A closed-form approximation for the median of the beta distribution
Jouni Kerman
TL;DR
This paper introduces a simple closed-form approximation for the median of the beta distribution, which is accurate for larger shape parameters and has a low relative error.
Contribution
The paper presents a novel, easy-to-use approximation formula for the median of the beta distribution, improving computational efficiency.
Findings
Approximation has less than 4% relative error for shape parameters greater than 1.
Error decreases rapidly as shape parameters increase.
The formula provides a practical alternative to numerical methods.
Abstract
A simple closed-form approximation for the median of the beta distribution Beta(a, b) is introduced: (a-1/3)/(a+b-2/3) for (a,b) both larger than 1 has a relative error of less than 4%, rapidly decreasing to zero as both shape parameters increase.
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Taxonomy
TopicsProbabilistic and Robust Engineering Design · Control Systems and Identification · Advanced Multi-Objective Optimization Algorithms