A Bayesian analysis of record statistics from the Gompertz model

Abstract

The Gompertz distribution has been used as a growth model and it can be used to fit tumor growth. Record values can be viewed as order statistics from a sample whose size is determined by the values and the order of occurrence of observations. Based on record values from the two-parameter Gompertz distribution, Bayes estimators for the two unknown parameters are obtained by using Laplace approximation. These estimates are obtained based on the squared error and LINEX loss functions. Predictions for future upper record values from the Gompertz model are obtained from a Bayesian approach. The maximum likelihood and Bayes estimates are compared via Monte Carlo simulation study and a numerical example is given to illustrate the results of prediction.