Martin Wiegand

• Doctor of Philosophy
• Senior Research Fellow at University College London

Lutz et al. (Ann Oper Res 289:463–472, 2020) derived an integral expression for the expected length of an orderly path. We show here that the integral expression can be reduced to a closed form expression in terms of the Gauss hypergeometric function, a generalised hypergeometric function and the Appell hypergeometric function of the first kind. We...

Objectives To develop a disease stratification model for COVID-19 that updates according to changes in a patient’s condition while in hospital to facilitate patient management and resource allocation. Design In this retrospective cohort study, we adopted a landmarking approach to dynamic prediction of all-cause in-hospital mortality over the next...

Objective: Previous studies have reported conflicting findings regarding aldosterone levels in patients hospitalised with COVID-19. We therefore used the gold-standard technique of liquid chromatography tandem mass-spectrometry (LCMSMS) to address this uncertainty. Design: All patients admitted to Addenbrooke’s Hospital Cambridge with COVID-19 betw...

The first statistical analysis of maximum rainfall in Zimbabwe is provided. The data are from 103 stations spread across the different climatic regions of Zimbabwe. More than 90% of the stations had at least 50 years of data. The generalized extreme value distribution was fitted to maximum rainfall by the method of maximum likelihood. Probability p...

Objective Previous studies have reported conflicting findings regarding aldosterone levels in patients hospitalised with COVID-19. We therefore used the gold-standard technique of liquid chromatography tandem mass-spectrometry (LCMSMS) to address this uncertainty. Design All patients admitted to Cambridge University Hospitals with COVID-19 between...

The 4C Deterioration model was developed and validated on data collected in UK hospitals until August 26, 2020, but has not yet been validated in the presence of SARS-CoV-2 variants and novel treatment regimens that have emerged subsequently. In this first validation study of the 4C Deterioration model on patients admitted between August 27, 2020 a...

The 4C Deterioration model was developed and validated on data collected in UK hospitals until August 26, 2020, but has not yet been validated in the presence of SARS-CoV-2 variants and novel treatment regimens that have emerged subsequently. In this first validation study of the 4C Deterioration model on patients admitted between August 27, 2020 a...

The Rosenbrock function is a ubiquitous benchmark problem in numerical optimisation, and variants have been proposed to test the performance of Markov Chain Monte Carlo algorithms on distributions with a curved and narrow shape. In this work we discuss the Rosenbrock distribution and the advantages and limitations of its current n‐dimensional exten...

Objectives To develop a disease stratification model for COVID-19 that updates according to changes in a patient’s condition while in hospital to facilitate patient management and resource allocation. Design In this retrospective cohort study we adopted a landmarking approach to dynamic prediction of all cause in-hospital mortality over the next 4...

Based on our previous works, we revise a simple series expansion for multivariate probability density functions (PDF) of the Rayleigh distribution. From there we derive a similar expression for the cumulative density function (CDF) of multivariate Rayleigh random variables of arbitrary dimension and covariance matrix. The CDF is of particular inter...

In this note we introduce multivariate extensions to the bivariate discrete analogue to continuous probability distributions proposed in Barbiero [Annals of Operations Research, doi: 10.1007/s10479-019-03388-8, 2019]. We furthermore show that identical properties of the bivariate case also hold for n-variate discrete analogues.

The multivariate Rayleigh distribution is of crucial importance to many applied problems of engineering, such as in the analysis of multi-antenna wireless systems. Due to the lack of a generalised closed form of the distribution, the dependence on effective approximation methods for evaluation has created numerous numerical approaches with consider...

Li and Nadarajah [Signal Processing 127 (2016) 185–190] derived expressions for mean and variance of roundoff error for any continuous random variable. Here, we derive expressions for general moments of the roundoff error, allowing one to study other aspects of roundoff error than just mean and variance. The expressions are specialized for 10 commo...

The Rosenbrock function is an ubiquitous benchmark problem for numerical optimisation, and variants have been proposed to test the performance of Markov Chain Monte Carlo algorithms. In this work we discuss the two-dimensional Rosenbrock density, its current $n$-dimensional extensions, and their advantages and limitations. We then propose our own e...

We introduce a new R package and its functions written by the authors. This package computes an empirical density function for arbitrary dimensions with adjustable grid sizes.

Based on the reformulation of the problem of galactic shape measurement, introduced by Tessore and Bridle, we develop and test new estimators which more e ciently solve what is now a statistical problem. Frequently only a single measurement is available from an observation made by telescopes, which may be distorted due to noise introduced in the me...

Based on the reformulation of the problem of galactic shape measurement, introduced by Tessore and Bridle, we develop and test new estimators which more e ciently solve what is now a statistical problem. Frequently only a single measurement is available from an observation made by telescopes, which may be distorted due to noise introduced in the me...

We introduce a new R package and its functions written by the authors. This package computes an empirical density function for arbitrary dimensions with adjustable grid sizes.

The characteristic function of the lognormal distribution is of interest in a number of scientific fields yet an analytic solution remains elusive, making reliable and efficient approximations necessary. In this article, we build on the results of N. C. Beaulieu and A. Saberali in ‘New approximations to the lognormal characteristic function’, by in...

The Rayleigh distribution is of paramount importance in signal processing and many other areas, yet an expression for random variables of arbitrary dimensions has remained elusive. In this note, we generalise the results of Beard and Tekinay [1] for quadrivariate random variables to cases of unconstrained order and provide a simple algorithm for ev...

Monte Carlo simulation methods for the valuation of financial instruments have become a staple of empirical economic analysis. A specific focus is dedicated to the feasibility of the stock price losses and barrier options as well as the sensitivity of partial time barrier options in dependence on their barrier values, which, to the best of our know...

The Rayleigh distribution is of paramount importance in signal processing and many other areas, yet an expression for random variables of arbitrary dimensions has remained elusive. In this note, we generalise the results of Beard and Tekinay for quadrivariate random variables to cases of unconstrained order and provide a simple algorithm for evalua...

Forbes Magazine offers an annual list of the 2000 largest publicly traded companies, shedding light on four different measurements: Sales, profits, market value and assets held. In this paper we have introduce different composite distribution models to more accurately describe the spread of these wealth metrics.

An R implementation to build interest rate curves based on portfolios, interpolate between them, and translate spot rates into par rates, as well as to change compounding methods.

Forbes Magazine offers an annual list of the 2000 largest publicly traded companies, shedding light on four different measurements: Sales, profits, market value and assets held. Soriano-Hernández et al. (2017) modeled these wealth metrics using composite distributions made up of two parts. In this note, we introduce different composite distribution...

Historically the Zipf power law has been widely used as modeling approach for word fre- quencies. We investigate the adequacy of this method in comparison to a number of Pareto type distributions. To substantiate our claims we provide a number of comparative plots and various error measures.

We introduce a new R package and its functions written by the authors of this paper. The package contains multi-sectioned composite distributions, frequently used for financial data among a multitude of applications. It offers a wide range of standard distributions for the individual sections.

The characteristic function of the lognormal distribution is of interest in a number of scientific fields yet an analytic solution remains elusive, making reliable and efficient approximations necessary. In this paper we build on the results of N.C. Belieu and A. Saberali in "New Approximations to the Lognormal Characteristic Function", and introdu...

Li and Nadarajah [11] derived expressions for mean and variance of roundo� error for any continuous random variable. Here, we derive expressions for general moment of the round o� error. The expressions are specialised for over ten commonly used distributions in signal processing. Numerical studies are given.