MUMBAI, India, Feb. 6 -- Intellectual Property India has published a patent application (202641007318 A) filed by Dr. K. Saranya; M. Balamurugan; R. Pandiarajan; Dr. A. Iravithul Basira; Dr. P. Velvizhi; Dr. R. Apparsamy; Dr. V. Bugcy Mettilda; Y. D. Christina Merline; G. Manjula Rajeswari; and Dr. S. Ramaprabha, Tiruchirappalli, Tamil Nadu, on Jan. 24, for 'a method for closed-form approximation of tail probabilities using moment-matching expansions.'
Inventor(s) include Dr. K. Saranya; M. Balamurugan; R. Pandiarajan; Dr. A. Iravithul Basira; Dr. P. Velvizhi; Dr. R. Apparsamy; Dr. V. Bugcy Mettilda; Y. D. Christina Merline; G. Manjula Rajeswari; and Dr. S. Ramaprabha.
The application for the patent was published on Feb. 6, under issue no. 06/2026.
According to the abstract released by the Intellectual Property India: "Estimating tail probabilities is essential in various fields, including statistical inference, reliability engineering, financial risk assessment, communication systems, and extreme-event modelling. Traditional numerical methods like Monte Carlo simulation, numerical integration, and saddle-point approximations frequently encounter challenges such as elevated computational expenses, instability in rare-event scenarios, or limited analytical manageability. This invention introduces a method for approximating tail probabilities of random variables in a closed form through moment-matching expansions, facilitating efficient, precise, and scalable assessment of distribution tails. The described approach begins by calculating a finite collection of statistical moments, such as mean, variance, skewness, kurtosis, and higher-order moments, derived from either empirical data or established probability distributions. The moments are subsequently aligned with a parametric or semi-parametric reference distribution through a structured expansion framework. The expansion framework could incorporate Gram-Charlier series, Edgeworth expansions, or orthogonal polynomial bases, adjusted to guarantee numerical stability and convergence in the tail region. The proposed method offers a closed-form correction mechanism that selectively re-weights expansion coefficients, ensuring that tail accuracy is maintained, unlike traditional series expansions which tend to degrade near extreme quantiles. This mechanism effectively mitigates oscillatory artefacts and divergence frequently encountered in traditional approximations. The resulting formulation provides clear analytical expressions for both upper and lower tail probabilities, eliminating the need for iterative computation or sampling-based estimation. The invention enhances the adaptive truncation of expansion terms by considering moment sensitivity and error bounds, facilitating a balance between computational complexity and precision in the approximation. This approach is relevant for a variety of random variables, encompassing both continuous and discrete types, as well as those characterised by heavy tails, skewness, and multimodal distributions. The suggested method greatly minimises computational demands while ensuring high precision in estimating rare-event probabilities. The invention proves to be exceptionally well-suited for real-time systems, embedded analytics, large-scale simulations, and decision-critical applications that demand rapid and dependable tail probability evaluation. The approach can be executed through software, firmware, or hardware-accelerated statistical engines, and can be incorporated into current probabilistic modelling workflows."
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