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A Flexible Count Data Regression Model for Risk Analysis
Author(s) -
Guikema Seth D.,
Goffelt Jeremy P.
Publication year - 2008
Publication title -
risk analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.972
H-Index - 130
eISSN - 1539-6924
pISSN - 0272-4332
DOI - 10.1111/j.1539-6924.2008.01014.x
Subject(s) - generalized linear model , count data , reliability (semiconductor) , statistics , variance (accounting) , poisson regression , quasi likelihood , poisson distribution , overdispersion , computer science , linear model , regression analysis , linear regression , econometrics , data mining , mathematics , power (physics) , population , physics , demography , accounting , quantum mechanics , sociology , business
In many cases, risk and reliability analyses involve estimating the probabilities of discrete events such as hardware failures and occurrences of disease or death. There is often additional information in the form of explanatory variables that can be used to help estimate the likelihood of different numbers of events in the future through the use of an appropriate regression model, such as a generalized linear model. However, existing generalized linear models (GLM) are limited in their ability to handle the types of variance structures often encountered in using count data in risk and reliability analysis. In particular, standard models cannot handle both underdispersed data (variance less than the mean) and overdispersed data (variance greater than the mean) in a single coherent modeling framework. This article presents a new GLM based on a reformulation of the Conway‐Maxwell Poisson (COM) distribution that is useful for both underdispersed and overdispersed count data and demonstrates this model by applying it to the assessment of electric power system reliability. The results show that the proposed COM GLM can provide as good of fits to data as the commonly used existing models for overdispered data sets while outperforming these commonly used models for underdispersed data sets.