- Research Article
- Open Access
© Jingfeng Tian et al. 2010
- Received: 8 October 2009
- Accepted: 12 December 2009
- Published: 4 January 2010
- Distribution Function
- Density Function
- Positive Integer
- Convex Function
- Measure Space
In 1974, the Japanese scholar Sugeno  presented a kind of typical nonadditive measure, Sugeno measure, which is an important generalization of probability measure [2–6]. As we all know, the definitions and properties of moment of random variable play an important role in probability theory [7–9]. Likewise, they are also very important for Sugeno measure. In this paper we present the analogous definitions and properties based on random variable on Sugeno measure space. Then some important moment estimation inequalities based on random variable are presented and proven.
Let us recall some definitions and facts from .
In order to present the analogous definitions and properties based on random variable on Sugeno measure space, we recall some definitions and facts from .
We begin this section with a short lemma (see ), which will be useful in the sequel.
Let be a random variable and a positive number. Then the expected value is called the th moment, the expected value is called the th absolute moment, the expected value is called the th central moment, and the expected value is called the th absolute central moment.
Similar to the case of credibility theory , we have the following: Theorems 3.5, 3.6, and 3.7.
This work was supported by the NNSF of China (no. 60773062), the NSF of Hebei Province of China (no. 2008000633), the foundation of North China Electric Power University (no. 200911033), the KSRP of Department of Education of Hebei Province of China (no. 2005001D), and the KSTRP of Ministry of Education of China (no. 206012).
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