Classical and Bayesian Inference of the Inverse Nakagami Distribution Based on Progressive Type-II Censored Samples

Wang, Liang; Dey, Sanku; Tripathi, Yogesh Mani

doi:10.3390/math10122137

Cited by 3 publications

(1 citation statement)

References 26 publications

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“…The weighted inverse Nakagami distribution with properties and applications was investigated by [10]. The inverse Nakagami distribution was studied by [12] under progressive Type-II censored data with applications on lifetime data.…”

Section: Introductionmentioning

confidence: 99%

A Three Parameter Power Nakagami Distribution: Properties and Application on the Tax Revenue Data

Bashir,

Waseem,

Rasul

2023

Int. J. Anal. Appl.

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Developing the probability distributions is increasing extensively over the decades but even though the newly developed distributions have elegant properties and variety of shapes which are applicable in wide areas of real-life situations and a numerous type of data sets. In this article, we introduced a three-parameter positively skewed model named Power Nakagami (PN) distribution based on power transformation. Various statistical properties of the Power Nakagami distribution are derived, including moments. Some reliability measures such as survival function, hazard function, cumulative hazard function and reversed hazard function are discussed also expressions for mills ratio, odd function, elasticity and Lorenz and Bonferroni Curve are developed. Graphical representation of probability density function, cumulative density function and reliability measures are presented. Maximum likelihood estimation is used to estimate the parameters. The distribution is fitted to real life dataset (Tax revenue) to demonstrate the comparison of the new distribution with the base distribution.

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Section: Introductionmentioning

confidence: 99%

A Three Parameter Power Nakagami Distribution: Properties and Application on the Tax Revenue Data

Bashir,

Waseem,

Rasul

2023

Int. J. Anal. Appl.

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Reliability evaluation for Weibull distribution with heavily Type II censored data

Liu,

Zheng,

Yang

2024

Quality & Reliability Eng

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The lifetime data collected from the field are usually heavily censored, in which case, getting an accurate reliability evaluation based on heavily censored data is challenging. For heavily Type‐II censored data, the parameters estimation bias of traditional methods (i.e., maximum likelihood estimation (MLE) and least squares estimation (LSE)) are still large, and Bayesian methods are hard to specify the priors in practice. Therefore, considering the existing range of shape parameter for Weibull distribution, this study proposes two novel parameter estimation methods, the three‐step MLE method and the hybrid estimation method. For the three‐step MLE method, the initial estimates of shape and scale parameters are first respectively derived using MLE, then are updated by the single parameter MLE method with the range constraint of shape parameter. For the hybrid estimation method, the shape parameter is estimated by the LSE method with the existing range constraint of shape parameter, then the scale parameter estimate can be obtained by MLE. On this basis, two numerical examples are performed to demonstrate the consistency and effectiveness of the proposed methods. Finally, a case study on turbine engines is given to verify the effectiveness and applicability of the proposed methods.

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The Process Capability Index of Pareto Model under Progressive Type-II Censoring: Various Bayesian and Bootstrap Algorithms for Asymmetric Data

et al. 2023

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It is agreed by industry experts that manufacturing processes are evaluated using quantitative indicators of units produced from this process. For example, the Cpy process capability index is usually unknown and therefore estimated based on a sample drawn from the requested process. In this paper, Cpy process capability index estimates were generated using two iterative methods and a Bayesian method of estimation based on stepwise controlled type II data from the Pareto model. In iterative methods, besides the traditional probability-based estimation, there are other competitive methods, known as bootstrap, which are alternative methods to the common probability method, especially in small samples. In the Bayesian method, we have applied the Gibbs sampling procedure with the help of the significant sampling technique. Moreover, the approximate and highest confidence intervals for the posterior intensity of Cpy were also obtained. Massive simulation studies have been performed to evaluate the behavior of Cpy. Ultimately, application to real-life data is seen to demonstrate the proposed methodology and its applicability.

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Classical and Bayesian Inference of the Inverse Nakagami Distribution Based on Progressive Type-II Censored Samples

Cited by 3 publications

References 26 publications

A Three Parameter Power Nakagami Distribution: Properties and Application on the Tax Revenue Data

A Three Parameter Power Nakagami Distribution: Properties and Application on the Tax Revenue Data

Reliability evaluation for Weibull distribution with heavily Type II censored data

The Process Capability Index of Pareto Model under Progressive Type-II Censoring: Various Bayesian and Bootstrap Algorithms for Asymmetric Data

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