Characteristic Functions

This chapter begins with a look at convolutions and the distribution of sums of random variables. It briefly surveys complex number theory before defining the characteristic function and studying its properties, with a range of examples. The concept of infinite divisibility is introduced. The important inversion theorem is treated and finally consideration is given to characteristic functions in conditional distributions.

The Distributions of Sums for Shanker, Akash, Ishita, Pranav, Rani, and Ram Awadh

In statistics and probability theory, one of the most important statistics is the sums of random variables. After introducing a probability distribution, determining the sum of n independent and identically distributed random variables is one of the interesting topics for authors. This paper presents the probability density functions for the sum of n independent and identically distributed random variables such as Shanker, Akash, Ishita, Pranav, Rani, and Ram Awadh. In order to determine all aforementioned distributions, the problem-solving methods are applied which is based on the change-of-variables technique.