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Bell-Touchard nonlinear regression model
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DOI：10.1080/02331888.2026.2649781.png)
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Abstract
En 中文
We introduce a novel class of nonlinear regression models based on the two-parameter Bell-Touchard family of distributions introduced recently in the statistical literature, which corresponds to a flexible yet tractable family of discrete distributions. We consider the maximum likelihood method to estimate the Bell-Touchard nonlinear model parameters, and provide an iterative process for obtaining these estimates numerically. We derive a closed-form expression for the Fisher information matrix. We propose deviance residuals in this class of nonlinear regression models. Monte Carlo simulations are also considered to evaluate the new nonlinear regression model. We provide and discuss an application of the Bell-Touchard nonlinear regression model to real data. In the empirical application, we also compare the novel regression model with the popular Poisson and negative binomial (linear and nonlinear) regression models, and the results are quite promising.
Keywords:
Bell-Touchard distribution
count data
Nonlinear regression
overdispersion