Approximate Analytical Method of Maximum Likelihood Estimation of Weibull Distribution

DOI

10.2991/978-94-6463-042-8_97How to use a DOI?

Keywords

Approximate Analytical Method; Perturbative Method; Artificial Parameter; Maximum Likelihood Estimation

Abstract

Weibull distribution is commonly applied in survival analysis and reliability analysis, whose shape and scale parameters are most commonly estimated by maximum likelihood estimation and related numerical methods. In this paper, by introducing an artificial parameter and then using the perturbative method, for the first time in the statistics literature, we conveniently obtain approximate analytical formulas of maximum likelihood estimates of the parameters in Weibull distributions, which are important complements to those tedious and unreliable numerical methods. Monte-Carlo simulations show that the approximate analytical method proposed in this paper is fairly feasible and accurate. Using the similar method, we can also obtain the approximate analytical formulas of maximum likelihood estimates in many other statistical problems.

Copyright

© 2023 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - Tian Ye
AU  - He Heping
AU  - Zhang Yu
PY  - 2022
DA  - 2022/12/29
TI  - Approximate Analytical Method of Maximum Likelihood Estimation of Weibull Distribution
BT  - Proceedings of the 2022 International Conference on mathematical statistics and economic analysis (MSEA 2022)
PB  - Atlantis Press
SP  - 674
EP  - 680
SN  - 2352-538X
UR  - https://doi.org/10.2991/978-94-6463-042-8_97
DO  - 10.2991/978-94-6463-042-8_97
ID  - Ye2022
ER  -