Negative Binomial Construction of Random Discrete Distributions on the Infinite Simplex

The Poisson-Kingman distributions, PK(ρ), on the infinite simplex, can be constructed from a Poisson point process having intensity density ρ or by taking the ranked jumps up till a specified time of a subordinator with Lévy density ρ, as proportions of the subordinator. As a natural extension, we replace the Poisson point process with a negative binomial point process having parameter r > 0 and Lévy density ρ, thereby defining a new class PK(r)(ρ) of distributions on the infinite simplex. The new class contains the two-parameter generalisation PD(α, θ) of [13] when θ > 0. It also contains a class of distributions derived from the trimmed stable subordinator. We derive properties of the new distributions, with particular reference to the two most well-known PK distributions: the Poisson-Dirichlet distribution PK(ρθ) generated by a Gamma process with Lévy density ρθ(x) = θe−x/x, x > 0, θ > 0, and the random discrete distribution, PD(α, 0), derived from an α-stable subordinator

Functional laws for trimmed Lévy processes

Two different ways of trimming the sample path of a stochastic process in [0, 1]: global ('trim as you go') trimming and record time ('lookback') trimming are analysed to find conditions for the corresponding operators to be continuous with respect to the (strong) J 1-topology. A key condition is that there should be no ties among the largest ordered jumps of the limit process. As an application of the theory, via the continuous mapping theorem, we prove limit theorems for trimmed Lévy processes, using the functional convergence of the underlying process to a stable process. The results are applied to a reinsurance ruin time problem.B. Buchmann and R. Maller’s research was partially funded by the Australian Research Council (ARC) (grant numbers DP1092502 and DP160104737). Y. Ipsen was formerly at the ARC Centre of Excellence for Mathematical and Statistical Frontiers, School of Mathematics and Statistics, University of Melbourne. She acknowledges support from the ARC

Phishing and Cybercrime Risks in a University Student Community

In an exploratory quasi-experimental observational study, 138 participants recruited during a university orientation week were exposed to social engineering directives in the form of fake email or phishing attacks over several months in 2017. These email attacks attempted to elicit personal information from participants or entice them into clicking links which may have been compromised in a real-world setting. The study aimed to determine the risks of cybercrime for students by observing their responses to social engineering and exploring attitudes to cybercrime risks before and after the phishing phase. Three types of scam emails were distributed that varied in the degree of individualization: generic, tailored, and targeted or ‘spear.’ To differentiate participants on the basis of cybercrime awareness, participants in a ‘Hunter’ condition were primed throughout the study to remain vigilant to all scams, while participants in a ‘Passive’ condition received no such instruction. The study explored the influence of scam type, cybercrime awareness, gender, IT competence, and perceived Internet safety on susceptibility to email scams. Contrary to the hypotheses, none of these factors were associated with scam susceptibility. Although, tailored and individually crafted email scams were more likely to induce engagement than generic scams. Analysis of all the variables showed that international students and first year students were deceived by significantly more scams than domestic students and later year students. A Generalized Linear Model (GLM) analysis was undertaken to further explore the role of all the variables of interest and the results were consistent with the descriptive findings showing that student status (domestic compared to international) and year of study (first year student compared to students in second, third and later years of study) had a higher association to the risk of scam deception. Implications and future research directions are discussed

Phishing and Cybercrime Risks in a University Student Community

In an exploratory quasi-experimental observational study, 138 participants recruited during a university orientation week were exposed to social engineering directives in the form of fake email or phishing attacks over several months in 2017. These email attacks attempted to elicit personal information from participants or entice them into clicking links which may have been compromised in a real-world setting. The study aimed to determine the risks of cybercrime for students by observing their responses to social engineering and exploring attitudes to cybercrime risks before and after the phishing phase. Three types of scam emails were distributed that varied in the degree of individualization: generic, tailored, and targeted or ‘spear.’ To differentiate participants on the basis of cybercrime awareness, participants in a ‘Hunter’ condition were primed throughout the study to remain vigilant to all scams, while participants in a ‘Passive’ condition received no such instruction. The study explored the influence of scam type, cybercrime awareness, gender, IT competence, and perceived Internet safety on susceptibility to email scams. Contrary to the hypotheses, none of these factors were associated with scam susceptibility. Although, tailored and individually crafted email scams were more likely to induce engagement than generic scams. Analysis of all the variables showed that international students and first year students were deceived by significantly more scams than domestic students and later year students. A Generalized Linear Model (GLM) analysis was undertaken to further explore the role of all the variables of interest and the results were consistent with the descriptive findings showing that student status (domestic compared to international) and year of study (first year student compared to students in second, third and later years of study) had a higher association to the risk of scam deception. Implications and future research directions are discussed

Limiting Distributions of Generalised Poisson-Dirichlet Distributions Based on Negative Binomial Processes

The \text {PD}_\alpha ^{(r)} distribution, a two-parameter distribution for random vectors on the infinite simplex, generalises the \text {PD}_\alpha distribution introduced by Kingman, to which it reduces when r=0. The parameter \alpha \in (0,1) arises from its construction based on ratios of ordered jumps of an \alpha -stable subordinator, and the parameter r>0 signifies its connection with an underlying negative binomial process. Herein, it is shown that other distributions on the simplex, including the Poisson-Dirichlet distribution \text {PD}(\theta ), occur as limiting cases of \text {PD}_\alpha ^{(r)}, as r\rightarrow \infty . As a result, a variety of connections with species and gene sampling models, and many other areas of probability and statistics, are made