A NEW BURR TYPE II DISTRIBUTION: PROPERTIES AND APPLICATION

Abstract

Burr Type II distribution (BIID), a type from the Burr family of distributions is used in
survival and reliability analysis. It is also used in modeling skewed data such as in finance
and in hydrology. To improve the flexibility of BIID in fitting different data sets, this
study derived a new three parameter BIID termed the New Burr Type II Distribution
(NBIID). The underlying characteristics of the new distribution were studied. Mean
Square Error (MSE) was adopted as a measure for evaluating the efficiency and
consistency of the two parameter estimation methods, Maximum Likelihood Estimation
(MLE) and Maximum Product of Spacing (MPS) proposed for estimating NBIID
parameters. Results indicate MPS a more efficient and consistent parameter estimation
method for NBIID. Furthermore, four model selection metrics; Bayesian Information
Criterion (BIC), Akaike Information Criterion (AIC), Hannan-Quinn Information
Criterion (HQIC) and Consistent Akaike Information Criterion (CAIC) were used to
evaluate the performance of NBIID amongst two comparative ones using four real-life
data sets. The NBIID performed better, demonstrating that it can provide a better fit in
comparison to comparative models and was concluded a good choice for modeling
different real-data sets.