A Discrete Analogue of Reciprocal Coordinate Subtangent and its Role in Characterization Problems

Abstract

Abtsrcat The concept of reciprocal coordinate subtangent (RCST) has been used in statistical literature as a useful tool to study the monotone behaviours of a continuous density function and for characterizing probability distributions through its functional forms. Motivated by this, in the present paper, we consider a discrete analogue of RCST introduced by Gupta et al. (1997) and study its usefulness in modeling probability mass functions. Characterization results are proved for models viz. geometric, discrete Burr and modified power series. The concept is also extended to the weighted models and proves some useful results as models such as logarithmic series, residual lifetime and partial sum (renewal) distributions. Finally, a new definition for discrete analogue of RCST is introduced and examined its usefulness in modeling proportional hazard models in discrete time.