Title: Threshold selection for extreme value estimation based on uncertainty theory

Authors: Justin Chirima; Frank Ranganai Matenda; Mabutho Sibanda

Addresses: Department of Mathematical Sciences, University of Malawi, P.O. Box 280, Zomba, Malawi ' School of Accounting, Economics and Finance, University of KwaZulu-Natal, Westville Campus, University Road, Westville, Private Bag X54001, Durban, 4000, South Africa ' School of Accounting, Economics and Finance, University of KwaZulu-Natal, Westville Campus, University Road, Westville, Private Bag X54001, Durban, 4000, South Africa

Abstract: This paper examines an inverse linear uncertainty distribution threshold selection approach for fitting the generalised Pareto distribution (GPD). The threshold is an unknown quantity which needs to be estimated. To estimate GPD parameters, the peaks-over-threshold method is applied. An algorithm based on the linear uncertainty distribution is developed and used in establishing the optimal threshold for fitting the GPD. Initially, the algorithm is tested on hypothetical data with known thresholds, fort Collins precipitation data and Newlyn, Cornwall wave height data found in R. Finally, Nikkei 225 index data and Hang Seng index data found on Yahoo finance is analysed using the proposed method to establish if the algorithm can be applied to real life data from financial markets. We discovered that the developed procedure is capable of determining distinct thresholds using information from the mean residual life plot and the threshold stability plot.

Keywords: linear uncertainty distribution; generalised Pareto distribution; GPD; threshold; financial markets; peaks-over-threshold; POT.

DOI: 10.1504/IJMOR.2026.156086

International Journal of Mathematics in Operational Research, 2026 Vol.34 No.4, pp.524 - 553

Received: 27 Sep 2023
Accepted: 12 May 2024
Published online: 03 Sep 2026 *

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