Distribution selection forStochastic modeling
The choice of appropriate probability distributions is the most important step in any complete stochastic system analysis and hinges upon knowing as much as possible about the characteristics of the potential distribution and the “physics” of the situation to be modeled. Generally, we have first to decide which probability distributions are appropriate to use for the relevant random phenomena describing the model. For example, the exponential distribution has the Markovian (memoryless) property. Is this a reasonable condition for the particular physical situation under study? Let us say we are looking to describe the repair mechanism of a complex maintained system. If the service for all customers is fairly repetitive, we might feel that the longer a failed item is in service for repair, the greater the probability that its service will be completed in the next interval of time (non-memoryless). In this case, the exponential distribution would not be a reasonable candidate...
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