Abstract
We introduce a log-linear regression model based on the beta generalized half-normal distribution (Pescim et al., 2010). We formulate and develop a log-linear model using a new distribution so-called the log-beta generalized half normal distribution. We derive expansions for the cumulative distribution and density functions which do not depend on complicated functions. We obtain formal expressions for the moments and moment generating function. We characterize the proposed distribution using a simple relationship between two truncated moments. An advantage of the new distribution is that it includes as special sub-models classical distributions reported in the lifetime literature. We also show that the new regression model can be applied to censored data since it represents a parametric family of models that includes as special cases several widely-known regression models. It therefore can be used more effectively in the analysis of survival data. We investigate the maximum likelihood estimates of the model parameters by considering censored data. We demonstrate that our extended regression model is very useful to the analysis of real data and may give more realistic fits than other special regression models.
Highlights
The fatigue is a structural damage which occurs when a material is exposed to stress and tension fluctuations
We propose a log-location regression model with censored observations, based on the BGHN distribution (Pescim et al, 2010), referred to as the log-beta generalized half-normal (LBGHN) regression model, which is a feasible alternative for modeling the four existing types of failure rate functions
We provide two simple formulae for the cumulative distribution function, probability density function and survival function of the LBGHN distribution depending if the parameter b > 0 is real non-integer or integer
Summary
The fatigue is a structural damage which occurs when a material is exposed to stress and tension fluctuations. Lawless (2003) discussed the generalized log-gamma regression models with censored data, Barros et al (2008) proposed a new class of lifetime regression models for which the errors follow the generalized BS distribution, Carrasco et al (2008) introduced a regression model considering the modified Weibull distribution, Silva et al (2008) studied a location-scale regression model using the Burr XII distribution and Silva et al (2009) worked a location-scale regression model suitable for fitting censored survival times with bathtub-shaped hazard rates. We propose a log-location regression model with censored observations, based on the BGHN distribution (Pescim et al, 2010), referred to as the log-beta generalized half-normal (LBGHN) regression model, which is a feasible alternative for modeling the four existing types of failure rate functions.
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