# Classical and Bayesian Inference for the Two-Parameter Rayleigh Distribution with Random Censored Data

## TL;DR

This paper introduces a two-parameter Rayleigh distribution to improve survival data analysis under random censoring.

## Contribution

The study proposes a two-parameter Rayleigh model with threshold to address estimation errors in traditional single-parameter models.

## Key findings

- The two-parameter model outperforms single-parameter Rayleigh in fitting survival data with threshold characteristics.
- Bayesian and maximum likelihood estimation methods are developed for the two-parameter model.
- Monte Carlo simulations confirm the improved accuracy of the proposed estimators.

## Abstract

This study focuses on parameter estimation and reliability analysis for the two-parameter Rayleigh distribution under random censoring. It is shown that directly fitting the standard Rayleigh distribution can lead to substantial estimation errors, especially when the dataset contains a markedly high minimum value. To overcome the limitation of the conventional single-parameter Rayleigh distribution, which lacks a threshold parameter in practical applications, a two-parameter Rayleigh distribution model is proposed. The main research contents include the following: establishing a randomly censored data model; deriving classical inference methods based on maximum likelihood estimation along with several other classical estimation techniques; and constructing a Bayesian estimation framework. We also analyze several reliability and experimental characteristics by deriving their corresponding estimates. A Monte Carlo simulation study is carried out to assess the performance of the proposed estimators. Finally, the practicality and superiority of the two-parameter model are validated using real strength datasets. The results demonstrate that the two-parameter Rayleigh distribution can more accurately describe survival data with threshold characteristics and outperforms the single-parameter model in terms of model fit and reliability estimation.