Goodness-of-Fit Testing in Statistical Distributions
Summary
Goodness-of-fit testing constitutes a cornerstone of statistical inference, providing formal means to assess whether empirical observations conform to theoretical probability distributions. Techniques range from empirical distribution-function based statistics—such as Kolmogorov–Smirnov, Anderson–Darling and Cramér–von Mises tests—to divergence-based measures including chi-square and phi-divergence, as well as likelihood-ratio and Stein’s methods. Tests are evaluated by their ability to maintain nominal size, achieve high power against relevant alternatives and offer computational tractability. They have broad applications in diverse fields such as finance (modelling asset returns), engineering (reliability analysis), environmental science (extreme-value modelling), medicine (survival-analysis) and genomics (distributional traits of gene expression). Contemporary developments address challenges posed by censored or truncated data, complex multivariate and high-dimensional settings, mixture distributions, and adaptive computational approaches employing Monte Carlo simulation and resampling. Through rigorous methodological innovation and practical implementation, goodness-of-fit testing continues to play a critical role in model validation, risk assessment and evidence-based decision-making worldwide.
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Goodness-of-Fit Testing in Statistical Distributions publication trend
The graph below shows the total number of articles in goodness-of-fit testing in statistical distributions across all publications each year (not limited to Nature Index journals).
Technical terms
Goodness-of-fit test: A statistical procedure to assess whether observed data follow a specified probability distribution.
Null hypothesis: The assumption that a data sample is drawn from the hypothesised distribution against which the test is conducted.
Statistical power: The probability that a test correctly rejects the null hypothesis when the alternative hypothesis is true.
Random right censoring: A feature of survival data where the event of interest is unobserved beyond a random time point.
Empirical characteristic function: A sample-based analogue of the theoretical characteristic function, used to construct tests via Fourier methods.
References
- New classes of tests for the Weibull distribution using Stein’s method in the presence of random right censoring. Computational Statistics (2022).
- Testing for the Pareto type I distribution: a comparative study. METRON (2023).
- Cauchy or not Cauchy? New goodness-of-fit tests for the Cauchy distribution. Statistical Papers (2022).
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