Constraints for generalized mixtures of Weibull distributions with a common shape parameter

2009 ◽  
Vol 79 (15) ◽  
pp. 1724-1730 ◽  
Author(s):  
Manuel Franco ◽  
Juana-María Vivo
Keyword(s):  
Shape Parameter ◽  
Weibull Distributions ◽  
Common Shape

Study on Sequential Compliance Method Influenced by Shape Parameter of Weibull Distribution

2011 ◽  
Vol 189-193 ◽  
pp. 4361-4364 ◽  
Author(s):  
Hong Liang Lou ◽  
Xing Lin Li ◽  
Xian Zhao Xu ◽  
Yang Ping Zhang ◽  
Zhong Hua Yu
Keyword(s):  
Weibull Distribution ◽  
Shape Parameter ◽  
Weibull Distributions ◽  
Simulation Test ◽  
Consumer’S Risk ◽  
Producer’S Risk ◽  
Rejection Probability

When sequential compliance method is used for Weibull distributions, the shape parameter is usually considered to be fixed. However, because of the life of products are determined by many factors, the shape parameter is variational in practice, that is to say, the shape parameter in the criterions is different from that in the practice. In this paper, the changes of acceptance and rejection probability are researched by the influence of shape parameter changes. Finally, by means of simulation test, changes on the shape parameter affecting on the probability of acceptance and rejection are quantitatively analyzed. As a result, the larger the gap on the shape parameter in the criterions and in the practice is, the larger the gap on the producer’s risk and the consumer’s risk.

International trade distributions and their relation with random fragmentation processes

2021 ◽  
Author(s):  
R. Bustos-Guajardo
Keyword(s):  
International Trade ◽  
Shape Parameter ◽  
Size Distributions ◽  
Weibull Distributions ◽  
Traded Goods ◽  
Power Law Decay ◽  
Approximate Power ◽  
Almost All ◽  
Data Log ◽  
Fragmentation Processes

A study of the distribution of the value of traded goods under the Harmonized System is presented. The ramifications of this classification system are found to exhibit an approximate power law decay, indicating complexity and self-organization in the nomenclature of traded merchandises. For almost all countries with available data, log-values of annually imported and exported goods are well described by three-parameter Weibull distributions. This distribution commonly appears in particles size distributions, suggesting a connection between random fragmentation processes and the mechanisms behind the international trade of merchandises. Analysis of the resulting values for the fitting parameters from 1995 to 2018 shows a nearly constant linear relationship between the parameters of the Weibull distributions, so that, for each country, the distribution of log-values can be approximately characterized by a single shape parameter [Formula: see text]. The empirical findings of this paper suggest that specialization on trading a constant set of goods prevents the values of all traded merchandises from growing/decreasing simultaneously.

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