TESA sub-model of upper truncated Abid system of distributions: properties, empirical inferences and application to plasma concentration measurements of indomethacin

Abstract

Truncation models natural boundary conditions, such as maximum possible earthquake magnitudes, top speeds, or
physical constraints, providing a more accurate, bounded range for modeling data. In this paper, we will present the upper truncated
Abid system of distributions and study in detail one of its sub-models, which we will call from now on the TESA distribution. Most
of the important theoretical properties of the TESA distribution will be derived, including Rényi entropy, Tsallis entropy, Extropy,
and the Stress-strength model. A detailed experimental study to evaluate maximum likelihood estimates under different TESA
distribution patterns will be conducted, along with an applied study of indomethacin plasma concentration measurements (in
µg/mL). In the applied study, the TESA distribution was compared with five competing distributions according to various criteria,
and it was concluded that the TESA distribution is the best suited to the application under consideration due to its superior practical
properties.