Maximum average roll value

Maximum average roll value (MaxARV) The value which historically yields a 97.7% confidence level. This value is defined as the average plus 2 standard deviations for a specific test method for a specific type of textile. Typically MaxARV is used to define the apparent opening size (AOS). 

The maximum CR of the aggressive investor with a 3-year horizon, for example, is 21.8% (row 3, column 4). A value of 19.4% in row 6, column 4 (quantile 95% for the aggressive investor) means that only 5% of the optimized portfolios realized a value higher than 19.4% in the 239 rolling calculations of the 3-year horizon. For the 10-year horizon and a risk averse attitude, the minimum CR was 7.2% per annum (row 4, column 7). The average CR for this investment horizon for the risk averse investor was 11.5% (row 9, column 7). 

The entropy Sipii,..., pij,... is a function of a set of probabilities. The distribution of p,j s that cause 5 to be maximal is the distribution that most fairly apportions the constrained scores between the individual outcomes. That is, the probability distribution is flat if there are no constraints, and follows the multiplication rule of probability theory if there are independent constraints. If there is a constraint, such as the average score on die rolls, and if it is not equal to the value expected from a uniform distribution, then maximum entropy predicts an exponential distribution of the probabilities. In Chapter 10, this exponential function will define the Boltzmann distribution law. With this law you can predict thermodynamic and physical properties of atoms and molecules, and their averages and fluctuations. How-ever, first we need the machinery of thermodynamics, the subject of the next three chapters. 

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