On classes of life distributions: Dichotomous Markov Noise Shock Model With Hypothesis Testing Applications

2012/10/01 by Mohammad Sepehrifar, Sepehrifar, Mohammad, Shantia Yarahmadian +3
Decision Sciences · Mathematics · Social Sciences · #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probabilistic and Robust Engineering Design #Probability (math.PR) #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1210.0291

openalex publication_date 2012/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the probabilistic characteristics of a unit driven by Dichotomous Markov Noise (DMN), as an external random life increasing and decreasing shocks. Using DMN, we will define two new aging classes of the overall increasing/decreasing (OIL/ODL) nature in the long time behavior, which are separated by an exponential steady state regime. In addition, a moment inequality is derived for the system whose life distribution is in an overall life decreasing (ODL) class. We use this inequality to devise a nonparametric testing procedure for exponentiality against an alternative overall decreasing life distribution.

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