On Making an Informed Choice between Two Lomax-based Continuous Probability Distributions Using Lifetime Data
Terna Godfrey Ieren *
Department of Statistics, University of Ibadan, Ibadan, Nigeria.
Samuel Oluwafemi Oyamakin
Department of Statistics, University of Ibadan, Ibadan, Nigeria.
Abubakar Yahaya
Department of Statistics, Ahmadu Bello University, Zaria, Nigeria.
Angela Unna Chukwu
Department of Statistics, University of Ibadan, Ibadan, Nigeria.
Adamu Abubakar Umar
School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia.
Samson Kuje
Department of Mathematical Science, Abubakar Tafawa Balewa University Bauchi, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Probability distributions and their generalisations have contributed greatly in the modeling and analysis of random variables. However, due to the increased introduction of new distributions there has been a major problem with choosing and applying the right distribution for a given set of data. In most cases, it is discovered that the data set in question fits two or more probability distributions and hence one must be chosen among others. The Lomax-Weibull and Lomax-Log-Logistic distributions introduced in an earlier study using a Lomax-based generator were found to be positively skewed and may be victims of this situation especially when modelling positively skewed datasets. In this article, we apply the two distributions to some selected datasets to compare their performance and provide useful insight on how to select the most fit among them when dealing with a real-life situation. We used the log-likelihood value, AIC, CAIC, BIC, HQIC, Cramér-Von Mises (W*) and Anderson Darling (A*) statistics as performance evaluation tools for selecting between the two distributions.
Keywords: Lomax-Weibull distribution, Lomax-Log-Logistic distribution, Lomax-based generator, performance evaluation