Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1510.06731

On the shadow moments of apparently infinite-mean phenomena

Nassim Nicholas Taleb·Pasquale Cirillo
View original source ↗Read source document ↗Export metadata ↓

Abstract

We propose an approach to compute the conditional moments of fat-tailed phenomena that, only looking at data, could be mistakenly considered as having infinite mean. This type of problems manifests itself when a random variable Y has a heavy- tailed distribution with an extremely wide yet bounded support. We introduce the concept of dual distribution, by means of a log-transformation that removes the upper bound. The tail of the dual distribution can then be studied using extreme value theory, without making excessive parametric assumptions, and the estimates one obtains can be used to study the original distribution and compute its moments by reverting the log- transformation. The central difference between our approach and a simple truncation is in the smoothness of the transformation between the original and the dual distribution, allowing use of extreme value theory. War casualties, operational risk, environment blight, complex networks and many other econophysics phenomena are possible fields of application.

Explore related subjects

stat.APstat.ME

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Nassim Nicholas Taleb, Pasquale Cirillo. 2016-02-07. On the shadow moments of apparently infinite-mean phenomena. https://arxiv.org/abs/1510.06731

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

From Metrics to Decisions in NBA Analytics: A Critical Integrative Review and Decision-Readiness Framework

National Basketball Association (NBA) teams have increasingly detailed metrics, but better predictions do not necessarily improve decisions. This critical integrative review draws on prior reviews, citation tracing, and topic searches across seven research streams: on-court action, player value, role, lineup synergy, availability, draft and development, and contracts and roster construction. An observation-state-action-decision-evaluation chain organizes the synthesis. Six decision-readiness gates guide our assessment: point-in-time validity, uncertainty, context portability, action feasibility, opportunity-set observability, and evaluation, with requirements matched to each claim. The reviewed literature is strongest in measuring and predicting individual components of a decision. Evidence is less developed at interfaces that combine components, transfer them across settings, and compare feasible actions. We outline a proposed deployment workflow, a reporting contract, and a research agenda covering player transport, role substitution, roster fragility, legal action generation, and asset valuation. The 2023 collective bargaining agreement and forthcoming 3-2-1 Draft Lottery illustrate how institutional changes generate research questions. Models should inform evaluable comparisons of feasible choices. While its effect on organizational decision quality remains an empirical question, the framework provides a diagnostic and reporting structure for matching decision claims to evidence requirements.

stat.AP↗
arXiv2026

Bayesian calibration of adaptive-behavior SIR models for multi-wave COVID-19 incidence in New York City

Epidemic incidence reflects both transmission dynamics and adaptive human behavior, yet these mechanisms may be difficult to distinguish from aggregate case data alone. We calibrated four susceptible--infected--recovered (SIR) specifications to weekly confirmed COVID-19 incidence in New York City from June to December 2020, comparing a single continuous SIR trajectory, a wave-initialized SIR model, and two adaptive-behavior models with either shared or wave-specific transmission. Inference was performed using rejection Approximate Bayesian Computation (ABC), and in-sample reconstruction was assessed using root mean squared error (RMSE) and the weighted interval score (WIS). Reinitializing the epidemic state by wave produced the largest structural improvement over the continuous SIR trajectory, reducing mean-based RMSE by 48.6\% and WIS by 17.6\%. Adding delayed prevalence-dependent behavioral adaptation with shared transmission further reduced mean-based RMSE by 23.4\%, but yielded essentially unchanged WIS relative to the wave-initialized SIR model. Allowing transmission to vary by wave did not provide a consistent additional advantage and produced strongly asymmetric posterior-simulation trajectories. Behavioral sensitivity, response midpoint, and delay remained only weakly to partially identified. The clearest posterior structure was a negative association between transmission intensity and the behavioral midpoint, indicating that higher transmission could be compensated by behavioral responses activated at lower prevalence. Sensitivity to ordered behavioral priors further showed that reconstruction and behavioral inference depend materially on structural prior assumptions. These results suggest that adaptive mechanisms can improve multi-wave incidence reconstruction, while aggregate incidence alone is insufficient to sharply separate transmission from behavioral adaptation.

stat.AP↗
arXiv2026

Short-term rental market occupancy - daily time series for 2017-2022 on 500 markets worldwide

Short-term vacation rentals, as promoted by platforms such as Airbnb, Homeaway, Vrbo, etc., are a growing component of the travel industry. This paper provides a unique, large dataset on global market occupancy for the short-term rental market using data from the American company Wheelhouse. The dataset consists of data for $500$ markets around the world. For each market, a daily occupancy time series from January $2017$ to December $2022$ is provided, allowing for studies of local and global patterns in the evolution of the short-term rental market. Additionally, the dataset includes curves representing the booking trajectory of each market and stay date up to one year prior to the stay date. This large dataset comprises a unique combination of time series and survival analysis data, and is suitable as a methodological benchmark for both classical statistical and machine learning models.

stat.AP↗