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