We summarize the statistical properties of statistics computed from independent random bitstreams including the commonly discussed support and cosine similarity. We derive the moments of the asymptotically normal approximation to the sampling distribution of the cosine similarity of independent...

We review the properties of a univariate probability distribution that is a possible candidate for the description of financial market price changes. This distribution is an “error” distribution that represents a generalized form of the Normal, possesses a natural multivariate form, has a...

Power laws as descriptions of word frequencies within a written corpus are familiar, omnipresent, and clearly approximate, relationships. We prepare a corpus from text collected from Twitter and study the word distribution. Although this is approximated by the Zipf distribution, and better...

The sampling error of the Sharpe Ratio is developed through the propagation of errors formula. The results of Monte-Carlo experiments that illustrate the dependence of this error on the magnitude of the population Sharpe Ratio

"This book provides insights into the true nature of financial and economic data, and is a practical guide on how to analyze a variety of data sources. The focus of the book is on finance and economics, but it also illustrates the use of quantitative analysis and data science in many different...

We propose a statistic for assessing a trader's performance by comparing their observed activity on a given price sequence to the trade sequence that would be generated by a fully informed trader. That is one which, at any given time, has access to perfect knowledge of the entire future price...

We develop a simple probit model to estimate the probability of a Republican win in the U.S. Presidential Election. We consider the relative height and weight of the candidates and also the electorates desire for change and the power of incumbency. We find that height difference and "change" are...

We introduce an apparently new parameterisation of the Wold decomposition of a standard Box-Jenkins time series model in terms of the Hypergeometric Function pFq(.). This parameterization is sufficiently flexible to treat both finite standard ARMA(p, q) models and also fractionally integrated...

[enter Abstract Body]A recipe for the construction of a multivariate probability density function from a normalized symmetric univariate function using a distance metric methodology is developed. A method to perform multivariate integration in a polar coordinate system in an arbitary number of...