Three Series Theorem for Independent Random Variables under Sub-linear Expectations with Applications

Modified Normal-based Approximation to the Percentiles of Linear Combination of Independent Random Variables with Applications

Linear code-based vector quantization for independent random variables

The computationally efficient vector quantization for a discrete time source can be performed using lattices over block linear codes or convolutional codes. For high rates (low distortion) and uniform distribution the performance of a multidimensional lattice depends mainly on the normalized second moment (NSM) of the lattice. For relatively low rates (high distortions) and non-uniform distribu...

Tail sums of convergent series of independent random variables

On the bounds in Poisson approximation for independent geometric distributed random variables

‎The main purpose of this note is to establish some bounds in Poisson approximation for row-wise arrays of independent geometric distributed random variables using the operator method‎. ‎Some results related to random sums of independent geometric distributed random variables are also investigated.

Pairwise Independent Random Variables

In this lecture we discuss how to derandomize algorithms. We will see a brute force algorithm (enumeration) for derandomization. We will also see that some random algorithms do not need true randomness. Specifically, we will see an example where only pairwise random bits are needed. Next, we will see how we can generate pairwise random values and how this conservation on the amount of randomnes...