Statistics
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Bootstrap DEA
Bootstrap Data Envelopment Analysis (Bootstrap DEA) is a resampling-based extension of standard DEA that provides statistically valid inference for efficiency scores. Introduced by Simar and Wilson in 1998, it addresses the core weakness of...
Bradley-Terry Model
The Bradley-Terry model is a probabilistic model for paired comparisons that assigns a latent strength parameter to each item and predicts the probability that one item beats another in a head-to-head contest. Introduced by Ralph A. Bradley...
Economic Order Quantity
The Economic Order Quantity (EOQ) is a classic deterministic inventory model that identifies the order quantity minimizing the sum of annual ordering and holding costs. Introduced by Ford W. Harris in 1913 and later popularized by R. H. Wil...
Elo Rating
The Elo Rating System is a pairwise comparison-based ranking method developed by Hungarian-American physicist and chess master Arpad Elo and formally published in 1978. Originally designed to assess the relative skill levels of chess player...
Erlang C Model
The Erlang C model is a steady-state queueing formula that determines the probability a customer must wait before being served in a system with c parallel servers, Poisson arrivals at rate lambda, and exponentially distributed service times...
GM(1,1) Grey Forecasting
GM(1,1) is the core forecasting model of grey system theory, introduced by Julong Deng in 1982, designed to predict from very few observations and incomplete information — situations where classical time-series models like ARIMA need far mo...
Imprecise Probability
Imprecise probability is a generalization of standard probability theory that represents epistemic uncertainty through sets of probability measures, called credal sets, rather than a single precise distribution. Introduced systematically by...
Little's Law
Little's Law is a fundamental theorem in queueing theory that relates the long-run average number of items in a stable system (L) to the long-run average arrival rate (λ) and the long-run average time an item spends in the system (W), expre...
M/M/1 Queue
The M/M/1 queue is the foundational single-server queueing model in which customers arrive according to a Poisson process with rate λ, are served one at a time by a single server with exponentially distributed service times at rate μ, and w...
M/M/c Queue
The M/M/c queue is a multi-server stochastic model in which customers arrive according to a Poisson process at rate λ, are served by c identical servers each with exponentially distributed service times at rate μ, and wait in a single commo...
Malmquist Productivity Index
The Malmquist Productivity Index (MPI) is a non-parametric measure of total factor productivity (TFP) change over time. Formally grounded in distance functions by Caves, Christensen, and Diewert (1982) and operationalized using Data Envelop...
Network DEA
Network Data Envelopment Analysis (Network DEA) is a nonparametric efficiency measurement framework introduced by Färe and Grosskopf (2000) that extends classical DEA to multi-stage or multi-division production processes. Rather than treati...
Newsvendor Model
The Newsvendor Model is a single-period stochastic inventory optimization framework that determines the profit-maximizing order quantity when demand is uncertain and unsold units cannot be carried forward. Formally introduced by Arrow, Harr...
Plackett-Luce Model
The Plackett-Luce model is a probabilistic framework for analysing and predicting rank-ordered data. Introduced by Robin Plackett (1975) — building on R. Duncan Luce's earlier axiom of choice (1959) — it models the probability of any comple...
Safety Stock
Safety stock is an additional quantity of inventory held beyond expected demand during a replenishment lead time, designed to protect against stockouts caused by demand or supply uncertainty. Reorder-point models formalize this buffer by se...
Stochastic Frontier Analysis
Stochastic Frontier Analysis is a frontier regression model, introduced by Aigner, Lovell and Schmidt in 1977, that estimates a production, cost, or profit function while separating each unit's technical inefficiency from ordinary statistic...
Stochastic Frontier Firm Efficiency Analysis
Stochastic frontier analysis (SFA) estimates how far a firm falls short of the best attainable output for its inputs while explicitly separating that shortfall from random noise. Aigner, Lovell and Schmidt's 1977 model introduced the defini...
Super-Efficiency DEA
Super-Efficiency DEA is a nonparametric linear programming extension of classical Data Envelopment Analysis (DEA) introduced by Andersen and Petersen (1993). While standard DEA assigns a maximum efficiency score of 1.0 to all units on the e...
Tourism Input-Output Analysis
Tourism input-output analysis applies Wassily Leontief's inter-industry framework to measure how tourist spending reverberates through an entire economy. An input-output table records, sector by sector, how much each industry buys from ever...
Tourism Multiplier Analysis
Tourism multiplier analysis quantifies how much total economic activity a destination gains from each unit of tourist spending, once that spending circulates through the local economy. When a visitor pays for a hotel room, the money does no...
TrueSkill
TrueSkill is a Bayesian skill rating system developed by Herbrich, Minka, and Graepel at Microsoft Research and introduced at NeurIPS 2006. It represents each player's skill as a Gaussian distribution parameterized by a mean (estimated skil...
Window DEA
Window Data Envelopment Analysis (Window DEA) is a non-parametric panel efficiency method that evaluates decision-making units (DMUs) over time by embedding each DMU's observations across a rolling temporal window into a single cross-sectio...