Statistical inequalities refer to mathematical expressions that describe the relationships between different statistical quantities, often indicating how one quantity compares to another under certain conditions or assumptions. These inequalities can be used in various fields, including statistics, probability theory, economics, and information theory.
Probabilistic inequalities are mathematical inequalities that involve probabilities and provide bounds on the likelihood of certain events or random variables. These inequalities are useful in probability theory and statistics, as they help in understanding the behavior of random variables, enabling us to make predictions and infer properties of distributions.