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New methods to compute the generalized chi-square distribution
Published 7 Apr 2024 in stat.CO, cs.LG, stat.ME, and stat.ML | (2404.05062v3)
Abstract: We present four new mathematical methods, two exact and two approximate, along with open-source software, to compute the cdf, pdf and inverse cdf of the generalized chi-square distribution. Some methods are geared for speed, while others are designed to be accurate far into the tails, using which we can also measure large values of the discriminability index $d'$ between multivariate normal distributions. We compare the accuracy and speed of these and previous methods, characterize their advantages and limitations, and identify the best methods to use in different cases.
- DA Jones. Statistical analysis of empirical models fitted by optimization. Biometrika, 70(1):67–88, 1983.
- Counter-intuitive effect of null hypothesis on moran’s i tests under heterogenous populations (short paper). In 12th International Conference on Geographic Information Science (GIScience 2023). Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2023.
- Adaptive minimax optimality in statistical inverse problems via solit–sharp optimal lepskii-inspired tuning. arXiv preprint arXiv:2304.10356, 2023.
- Exact consistency tests for gaussian mixture filters using normalized deviation squared statistics. arXiv preprint arXiv:2312.17420, 2023.
- Unfair ai: It isn’t just biased data. In 2022 IEEE International Conference on Data Mining (ICDM), pages 957–962. IEEE, 2022.
- Prior-informed uncertainty modelling with bayesian polynomial approximations. arXiv preprint arXiv:2203.03508, 2022.
- Methods to integrate multinormals and compute classification measures. arXiv preprint arXiv:2012.14331, 2020.
- Analytic distribution of the optimal cross-correlation statistic for stochastic gravitational-wave-background searches using pulsar timing arrays. arXiv preprint arXiv:2305.01116, 2023.
- Hellings and downs correlation of an arbitrary set of pulsars. Physical Review D, 108(4):043026, 2023.
- Detection of weak transient signals using a broadband subspace approach. In 2021 Sensor Signal Processing for Defence Conference (SSPD), pages 1–5. IEEE, 2021.
- Yao-Wen Hsu. Statistical model for approximating gains of arrays with unequal normally distributed errors. IEEE Transactions on Antennas and Propagation, 70(12):11653–11664, 2022.
- Purposeful co-design of ofdm signals for ranging and communications. arXiv preprint arXiv:2309.03076, 2023.
- A framework for gnss spoofing detection through combinations of metrics. IEEE Transactions on Aerospace and Electronic Systems, 57(6):3633–3647, 2021.
- Optimal ins monitor for gnss spoofer tracking error detection. NAVIGATION: Journal of the Institute of Navigation, 71(1), 2024.
- Paolo Manfredi. Probabilistic uncertainty quantification of microwave circuits using gaussian processes. IEEE Transactions on Microwave Theory and Techniques, 2022.
- Linear attacks against remote state estimation: Performance analysis under an encryption scheme. IEEE Transactions on Control of Network Systems, 2024.
- Kristoffer M Frey. Belief-Space Planning for Real-World Systems: Efficient SLAM-Based Belief Propagation and Continuous-Time Safety. PhD thesis, Massachusetts Institute of Technology, 2021.
- Probabilistically safe mobile manipulation in an unmodeled environment with automated feedback tuning. In 2022 American Control Conference (ACC), pages 1214–1221. IEEE, 2022.
- Provable probabilistic safety and feasibility-assured control for autonomous vehicles using exponential control barrier functions. In 2022 IEEE Intelligent Vehicles Symposium (IV), pages 952–957. IEEE, 2022.
- Stochastic-skill-level-based shared control for human training in urban air mobility scenario. ACM Transactions on Human-Robot Interaction, 2023.
- Harold Ruben. Probability content of regions under spherical normal distributions, iv: The distribution of homogeneous and non-homogeneous quadratic functions of normal variables. The Annals of Mathematical Statistics, 33(2):542–570, 1962.
- Jean-Pierre Imhof. Computing the distribution of quadratic forms in normal variables. Biometrika, 48(3/4):419–426, 1961.
- J Gil-Pelaez. Note on the inversion theorem. Biometrika, 38(3-4):481–482, 1951.
- Robert B Davies. Numerical inversion of a characteristic function. Biometrika, 60(2):415–417, 1973.
- Egon S Pearson. Note on an approximation to the distribution of non-central χ2superscript𝜒2\chi^{2}italic_χ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT. Biometrika, 46(3/4):364, 1959.
- A new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables. Computational Statistics & Data Analysis, 53(4):853–856, 2009.
- A fast and accurate approximation to the distributions of quadratic forms of gaussian variables. Journal of Computational and Graphical Statistics, 31(1):304–311, 2022.
- Computing the distribution of quadratic forms: Further comparisons between the liu–tang–zhang approximation and exact methods. Computational Statistics & Data Analysis, 54(4):858–862, 2010.
- A comparison of efficient approximations for a weighted sum of chi-squared random variables. Statistics and Computing, 26(4):917–928, 2016.
- BK Shah and CG Khatri. Distribution of a definite quadratic form for non-central normal variates. The Annals of Mathematical Statistics, pages 883–887, 1961.
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