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Abstract Lifetime distributions have been considered in variety fields such as insurance, engineering and biology studies. In recent years, some procedures are suggested to generate a new lifetime distribution which providing an adequate describe and high flexibility to the studied population. Among these methods, the compounding of some discrete and important lifetime distributions has been in the vanguard of lifetime modeling. The basic concept behind introducing these distributions is connected with reliability problems when lifetime can be expressed as the maximum or minimum of a sequence of independent and identically distributed random variables which represents the risk times of the system components |