Browsed by
Category: Spire

On Permuted First-Kind Dependence of Categorical Random Variables

On Permuted First-Kind Dependence of Categorical Random Variables

  This paper discusses the notion of horizontal dependency in sequences of first-kind dependent categorical random variables. We examine the necessary and sufficient conditions for a sequence of first-kind dependent categorical random variables to be identically distributed when the conditional probability distribution of subsequent variables after the first are permuted from the identity permutation used…

On Server Efficiency

On Server Efficiency

For the full text of the paper, including all proofs and supplementary lemmata, click to download  Abstract Editor's note: This paper comprises the second chapter of the PhD dissertation by Rachel Traylor. Cha and Lee defined a mathematical notion of server performance by measuring efficiency defined as the long run average number of jobs completed per…

A Generalized Geometric Distribution from Vertically Dependent Bernoulli Random Variables

A Generalized Geometric Distribution from Vertically Dependent Bernoulli Random Variables

 For full proofs and derivations, read here. Abstract This paper generalizes the notion of the geometric distribution to allow for dependent Bernoulli trials generated from dependency generators as defined in Traylor and Hathcock's previous work. The generalized geometric distribution describes a random variable that counts the number of dependent Bernoulli trials until the first success. The…

Vertical Dependency in Sequences of Categorical Random Variables

Vertical Dependency in Sequences of Categorical Random Variables

For the full text, including proofs, download the pdf here. Abstract This paper develops a more general theory of sequences of dependent categorical random variables, extending the works of Korzeniowski (2013) and Traylor (2017) that studied first-kind dependency in sequences of Bernoulli and categorical random variables, respectively. A more natural form of dependency, sequential dependency, is…

Summation Chains of Sequences Part 3: Sequence Chains from Linear Functions

Summation Chains of Sequences Part 3: Sequence Chains from Linear Functions

For the full paper, which includes proofs, click here. Abstract (Editor's note:) This paper represents the third installment of a masters thesis by Jonathan Johnson. The first two can be found here and here. This paper continues the development of the theory of summation chains of sequences. Since summation chains are doubly infinite, it's important to know how little…

Summation Chains of Sequences Part 2: Relationships between Sequences via Summation Chains

Summation Chains of Sequences Part 2: Relationships between Sequences via Summation Chains

For the full paper with proofs,click here. Abstract Editor's note: This paper represents the second installment of a masters thesis by Jonathan Johnson. This paper continues the development of the theory of summation chains of sequences. The concept of sum-related is defined: two sequences are sum-related if one sequence appears in the summation chain of the…

Summation Chains of Sequences Part 1: Introduction, Generation, and Key Definitions

Summation Chains of Sequences Part 1: Introduction, Generation, and Key Definitions

For the full paper, which includes all proofs, download the pdf here Abstract (Editor's note:) This paper represents the first installment of a masters thesis by Jonathan Johnson. This work introduces the notion of summation chains of sequences. It examines the sequence of sequences generated by partial sums and differences of terms in each level of…

A Generalized Multinomial Distribution from Dependent Categorical Random Variables

A Generalized Multinomial Distribution from Dependent Categorical Random Variables

For the full paper, which includes all proofs, download the pdf  here. Abstract Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm effectiveness, such as feature ranking and random forests.…