Properties of aging functions and their means
Subarna Bhattacharjee, Indramani Mohanty, Magdalena Szymkowiak, Asok K. Nanda
Abstract
Recently, a lot of works have been done on the study of the failure rate (FR), the aging intensity function (AI) and their properties. In the article, we analyze the aging classes based on monotonicity of new functions viz., arithmetic mean, geometric mean, and harmonic mean of AI function, respectively. Also, the relationships between these functions and the classical AI function are discussed. Moreover, some characterizations of distributions based on these functions are established. Some characterizations of proportional hazard rate and AI family of distributions are discussed. Investigations are illustrated by some examples and applications of aging functions in data analysis.