A Discussion on Methods Obtaining Lower and Upper bounds of Statistical Quantities Based on Probability Mass Function of Discrete Probability Distribution

Abstract

Uncertainty plays an important role in our daily life. The belief function, commonality function, and plausibility function deal with uncertainty. The Belief function and the plausibility function give one of the important pairs of lower and upper bounds of the probability function respectively. From [8], we have another basic belief assignment based on probability mass function which is different from Shafer‘s basic belief assignment [12]. From this basic belief assignment, the belief function, commonality function, and plausibility function are obtained. In this paper, it is used to obtain lower and upper bounds of statistical quantities viz. distribution function, mean, variance, standard deviation, raw moments, central moments, coefficient of skewness, and coefficient of kurtosis of probability distribution under study with two methods. With help of algorithms, computer programs are written or constructed. Also, we obtain algorithms to obtain lower and upper bounds of statistical quantities of probability distribution under study. These bounds consist of probabilities given by the probability mass function of a probability distribution.