Inflated Mixture Models: Applications to Multimodality in Loss Given Default

Modelling the Loss Given Default Distribution via a Family of Zero-and-one Inflated Mixture Models

“…In comparison with the rankings that were reported for the previous data set, the zero‐and‐one inflated mixture based on the beta distribution performs worse, whereas the mixture that is based on the logit–normal distribution is still competitive, although with a greater number ( k =4) of mixture components; this highlights the need, for these mixtures fitted on these data, of more than two mixture components (compare with Calabrese (), Hlawatsch and Ostrowski () and de Oliveira et al . ()). The continuous part of the zero‐and‐one inflated mixture models selected by BIC and AIC is shown in Fig.…”

“…Differently from de Oliveira et al . (), where the number of mixture components is limited to 2, we left this number to be selected by commonly used information criteria such as AIC and BIC. Moreover, we extended the family of candidate distributions on (0,1), to be used as mixture components, by applying the inverse logit transformation to some classical distributions with support (−∞,∞).…”

“…Special cases of model (1), based on the beta distribution, already exist (see Ospina and Ferrari () for the cases k =1, and de Oliveira et al . () for k =2). However, the extension to a generic number of components, as well as the alternative use of GB1, are new in our knowledge.…”

“…de Oliveira et al . () employed a mixture of two beta distributions to model the continuous part on (0,1), maintaining a Bernoulli distribution at the boundaries. Kalotay and Altman () suggested conditional mixtures of distributions, allowing time variation in the LGD distribution.…”

“…The models of Calabrese and Zenga (), Calabrese (, b) and de Oliveira et al . () are also known as zero‐and‐one inflated models (Ospina and Ferrari, ). Our proposal is placed in this branch of literature.…”