A zero-inflated non default rate regression model for credit scoring data

Abstract

The aim of this paper is to propose a survival credit risk model that jointly accommodates three types of time-to-default found in bank loan portfolios. It leads to a new framework that extends the standard cure rate model introduced by Berkson & Gage [8] regarding the accommodation of zero-inflations. In other words, we propose a new survival model that takes into account three different types of individuals which have so far not been jointly accounted for: (i) an individual with an event at the starting time (zero time); (ii) non-susceptible for the event, or (iii) susceptible for the event. Considering this, the zero-inflated Weibull non-default rate regression models, which include a multinomial logistic link for the three classes, are presented using an application for credit scoring data. The parameter estimation is reached by the maximum likelihood estimation procedure and Monte Carlo simulations are carried out to assess its finite sample performance.

Zero-inflated-censored Weibull and gamma regression models to estimate wild boar population dispersal distance

“…We propose an alteration of the zero-inflated non-default regression model (Louzada et al, 2018), using the zero-inflated and regression parts while removing the cure rate part of the model. Thus, the probability density function (PDF) and the cumulative density function (CDF) of the observable lifetime time T of the zero-inflated model are, respectively, given by where p 0 ∈ (0, 1) is the zero-inflation probability, f(t) is the probability density function, and F(t) is the cumulative density function of the observable lifetime time.…”

“…According to Ospina and Ferrari (2012), the confidence intervals of the components of the vector can be obtained through ̂± z 1− ∕2 [K(̂̂̂) −1 ] 1∕2 , with asymptotic coverage 100(1 − )% , and z 1− ∕2 is the (1 − ∕2)-th quantile of the standard normal distribution. For more details on the asymptotic theory, see Ospina and Ferrari (2012) and Louzada et al (2018).…”

“…provide the connection between the linear predictor and the parameters of the probability density function. According to the fit by Louzada et al (2018), G 1 (.) is set as…”

“…The wild boar (Sus scrofa) is considered to have one of largest geographical incorporating the right-censored observations in the continuous values through the gamma regression. Furthermore, we consider the zero-inflated, right-censored Weibull regression (Louzada et al, 2018), discarding the cure rate of the model. In the models proposed in this paper, both techniques allow the incorporation of the whole data (without excluding zeros and the right-censored observations) to make inferences.…”

Special feature: Recent statistical methods for survival analysis

“…de Freitas Costa et al (2021) suggest zero-inflated Weibull and gamma regression models to fit right-censored dispersal data of the wild boars. The Weibull model is a special case of Louzada et al (2018) and the gamma model is an extension of Lee et al (2010). The methodological and computational details (including R codes) allow ecological researchers to apply the proposed methods.…”