Univariate and bivariate extensions of the truncated inverted arctan power distribution with applications

Abstract

The importance of (probability) distributions in engineering science is undeniable. They are extensively used in this sector to carry out statistical studies and draw conclusions. In this article, we construct a new trigonometric distribution with support [0,1] called the truncated inverted arctan power (TIAP) distribution and demonstrate its use with engineering data. The corresponding probability density function is particularly flexible in the sense that it has various decreased right-skewness and unimodal forms. The associated hazard rate function shows that the TIAP distribution may adapt data with monotonic, U-shaped, and N-shaped failure rates. To reflect the interdependence of two random variables or sets of data, a bivariate variant of the TIAP distribution is also elaborated. All these distributional tools are then applied from a statistical perspective. In particular, the involved parameters are estimated using a maximum likelihood technique. Applications to engineering data indicate that the univariate and bivariate extensions for the TIAP distribution have a better fit compared to various current distributions.

Keywords

• Unit distributions
• Trigonometric distributions
• Bivariate distributions
• Copulas
• Engineering data analysis