The Type I Half Logistic Skew-t Distribution: A Heavy-Tail Model with Inverted Bathtub Shaped Hazard Rate
O. D. Adubisi *
Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria and Department of Mathematical Sciences, Abubakar Tafawa Balewa University, Bauchi State, Nigeria.
A. Abdulkadir
Department of Mathematical Sciences, Abubakar Tafawa Balewa University, Bauchi State, Nigeria.
H. Chiroma
Department of Mathematical Sciences, Abubakar Tafawa Balewa University, Bauchi State, Nigeria.
U. F. Abbas
Department of Mathematical Sciences, Abubakar Tafawa Balewa University, Bauchi State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this article a new generalization of the skew student-t distribution was introduced. The two-parameter model called the type I half-logistic skew-t (TIHLST) distribution can fit skewed, heavy-right tail, and long-tail datasets. Statistical properties of the type I half-logistic skew-t (TIHLST) distribution were derived and the maximum likelihood method parameter estimates assessed through a simulation study. A well-known dataset was analysed, illustrating the usefulness of the new distribution in modeling skewed and heavy-tailed data. The hazard rate shape was found to be increasing, decreasing and inverted bathtub shaped which was also reflected in the application result.
Keywords: Entropy, maximum likelihood estimation, simulation, Skew-t distribution, type I half-logistic distribution