Maxentropic Continuous Distributions Based on the Mean and Range
Juan José Fernández-Durán · AIP conference proceedings · 2005
In many practical situations it is common to have information about the values of the mean and range of certain population. In these cases it is important to specify the population distribution from the given values of its mean and range. The article by de Alba, Fernández‐Durán and Gregorio‐Domínguez (2004) includes a bibliography with articles dealing with the case of making inference about the mean and standard deviation of a normal population in terms of the observed sample mean and range. In this paper, the maximum entropy principle is used to specify the population distribution given its mean and range. This problem has the particular difficulty that it is necessary to determine the unknown support of the maximum entropy distribution given its length which is equal to the specified value of the range.