A NEW LOG-LOCATION REGRESSION MODEL WITH INFLUENCE DIAGNOSTICS AND RESIDUAL ANALYSIS

Abstract

A new four-parameter lifetime model called Odd Log-Logistic Burr XII distribution is defined and investigated. Some of its mathematical properties are derived. Some useful characterization results based on the ratio of two truncated moments, based on the hazard function, as well as on the conditional expectation of certain functions of a random variable, are presented. The maximum likelihood method is used to estimate the model parameters by means of a graphical Monte Carlo simulation study. Moreover, we introduce a new log-location regression model based on the proposed distribution. The Jackknife estimation method as an alternative method is used to estimate the unknown parameters of a new regression model. The generalized cook distance and likelihood distance measures are used to detect possible influential observations. Martingale and modified deviance residuals are defined to detect outliers and evaluate the model assumptions. The potentiality of the new regression model is illustrated by means of a real data set.