Some properties of reciprocal coordinate sub-tangents in the context of stochastic modeling. (English) Zbl 1462.62096
Summary: The concept of reciprocal coordinate subtangent (RCST) has been used as a useful tool to study the monotone behaviour of a continuous density function and for characterizing probability distributions through its functional forms (see [S. P. Mukherjee and D. Roy, Bull., Calcutta Stat. Assoc. 38, No. 151–152, 169–180 (1989; Zbl 0715.62024)]). In this paper, we prove that the monotone failure properties of probability models are invariant under non-singular transformation. We obtain characterizations to mixtures of exponential, Lomax and beta distributions based on RCST. Finally, characterizations based on RCST of record values are proved for important probability models.
MSC:
62E10 | Characterization and structure theory of statistical distributions |
60E15 | Inequalities; stochastic orderings |
62N05 | Reliability and life testing |