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Block Adaptive Progressive Type-II Censored Sampling for the Inverted Exponentiated Pareto Distribution: Parameter Inference and Reliability Assessment

Rajendranath Mondal, Aditi Kar Gangopadhyay, Raju Bhakta, Kousik Maiti

TL;DR

This work develops parameter inference and reliability assessment for lifetimes following the Inverted Exponentiated Pareto distribution under a block adaptive progressive Type-II censoring framework. It derives maximum likelihood estimators with guaranteed existence and uniqueness, and also introduces pivotal inference, asymptotic, and generalized confidence intervals for model parameters and derived reliability measures. A substantial simulation study and a real-data analysis on carbon-fibre strengths demonstrate that pivotal methods often outperform classical MLE in accuracy and interval sharpness, while the IEP model provides superior fit relative to several competing distributions. The approach leverages order statistics and a detailed censoring scheme to deliver efficient, robust inference in reliability contexts with complex censoring.

Abstract

This article explores the estimation of unknown parameters and reliability characteristics under the assumption that the lifetimes of the testing units follow an Inverted Exponentiated Pareto (IEP) distribution. Here, both point and interval estimates are calculated by employing the classical maximum likelihood and a pivotal estimation methods. Also, existence and uniqueness of the maximum likelihood estimates are verified. Further, asymptotic confidence intervals are derived by using the asymptotic normality property of the maximum likelihood estimator. Moreover, generalized confidence intervals are obtained by utilizing the pivotal quantities. Additionally, some mathematical developments of the IEP distribution are discussed based on the concept of order statistics. Furthermore, all the estimations are performed on the basis of the block censoring procedure, where an adaptive progressive Type-II censoring is employed to every block. In this regard, the performances of two estimation methods, namely maximum likelihood estimation and pivotal estimation, is evaluated and compared through a simulation study. Finally, a real data is illustrated to demonstrate the flexibility of the proposed IEP model.

Block Adaptive Progressive Type-II Censored Sampling for the Inverted Exponentiated Pareto Distribution: Parameter Inference and Reliability Assessment

TL;DR

This work develops parameter inference and reliability assessment for lifetimes following the Inverted Exponentiated Pareto distribution under a block adaptive progressive Type-II censoring framework. It derives maximum likelihood estimators with guaranteed existence and uniqueness, and also introduces pivotal inference, asymptotic, and generalized confidence intervals for model parameters and derived reliability measures. A substantial simulation study and a real-data analysis on carbon-fibre strengths demonstrate that pivotal methods often outperform classical MLE in accuracy and interval sharpness, while the IEP model provides superior fit relative to several competing distributions. The approach leverages order statistics and a detailed censoring scheme to deliver efficient, robust inference in reliability contexts with complex censoring.

Abstract

This article explores the estimation of unknown parameters and reliability characteristics under the assumption that the lifetimes of the testing units follow an Inverted Exponentiated Pareto (IEP) distribution. Here, both point and interval estimates are calculated by employing the classical maximum likelihood and a pivotal estimation methods. Also, existence and uniqueness of the maximum likelihood estimates are verified. Further, asymptotic confidence intervals are derived by using the asymptotic normality property of the maximum likelihood estimator. Moreover, generalized confidence intervals are obtained by utilizing the pivotal quantities. Additionally, some mathematical developments of the IEP distribution are discussed based on the concept of order statistics. Furthermore, all the estimations are performed on the basis of the block censoring procedure, where an adaptive progressive Type-II censoring is employed to every block. In this regard, the performances of two estimation methods, namely maximum likelihood estimation and pivotal estimation, is evaluated and compared through a simulation study. Finally, a real data is illustrated to demonstrate the flexibility of the proposed IEP model.
Paper Structure (8 sections, 1 theorem, 30 equations, 5 figures, 8 tables, 1 algorithm)

This paper contains 8 sections, 1 theorem, 30 equations, 5 figures, 8 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Maximum Likelihood Estimation
  3. Asymptotic Confidence Intervals
  4. Pivotal Inference
  5. Order Statistics and Applications
  6. Simulation Study
  7. Real Data Analysis
  8. Concluding Remarks

Key Result

Theorem 4.1

The pivotal quantity $\mathcal{P}(\beta) = \sum_{i=1}^{k}\mathcal{P}_i(\beta)$ is a strictly decreasing function of $\beta > 0$.

Figures (5)

  • Figure 1: Plot of the empirical CDF of the real data along with the proposed theoretical CDFs.
  • Figure 2: Plot of the histogram of the real data along with the proposed theoretical PDFs.
  • Figure 3: P-P plot of the dataset vs fitted (a) IEP distribution, (b) GP distribution, (c) EP distribution, (d) IER distribution, and (e) IL distribution.
  • Figure 4: Q-Q plot of the dataset vs fitted (a) IEP distribution, (b) GP distribution, (c) EP distribution, (d) IER distribution, and (e) IL distribution.
  • Figure 5: Plot of the scaled total time on test based on the real data.

Theorems & Definitions (2)

  • Theorem 4.1
  • proof