Power law model. Goodness-of-fit tests and estimation methods

2013 ◽  
Keyword(s):  
Power Law ◽  
Goodness Of Fit ◽  
Estimation Methods ◽  
Power Law Model ◽  
Goodness Of Fit Tests

The Changing Size Distribution of California's North Coast Wineries

2014 ◽  
Vol 9 (1) ◽  
pp. 51-61 ◽  
Author(s):  
Don Cyr ◽  
Joseph Kushner ◽  
Tomson Ogwang
Keyword(s):  
Size Distribution ◽  
Small Firms ◽  
Goodness Of Fit ◽  
Nonparametric Density Estimation ◽  
Wine Industry ◽  
Estimation Methods ◽  
North Coast ◽  
Size Distribution Of Firms ◽  
Goodness Of Fit Tests ◽  
Kernel Density Estimates

AbstractIn this paper, we use three different goodness-of-fit tests for log-normality in conjunction with kernel nonparametric density estimation methods to examine both the size distribution of California North Coast wineries over time and by age. Our kernel density estimates indicate that the size distribution of wineries has changed from positively skewed to bimodal. These results are inconsistent with those in other industries, but are consistent with recent empirical research in the wine industry, which finds that smaller firms are comprising a larger component of market share. In terms of the distribution of firm size by age, our results indicate that as wineries age, the size distribution of firms becomes less skewed and more bimodal, which is also inconsistent with the research on other industries which finds that as firms age, the size distribution becomes more normal. Our results indicate that unlike other industries, where entry is very difficult, small firms can enter the wine industry and survive. (JEL Classifications: L11, L22, L25)

More goodness-of-fit tests for the power-law process

1994 ◽  
Vol 43 (2) ◽  
pp. 275-278 ◽  
Author(s):  
W.J. Park ◽  
M. Seoh
Keyword(s):  
Power Law ◽  
Goodness Of Fit ◽  
Power Law Process ◽  
Goodness Of Fit Tests

A COMPARATIVE RESEARCH ON FACEBOOK NETWORKS IN DIFFERENT INSTITUTIONS

2012 ◽  
Vol 15 (05) ◽  
pp. 1250030 ◽  
Author(s):  
HAI-BO HU ◽  
JIN-LI GUO
Keyword(s):  
Power Law ◽  
Comparative Research ◽  
Goodness Of Fit ◽  
Significant Degree ◽  
Power Law Model ◽  
Scale Free ◽  
Scale Free Networks ◽  
Plausible Hypothesis ◽  
Log Normal ◽  
Best Fit

We study Facebook networks at 40 American universities, with focus on the comparison of their degree distributions and mechanism governing their evolution. We find that the heterogeneity indexes of these networks are all small compared with scale-free networks, and different from real-world social networks 5 Facebook networks show significant degree disassortativity; the exponent γ for the power-law model of the degree distributions is large for the networks, indicating obvious homogeneity of network structure. We calculate the goodness-of-fit between the data and power law and find that the p-values are larger than threshold 0.1 for 20 networks, implying that power law is a plausible hypothesis; we compare the power-law model with 4 alternative competing distributions and find that power-law model gives the best fit for all 40 networks. However in wider interval of degrees some other distributions, such as log-normal or stretched exponential, can give the best fit. Further based on the homogeneity of Facebook we propose an analyzable model that integrates the introduction of new vertices and edges. The edges can be established either between new vertices and old vertices or between old vertices. The model captures the real evolution processes of Facebook networks and can well reproduce their degree distributions.

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