A Class of Conjugate Priors for Log‐Normal Claims Based on Conditional Specification

Abstract

In this article, a new methodology for obtaining a premium based on a broad class of conjugate prior distributions, assuming lognormal claims, is presented. The new class of prior distributions arise in a natural way, using the conditional specification technique introduced by Arnold, Castillo, and Sarabia (1998, 1999). The new family of prior distributions is very flexible and contains, as particular cases, many other distributions proposed in the literature. Together with its flexibility, the main advantage of this distribution is that, due to its dependence on a large number of hyperparameters, it allows incorporating a wide amount of prior information. Several methods for hyperparameter elicitation are proposed. Finally, some examples with real and simulated data are given. Copyright The Journal of Risk and Insurance.

Bayesian Inference for Median of the Lognormal Distribution

“…This was extended by Padgett and Johnson (1983), where they obtained lower bounds on reliability function of the two parameter lognormal distribution. Sarabia, Castillo, Gómez-Déniz, and Vázquez-Polo (2005) proposed a class of bivariate conjugate priors for μ and σ of the lognormal distribution using the conditional specification. Several procedures were also suggested for the estimation of the hyperparameters.…”

Bayesian estimation of incomplete data using conditionally specified priors

“…The property of multimodality appears in other models with conditional specification (see Arnold et al, 2000, Arnold, Castillo andSarabia (2001) and Sarabia et al (2005)). …”

“…For the elicitation of the hyperparameters in the general case we can use the methods proposed in Arnold, Castillo and Sarabia (1999) and Sarabia et al (2005). Assume that we have information about the mean and variance of the two conditional distributions λ|θ and θ|λ, i.e.,…”

Joint modelling of the total amount and the number of claims by conditionals

“…Some applications have been provided by Sarabia et al (2004) and Sarabia et al (2005). The class of bivariate distributions with lognormal conditionals has been fully characterized by Sarabia et al (2007).…”