Improved likelihood inference for the shape parameter in Weibull regression

Silva, Michel Ferreira Da; Ferrari, Silvia L. P.; Cribari‐Neto, Francisco

doi:10.1080/00949650701421964

Cited by 12 publications

(4 citation statements)

References 11 publications

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“…Here ℓ( χψ , ψ; χ, ψ, a) and j χχ ( χψ , ψ; χ, ψ, a) are the log likelihood function and the observed information for χ respectively. They depend on the data only through the minimal sufficient statistic [(Da Silva, Ferrari, & Cribari-Neto, 2008)]. An alternative formula for (4), which is obtained through approximating ancillary statistic is given by…”

Section: Methodsmentioning

confidence: 99%

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Improved Likelihood Estimation for the Generalized Extreme Value and the Inverse Gaussian Lifetime Distributions

Islam¹,

Khan²

2016

Preprint

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In presence of nuisance parameters, profile likelihood inference is often unreliable and biased, particularly in small sample scenario. Over past decades several adjustments have been proposed to modify profile likelihood function in literature including a modified profile likelihood estimation technique introduced in Barndorff-Nielsen. In this study, adjustment of profile likelihood function of parameter of interest in presence of nuisance parameter is investigated. We particularly focuss to extend the Barndorff-Nielsen's technique on Inverse Gaussian distribution for estimating its dispersion parameter and on generalized extreme value (GEV) distribution for estimating its shape parameter. The accelerated failure time models are used for lifetimes having GEV distribution and the Inverse Gaussian distribution is used for lifetime distribution. Monte-Carlo simulation studies are conducted to demonstrate the performances of both approaches. Simulation results suggest the superiority of the modified profile likelihood estimates over the profile likelihood estimates for the parameters of interest. Particularly, it is found that the modifications can improve the overall performance of the estimators through reducing their biases and standard errors.

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Section: Methodsmentioning

confidence: 99%

“…The simulations are based on 1000 runs and different summary statistics namely, mean, variance, bias, mean squared error (MSE), and relative bias (RB) are used for comparison purpose. The relative bias is calculated using the formula bias/true parameter and expressed as percentage ((Da Silva et al, 2008)).…”

Section: Numerical Analysismentioning

confidence: 99%

Improved Likelihood Estimation for the Generalized Extreme Value and the Inverse Gaussian Lifetime Distributions

Islam¹,

Khan²

2016

Preprint

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“…The parameter q of a DW distribution is equivalent to e−λ in the continuous case. Reference [25], Weibull regression imposes a log link between the parameter λ and the predictors. DW regression can be introduced through the parameter q.…”

Section: Dw Regression Modelmentioning

confidence: 99%

Discrete Weibull and Artificial Neural Network Models in Modelling Over-dispersed Count Data

Collins¹,

Waititu²,

Wanjoya³

2020

IJDSA

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“…Recalling that the distribution function of a continuous Weibull distribution is given by

with scale parameter

, one can see that the parameter q of a DW distribution is equivalent to

in the continuous case. Because Weibull regression imposes a log link between the parameter

and the predictors [ 16 , 17 ], the DW regression can be introduced via the parameter q . Figure 3 shows how the parameter q affects the scale and the shape of the probability mass function of the DW distribution.…”

Section: Dw Regression Modelmentioning

confidence: 99%

A Simple and Adaptive Dispersion Regression Model for Count Data

Klakattawi

Vinciotti

2018

Entropy

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Regression for count data is widely performed by models such as Poisson, negative binomial (NB) and zero-inflated regression. A challenge often faced by practitioners is the selection of the right model to take into account dispersion, which typically occurs in count datasets. It is highly desirable to have a unified model that can automatically adapt to the underlying dispersion and that can be easily implemented in practice. In this paper, a discrete Weibull regression model is shown to be able to adapt in a simple way to different types of dispersions relative to Poisson regression: overdispersion, underdispersion and covariate-specific dispersion. Maximum likelihood can be used for efficient parameter estimation. The description of the model, parameter inference and model diagnostics is accompanied by simulated and real data analyses.

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Improved likelihood inference for the shape parameter in Weibull regression

Cited by 12 publications

References 11 publications

Improved Likelihood Estimation for the Generalized Extreme Value and the Inverse Gaussian Lifetime Distributions

Improved Likelihood Estimation for the Generalized Extreme Value and the Inverse Gaussian Lifetime Distributions

Discrete Weibull and Artificial Neural Network Models in Modelling Over-dispersed Count Data

A Simple and Adaptive Dispersion Regression Model for Count Data

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