Triparna Kundu

Classical skewness and kurtosis require finite third and fourth moments and are therefore undefined for Pareto-type and extreme-value models with small tail index. We study shape measures based on the mean absolute deviation (MAD), which require only a finite mean, and ask how they compare with L-moment ratios in interpretation, computation, and parameter estimation. For the Pareto I–IV, Fréchet, Gumbel, and Weibull families, we derive closed-form expressions, verified by numerical quadrature, for the MAD about any quantile, for MAD skewness and kurtosis, and for the corresponding L-moment ratios, using incomplete beta and gamma functions. The MAD measures are bounded and have a simple interpretation in terms of sub-means. We then propose MAD-Q, which matches theoretical and empirical MAD at the quartiles, gives its Jacobian in closed form, and characterizes identifiability: with known scale, the estimating equations have a unique solution, whereas with unknown scale, the MAD ratio is not monotone and a quartile-consistency step is required. In Monte Carlo experiments with known scale, MAD-Q is the most accurate non-likelihood method for most families and remains usable under lower-tail contamination that breaks the Pareto I likelihood; with unknown scale, its advantage is confined to infinite-variance tails. Financial loss and wind-speed applications illustrate both the strengths and limitations of the approach.

Commodity prices are notoriously hard to forecast, and whether the returns of commodity exchange-traded funds (ETFs) can be predicted remains an open question. We compare three deep learning models, Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Transformer, for forecasting the returns of six Deutsche Bank commodity ETFs covering agriculture (DBA), base metals (DBB), broad commodities (DBC), energy (DBE), oil (DBO), and precious metals (DBP). Using daily price data from January 2007 to December 2025, we predict daytime returns (open to close) and overnight returns (previous close to open) separately, over five horizons of 1, 5, 30, 60, and 180 trading days. Each model sees a 20-day window of price-based features, returns, rolling averages and volatilities, momentum, and recent lags, built from all six ETFs. All models are trained on a strict chronological split and judged by two simple, decision-oriented measures: how often they call the direction correctly, and the risk-adjusted return (annualized Sharpe ratio) of a stylized long–short strategy that ignores transaction costs. Formal significance tests with HAC corrections for overlapping targets, bootstrap confidence intervals, and comparisons with ARIMA, random forest, and simpler benchmarks corroborate strong predictability in overnight DBP and daytime DBB at medium horizons. Predictability turns out to be highly specific to the asset, the trading session, and the horizon. Overnight returns of the precious metals ETF (DBP) are by far the most predictable: the correct direction is called 71.6% of the time at 60 days and 76.7% at 180 days, with Sharpe ratios reaching about 15. Base metals (DBB) daytime returns are predictable at 30 days and oil (DBO) daytime returns at 180 days, whereas one-day-ahead forecasts and agricultural returns (DBA) stay essentially unpredictable. The Transformer has a slight edge at longer horizons and the GRU at shorter ones. Key directional accuracy and Sharpe ratio results are confirmed by Newey–West HAC significance tests and Diebold–Mariano forecast comparison tests with the Harvey–Leybourne–Newbold small-sample correction; HAC standard errors at the 180-day horizon exceed naïve OLS errors by a factor of approximately 7.4, and we explicitly flag results that do not survive this correction. A three-fold expanding walk-forward validation scheme corroborates the main findings, with DBP overnight and DBO daytime predictability persisting across all evaluation windows. Deep learning architectures statistically and economically outperform logistic regression, ridge regression, and momentum baselines on the most predictable configurations. An anomalous failure of all models on DBA daytime returns at the 180-day horizon is diagnosed as a regime-driven artefact associated with post-2021 commodity inflation, not a general feature of agricultural return dynamics. The broader lesson is that splitting returns into daytime and overnight components exposes predictable structure that conventional close-to-close returns hide.

In both experimental and theoretical analyses of data, we often look to select a set of simple components that can be combined to create an appropriate model for the data. A convenient way to do this is to use quantile functions that can be added or transformed to obtain new distributions. In this work, we connect quantile statistics and mean absolute deviations (MADs) by deriving a general class of MAD-based shape metrics expressed as integrals of the quantile function, with a direct geometric interpretation. Our approach is applicable to distributions with finite mean that include many of the commonly used distributions, including those without a variance, such as the Pareto. When simple midpoint quadrature is used, the proposed metrics recover widely used quantile-shape metrics, including the interquartile range, Galton skewness, and Moore’s octile kurtosis as special cases. We further propose a C-Trapezoid quadrature approximation that combines cubic polynomial endpoint extrapolation with trapezoidal integration, achieving approximation errors that are significantly lower than those of the midpoint approximation for many common distributions. The proposed approximation provides simple-to-compute formulas for shape analysis and yields closed-form, non-iterative parameter-estimation formulas. These formulas are easy to compute and interpret, and they are applicable to a wide class of distributions, including those without an explicit cumulative distribution function or some with heavy tails. Unlike maximum likelihood estimation, the proposed method is more robust and has simple geometric interpretation. We illustrate the methodology with two detailed case studies. The proposed approach gives a simple way to quickly assess distributional shape without any specialized tools.

High-stakes logistics, defined as supply chains where delays, quality loss, or noncompliance have serious human, safety, financial, or geopolitical consequences, are a prominent case of a broader reality: global supply chains are safety-, cost-, and time-critical socio-technical systems where forecasting quality, vendor coordination, and operational decisions shape service levels and stakeholder welfare. At the same time, decarbonization pressures and the growing use of AI for planning and control introduce new risks and trade-offs across energy, computation, and physical logistics. We develop a multi-agent framework that models supply chain system-of-systems dynamics drawing on (1) supply chain decision functions (shipment planning, sourcing and vendor management), (2) national energy-transition conditions that determine grid carbon intensity, and (3) carbon-aware computation accounting for AI-enabled decision support. Methodologically, we combine predictive analytics, unsupervised segmentation, and a carbon-cost-of-intelligence layer in a scenario-based assessment of how national energy-transition profiles–from Norway to India–affect the intensity of AI compute carbon, meaning the carbon emissions generated by the hardware and data centers required to train and run AI models. We introduce the carbon-adjusted supply chain performance (CASP) metric that integrates physical transport carbon, cold-chain overhead where applicable, and AI compute carbon into a per-package-type performance measure. Our analysis yields three actionable outputs for systems engineering and environmental management: carbon, service, and cost trade-off frontiers; governance levers (sourcing portfolio rules, buffers, and compute policies); and system-level early-warning indicators for disruption amplification. This study implements a tool-augmented multi-agent system (orchestrator, risk, and sourcing agents) using AWS bedrock and strands agents, where LLM-based agents orchestrate deterministic analytical engines through structured tool interfaces with adaptive query generation. Theoretically, we extend previous systems-of-systems and sustainable supply chain findings by formalizing package-type-specific carbon–service frontiers and by embedding AI compute carbon into a socio-technical resilience framework. Practically, the CASP benchmark, governance lever analysis, and multi-agent implementation provide decision-makers with concrete tools to compare carriers, routes, and compute strategies across countries while making transparent the trade-offs between service reliability and total carbon.

The accelerating energy demands from artificial intelligence (AI) deployment introduce systemic challenges for achieving carbon neutrality. Large language models (LLMs) represent a dominant driver of AI energy consumption, with inference operations constituting 80–90% of total energy usage. Current energy benchmarks report aggregate metrics without domain-level breakdowns, preventing accurate carbon footprint estimation for workloadspecific operations. This study addresses this critical gap by introducing a carbon-aware framework centered on the carbon cost of intelligence (CCI), a novel metric enabling workload-specific energy and carbon calculation that balances accuracy and efficiency across heterogeneous domains. This paper presents a comprehensive cross-domain energy benchmark using the massive multitask language understanding (MMLU) dataset, measuring accuracy and energy consumption in five representative domains: clinical knowledge (medicine), professional accounting (finance), professional law (legal), college computer science (technology), and general knowledge. Empirical analysis of GPT-4 across 100 MMLU questions, 20 per domain, reveals substantive variations: legal queries consume 4.3× more energy than general knowledge queries (222 J vs. 52 J per query), while energy consumption varies by domain due to input length differences. Our analysis demonstrates the evolution from simple ratio-based approaches (weighted accuracy divided by weighted energy) to harmonic mean aggregation, showing that the harmonic mean, by preventing bias from extreme values, provides more accurate carbon usage estimates. The CCI metric, calculated using weighted harmonic mean (analogous to P/E ratios in finance, where A/E represents accuracy-to-energy ratio), enables practitioners to accurately estimate energy and carbon emissions for specific workload mixes (e.g., 80% medicine + 15% general + 5% law). Results demonstrate that the domain workload mix significantly impacts carbon footprint: a law firm workload (60% law) consumes 96% more energy per query than a hospital workload (80% medicine), representing 49% potential savings through workload optimization. Carbon footprint analysis using US Northeast grid intensity (320 gCO₂e/kWh) shows domain-specific emissions ranging from 0.0046–0.0197 gCO₂ per query. CCI is validated through comparison with simple weighted average, demonstrating differences up to 12.1%, confirming that the harmonic mean provides more accurate and conservative carbon estimates essential for carbon reporting and neutrality planning. Our findings provide a novel cross-domain energy benchmark for GPT-4 and establish a practical carbon calculator framework for sustainable AI deployment aligned with carbon neutrality goals.

Pharmaceutical manufacturing and logistics rely on accurate prediction and decision making to safeguard product quality, delivery reliability, and patient outcomes. Despite rapid advances in artificial intelligence (AI) and machine learning (ML), few studies benchmark model performance across the diverse operational demands of global pharmaceutical supply chains. Predictive setbacks contribute to financial losses, reduced supply chain efficacy, and potential adverse health consequences, yet understanding these failures offers firms opportunities to refine strategy and strengthen resilience. Drawing on 1.2 million shipments spanning 39 countries, we compare traditional statistical models (ARIMA), ensemble methods (random forests, gradient boosting), and deep neural networks (LSTM, GRU, CNN, ANN) across pricing, demand forecasting, vendor management, and shipment planning. Gradient boosting produced the strongest pricing performance, while ARIMA delivered the lowest demand-forecasting errors but with limited explanatory power; neural networks captured nonlinear demand shocks and achieved superior maintenance-risk classification. We also identified three vendor performance clusters—high-performing, cost-efficient, and mixed-reliability vendors—enabling firms to better align shipment criticality with vendor capabilities by prioritizing high performers for urgent deliveries, leveraging cost-efficient vendors for non-urgent volumes, and managing mixed performers through targeted oversight. These insights highlight the value of our evidence-based roadmap for selecting algorithms in high-stakes healthcare logistics, in rapidly evolving, technologically complex global contexts where increasing algorithmic sophistication elevates the standards for safer, smarter pharmaceutical supply chains.