Bayesian and non-Bayesian inference for the compound Poisson log-normal model with application in finance

Abstract

In this article, we described a novel class of distributions that can be analyzed in complex and skewed real data sets. We called the proposed distribution as compound Poisson log-normal model, and it obtained by compounding the truncated Poisson and log-normal random variables. The baseline distribution can be obtained as a special case. The article derives different fundamental statistical properties of the proposed model, such as the quantile function, moments, moment-generating function, and information measures. Further, the estimation of unknown parameters is derived using classical and Bayesian procedures via numerous loss functions. The associated confidence intervals can also be obtained from approximate and bootstrap methods. The potential of the proposed estimators is computed using experiment simulation studies to show the best and most efficient method of estimation. Finally, we illustrate two financial data sets to see the effectiveness of the suggested model among other proposed distributions.

Keywords

• Bayesian method
• Bootstrap method
• Classical estimation
• Log-normal distribution
• Monte Carlo simulation
• Poisson distribution