Bayesian estimation and prediction for linear exponential models using ordered moving extremes ranked set sampling in medical data

Haidy A. Newer; Bader S Alanazi; Haidy A. Newer; Bader S Alanazi

doi:10.3934/math.2025055

AIMS Mathematics

2025, Volume 10, Issue 1: 1162-1182. doi: 10.3934/math.2025055

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Bayesian estimation and prediction for linear exponential models using ordered moving extremes ranked set sampling in medical data

Haidy A. Newer ^{1
,
,},
Bader S Alanazi ²

1.
Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11511, Egypt
2.
Department of Mathematics, College of Science, Northern Border University, Arar 73222, Saudi Arabia

Received: 29 September 2024 Revised: 01 January 2025 Accepted: 10 January 2025 Published: 20 January 2025
MSC : 62E15, 62F25, 62G30, 62G32, 62M20

Our study aimed to compare ordered ranked set sampling with moving extremes ranked set sampling in the context of type Ⅱ censoring. We focused on deriving Bayesian estimations and predictions using the linear exponential model. This analysis included various loss functions, such as squared error, Al-Bayyati, and general entropy. To evaluate the efficiency of the estimators we produced, we assessed their mean squared error and relative absolute bias. Additionally, we provide Bayesian point and interval predictions for the ordered future lifetime, considering both squared error and general entropy loss functions. To ensure the accuracy and effectiveness of these estimation and prediction methods, we conducted numerical tests using Monte Carlo simulations. Finally, we illustrated these theoretical concepts with a practical example that utilized real-world medical data.
- ordered moving extremes ranked set sampling,
- Bayes estimation,
- squared error loss function,
- Al-Bayyati loss function,
- general entropy loss function,
- Bayesian prediction
Citation: Haidy A. Newer, Bader S Alanazi. Bayesian estimation and prediction for linear exponential models using ordered moving extremes ranked set sampling in medical data[J]. AIMS Mathematics, 2025, 10(1): 1162-1182. doi: 10.3934/math.2025055

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Abstract

Our study aimed to compare ordered ranked set sampling with moving extremes ranked set sampling in the context of type Ⅱ censoring. We focused on deriving Bayesian estimations and predictions using the linear exponential model. This analysis included various loss functions, such as squared error, Al-Bayyati, and general entropy. To evaluate the efficiency of the estimators we produced, we assessed their mean squared error and relative absolute bias. Additionally, we provide Bayesian point and interval predictions for the ordered future lifetime, considering both squared error and general entropy loss functions. To ensure the accuracy and effectiveness of these estimation and prediction methods, we conducted numerical tests using Monte Carlo simulations. Finally, we illustrated these theoretical concepts with a practical example that utilized real-world medical data.

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