Related papers: Mathematical analysis of long tail economy using s…
We review several competing chaining methods to estimate the supremum, the diameter of the range or the modulus of continuity of a stochastic process in terms of tail bounds of their two-dimensional distributions. Then we show how they can…
This paper analyzes customer product-choice behavior based on the recency and frequency of each customer's page views on e-commerce sites. Recently, we devised an optimization model for estimating product-choice probabilities that satisfy…
To draw inference on serial extremal dependence within heavy-tailed Markov chains, Drees, Segers and Warcho{\l} [Extremes (2015) 18, 369--402] proposed nonparametric estimators of the spectral tail process. The methodology can be extended…
In this study, we present a simple stochastic order-book model for investors' swarm behaviors seen in the continuous double auction mechanism, which is employed by major global exchanges. Our study shows a characteristic called "fat tail"…
We introduce a trimmed version of the Hill estimator for the index of a heavy-tailed distribution, which is robust to perturbations in the extreme order statistics. In the ideal Pareto setting, the estimator is essentially finite-sample…
The study of loss function distributions is critical to characterize a model's behaviour on a given machine learning problem. For example, while the quality of a model is commonly determined by the average loss assessed on a testing set,…
Many recommender systems suffer from popularity bias: popular items are recommended frequently while less popular, niche products, are recommended rarely or not at all. However, recommending the ignored products in the `long tail' is…
Understanding the shape of a distribution of data is of interest to people in a great variety of fields, as it may affect the types of algorithms used for that data. We study one such problem in the framework of distribution property…
Recent studies of cluster distribution in various ecosystems revealed Pareto statistics for the size of spatial colonies. These results were supported by cellular automata simulations that yield robust criticality for endogenous pattern…
The success of a cross-sectional systematic strategy depends critically on accurately ranking assets prior to portfolio construction. Contemporary techniques perform this ranking step either with simple heuristics or by sorting outputs from…
We empirically investigate fluctuations in product prices in online markets by using a tick-by-tick price data collected from a Japanese price comparison site, and find some similarities and differences between product and asset prices. The…
We consider the problem of online allocation (matching and assortments) of reusable resources where customers arrive sequentially in an adversarial fashion and allocated resources are used or rented for a stochastic duration that is drawn…
This paper studies stochastic mechanisms under which light-tailed latent price dynamics yield realized prices with power-law tails. The realized price is modeled as $P_T=e^{X_T}$, where $X$ is a Markov-modulated L\'evy process and $T$ is…
We study the tails of closing auction return distributions for a sample of liquid European stocks. We use the stochastic call auction model of Derksen et al. (2020a), to derive a relation between tail exponents of limit order placement…
Product ranking is the core problem for revenue-maximizing online retailers. To design proper product ranking algorithms, various consumer choice models are proposed to characterize the consumers' behaviors when they are provided with a…
One dimensional stylized model taking into account spatial activity of firms with uniformly distributed customers is proposed. The spatial selling area of each firm is defined by a short interval cut out from selling space (large interval).…
Most extreme events in real life can be faithfully modeled as random realizations from a Generalized Pareto distribution, which depends on two parameters: the scale and the shape. In many actual situations, one is mostly concerned with the…
Recent advances in machine learning have spurred significant interest in learning-augmented algorithms, particularly for online optimization. A growing body of work has studied online bidding in this framework, aiming to characterize the…
We present an overview of possible reasons for the appearance of heavy-tailed distributions in applications to the natural sciences. These distributions include the laws of Pareto, Lotka, and some new ones. The reasons are illustrated using…
Recently some papers, such as Aban, Meerschaert and Panorska (2006), Nuyts (2010) and Clark (2013), have drawn attention to possible truncation in Pareto tail modelling. Sometimes natural upper bounds exist that truncate the probability…