Probability Density Function Estimation using theMinMax

| The problem of initial probability assignment consistent with the available information about a probabilis-tic system is called a direct problem. Jaynes' maximum en-tropy principle (MaxEnt) provides a method for solving direct problems when the available information is in the form of moment constraints. On the other hand, given a probability distribution, the problem of nding a set of constraints which makes the given distribution a maximum entropy distribution is called an inverse problem. A method based on the MinMax measure to solve the above inverse problem is presented here. The MinMax measure of information, deened by Kapur, Baciu and Kesa-van 1], is a quantitative measure of the information contained in a given set of moment constraints. It is based on both maximum and minimum entropy. Computational issues in the determination of the MinMax measure arising from the complexity in arriving at minimum entropy probability distributions (MinEPD) are discussed. The method to solve inverse problems using the MinMax measure is illustrated by solving the problem of estimating a probability density function of a random variable based on sample data.