Convergence theorems form the backbone of probability theory and statistical inference, ensuring that sequences of random variables behave in a predictable manner as their index grows. These ...

In this study, we establish the Marcinkiewicz–Zygmund strong law of large numbers for randomly weighted sums of negatively orthant dependent random variables. The law of the single law of logarithm ...

A necessary condition is given for the convergence of distributions of the sums of a random number of independent random variables. This is made on the basis of a theorem which gives sufficient ...