: x 1 x 2 x 3... x, The cty sze dstrbuton of Zpf ndex can be calculated by the followng equaton: n 1 1 n 1 ln x ln x n Standard devaton representaton as: ( ) n 2 1/2 n 1 ln x ln x /2 n 2 n 1 Through the emprcal test of the Zpf rule of Chna's cty sze dstrbuton, the ordnary least square method s adopted. The least square error of the least square method s relatvely small, and t can ft the relatonshp between the sze and the poston of the cty. The premse of the Hll method s that f the cty sze obeys Pareto dstrbuton, the Zpf ndex of urban scale s tested, whch s not representatve and general. 2.2 Data Descrpton An urban scale s the populaton, economy and scence and technology n a certan area of the sze of the aggregaton. The general scale of the cty ncludes populaton scale, land use, buldng and facltes, and the scale of productvty and consumpton. Narrow cty scale only refers to the populaton sze n a certan cty. Compared to other measures of cty sze, the relevant data of urban populaton sze s more easy to collect, but also the most commonly used ndcators. The non-agrcultural populaton n Chna's urban resdence s the man measure of the urban scale. Take non agrculture populaton s: frst, non-agrcultural populaton n number and the bult area of the resdent populaton s close to; second, for the urban system, each cty non-agrcultural populaton and bult dstrct resdent populaton n general showed a lnear relatonshp; thrd, non-agrculture n 54

3 some extent to mantan statstcal consstency and comparablty. Secondly, because of Chongqng, Bejng, Shangha, Tanjn and other four muncpaltes have ther own specal characterstcs of the scale of the cty, the return of the four ctes are not consdered. In addton, Macau and Hong Kong n the late 1990s to revew the motherland, so Macao and Hong Kong's urban populaton data exst flaw phenomenon s serous, so we n the establshment of measurement model, wthout consderng the specal stuaton of Macau and Hong Kong. Smlarly, for the cty of Tawan scale, also temporarly do not consder. Fnally, due to the vast terrtory of Chna, the statstcal data of the urban populaton of Tbet autonomous regon has a serous defcency n the statstcal yearbook of Chna n recent years. And Tbet have a certan number of the scale of the cty s relatvely small, n order to prevent the statstcal results and the model brought large errors, we selected Chna statstcal yearbook data of cty sze dstrbuton test wll Tbet Autonomous Regon exclude outsde. Accordng to the orgnal data of the Chna Urban Statstcal Yearbook, a descrptve statstcal table of the urban populaton was obtaned, whch was shown n Table 1. Table 1. Descrptve statstcs of urban populaton n Chna from 1990 to 2010 Unt:10 thousand populaton Year Sample quantty Mn Max Med Average Emprcal Result 3.1 The Results of Regresson Analyss of Chna s Urban Scale Dstrbuton from 1990 to 2010 Accordng to regresson equaton ln R ln A ln S,based on Matlab R2013a, by usng least square fttng to analyze Chna s populaton from 1990 to 2010 wth regresson model, the results and analyss are shown n Table 2. Table 2. The results of regresson analyss of chna s urban scale dstrbuton from 1990 to 2010 Coeffcent Standard Devaton T Value PValue Accordng to the results from Table 2, P value are all 0 when usng double logarthmc model to do regresson analyss. They can all pass the hypothess test wth confdence level of 1%. Thus, we can conclude that the regresson analyss model s sgnfcant. The model well explans the good lnear relatonshp between the urban scale and the order of the cty. To better descrbe the trend of Zpf ndex of urban scale dstrbuton from 1990 to 2010, we made Fgure 1 based on Table 2. 55

4 Trend of Zpf ndex Fgure 1. The trend of Zpf ndex of urban scale dstrbuton from 1990 to 2010 It s shown that there are mnor fluctuaton of Zpf ndex of urban scale dstrbuton around 1, whch means that Zpf ndex of Chna s urban scale dstrbuton from 1990 to 2010 are balanced, conformng to the deal status of Zpf dstrbuton. Its basc trend s that Zpf ndex ncreased steadly from 1990 to 2005 but t began to fall around The urban scale dstrbuton ndex n 1990 was ( 1). Ths shows that Chna's urban populaton dstrbuton s relatvely concentrated n 1990, the prmacy degree s hgher, the larger ctes are relatvely promnent, whle the small and medum szed ctes are nsuffcent. Compared to 1990, urban scale dstrbuton n 1995 and 2000 were more close to 1, whch means that urban scale dstrbuton were more balanced and reached the deal status of Zpf dstrbuton. Zpf dstrbuton of 2005 was relatvely hgh, however f fell back to deal status n Testng Analyss of Chna's Urban Scale Provnces from 1990 to 2010 From 1990 to 2010, Chna's urban sze dstrbuton equlbrum, close to the deal state of the Zpf ndex dstrbuton. At the same tme, n recent years, Chna's economy has also been a good development, the cty's sze dstrbuton has also changed sgnfcantly. To ths end, n order to explore the status of the dstrbuton of urban sze and change n varous provnces and ctes, by the sze of ctes n varous provnces of Chna Zpf rule test. Analyss table 3 can found that, n the s, the Zpf dstrbuton of the provnces n Chna s more complex, and not sgnfcant. Between the provnces, and of dfferent perods, the dstrbuton of urban sze dfferences are great. Further analyss found that n 1990 Chna's urban sze dstrbuton n the Zpf deal state of the provnce a total of 13( ),whch shows that the sze dstrbuton of ctes n varous provnces of Chna has not reached the deal state dstrbuton. And n the 1995, 2000, 2005, 2010, Avenue equlbrum dstrbuton of provnces respectvely, 19, 19, 26, 26, from a natonwde perspectve, Chnese cty scale n provnces n recent ten years of the Zpf dstrbuton ndex n general has reached the deal state of the Zpf dstrbuton. In order to further study the Chna n years all the provnces of the urban scale dstrbuton, we re on the regresson analyss of Zpf's ndex evoluton of smlarty analyss, to classfy the varous provnces of the country of urban scale. The results shows that Chnese provnces, cty sze dstrbuton s manly dvded nto the followng categores: The frst category s Zpf's ndex s relatvely hgh, ndcatng that the provnces and ctes development s good, and the frst cty sze on the nfluence of the sze of the populaton of the provnce's s not obvous, the cty sze and rank are more balanced dstrbuton. Includng Laonng, Hunan, Schuan, Xnjang, Henan, Anhu. The second category are the provnces cty sze dstrbuton s bascally consstent wth the Zpf's law of an deal state of dstrbuton, provnces wth the central cty, and small and medum-szed ctes scale development of good, hgh order ctes complete s generally Chna's economy s relatvely developed, or scale economy relatvely large provnces. Includng Guangdong, Zhejang, Jangsu, Jln, Hube, Shandong, Fujan. The thrd category s the Zpf's ndex s relatvely small, belongng to the general economy s relatvely less 56

5 developed provnces, area economy s relatvely backward, center cty development s not perfect, resultng n center cty scale, thus hghlghtng has obvous frst features. At the same tme, the rapd development of economy n recent years promoted the rapd development, two provnces cty, provnce s n the frst degree dstrbuton to Zpf deal equlbrum dstrbuton of the transton state, these provnces ncludng Guangx, Jangx, Shanx, Hebe, Shaanx, Guzhou, Gansu. The fourth category s the Zpf's ndex s very small, provnces n general n addton to the center of the captal cty, other ctes are not perfect development, urban populaton hghly concentrated n the captal cty, s typcal of the frst feature, the cty sze dstrbuton belongs to the frst dstrbuton. Includng Nngxa, Qngha, Inner Mongola, Yunnan, Helongjang. Table 2. Zpf ndex measurement regresson results of urban scale dstrbuton n provnces of Hebe Henan Helongjang Hube Hunan Jln Jangsu Jangx Laonng Inner Mongola Nngxa Qngha Shandong Shanx Shanx Schuan Xnjang Yunnan Zhejang Anhu Fujan Gansu Guangdong Guangx Guzhou Concluson Through the collecton of urban populaton data from 1990 to 2010, the Zpf rules of urban sze and urban order 57

6 were tested and found that the sze dstrbuton of Chnese ctes was more balanced, whch was bascally consstent wth the Zpf rule. Zpf ndex values from 1990 to 2005 contnued to grow, showng an ncreasng trend n 2010 Zpf ndex fell more close to the Zpf dstrbuton of the deal state. Through the research and analyss of the cty scale data of each provnce n Chna from 1990 to 2010, the cty sze dstrbuton of each provnce n Chna s more complex, and whch s not 1. Zpf ndex gradually ncreased, ndcatng that the cty sze dstrbuton gradually changed from the frst degree dstrbuton to the Zpf rule. At the same tme, for all provnces of cty sze dstrbuton of Zpf's ndex were further analyss classfed, found across Chnese provnces cty sze dstrbuton state can be dvded nto four types: already reached the deal state of Zpf's law dstrbuton; close to the deal of Zpf's law dstrbuton; by the frst degree dstrbuton to the Zpf's dstrbuton of the transton state; typcal frst degree dstrbuton. Reference Berry, B. J. (1961). Cty sze dstrbuton and economc development. Economc Development and Cultural Change, 9, Chen, Z. (2008). A revew of theory and emprcal research on optmal cty sze. Internatonal Urban Plannng n Chna, 6, Deng, Y., Lu, S., Ca, J., & Lan, X. (2014). Comparson of the methods of urban nfluence scope dvson n Central Chna. Chnese Geographc Research, 7, Madden, C. J. (1956). Some ndcatons of stablty n the growth of ctes n the Unted States. Economc Development and Cultural Change, 4, Soo, K. T. (2005). Zpf s Law for ctes: a cross-country nvestgaton. Regonal Scence and Urban Economcs, 35(3), Tan, J. (2014). Revew of Zpf's law of cty sze dstrbuton. Scence and Industry n Chna, 7, Xu, X., & Ye, J. (1996). Inter provncal dfferences of urbanzaton n Chna. Journal of Geography n Chna, 7, Ye, H., Pu, L., & Zhang, P. (2012). The nter provncal dfferences of urban spatal dstrbuton n Chna and ts nfluencng factors. Chna's populaton resources and envronment, 12, Yu, J., Zhou, G., & Duan, Y. (2013). Research on the evoluton trend of urban scale dstrbuton n Chna -- Based on the Natonal Populaton Census. Populaton and Economcs n Chna, 2, Zpf, G. K. (1949). Human Behavor and the prncple of Least Effort. MA: Addson-Wesley Press. Copyrghts Copyrght for ths artcle s retaned by the author(s), wth frst publcaton rghts granted to the journal. Ths s an open-access artcle dstrbuted under the terms and condtons of the Creatve Commons Attrbuton lcense ( 58