Estimation of the Unknown Parameters for the Compound Rayleigh Distribution Based on Progressive First-Failure-Censored Sampling

Abushal, Tahani A.

doi:10.4236/ojs.2011.13020

Cited by 12 publications

(4 citation statements)

References 29 publications

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“…Observed Probability Dataset-II This real dataset comprises a subset extracted from the findings presented by Tahani, 2011 20 . It delineates the survival duration, measured in years, for a cohort of patients subjected to chemotherapy.…”

Section: Pexpmentioning

confidence: 99%

A New Exponential Family of Distributions with Applications to Engineering and Medical Data

Sapkota,

Bam,

Kumar

2024

Preprint

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This research is centered on exploring a mathematically tractable and versatile family of probability distributions, specifically focusing on one family member. We have used the exponential distribution as a base distribution to create a novel distribution, which we have aptly named the "new odd-type-exponential distribution." In this paper, we provide an overview of the essential characteristics inherent to this innovative distribution. This model showcases a variety of hazard functions, including the reverse-j, decreasing and constant, increasing and constant, and S-shaped shapes. The estimation of the distribution’s parameters is conducted through both classical and Bayesian methods. We validate the accuracy of the classical estimation procedure through simulation studies. These simulations demonstrate a reduction in biases and mean square errors as sample sizes increase, even for smaller samples. To showcase the practicality of the proposed distribution, we apply it to two sets of real-world data, employing both classical and Bayesian approaches. We evaluate the performance of our suggested distribution model using various model selection criteria and goodness-of-fit test statistics. Empirical evidence from these evaluations confirms that our proposed model surpasses some existing models in the literature. Further, the suggested model was analyzed under the Bayesian approach using the Hamiltonian Monte Carlo method. Its predicting capability was also explored and it can predict the data consistently.

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Section: Pexpmentioning

confidence: 99%

A New Exponential Family of Distributions with Applications to Engineering and Medical Data

Sapkota,

Bam,

Kumar

2024

Preprint

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“…For this reason, Wu and Kuş [8] introduced life testing, which combines first-failure censoring with progressive type-II censoring, namely as a progressive first-failure censoring (PFFC) scheme. Several authors have discussed inference under a PFFC scheme for different lifetime distributions; see, for example, Haj et al [9], Abushal [10], Soliman et al [11,12], Mahmoud et al [13], Ahmed [14], Xie and Gui [15] and Shi and Shi [16]. This censoring scheme has advantages in terms of reducing test time in which more items are used but only m of n × k items are failures.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Inferential Approaches and Bootstrap for the Reliability and Hazard Rate Functions under Progressive First-Failure Censoring for Coronavirus Data from Asymmetric Model

et al. 2022

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This paper deals with the estimation of the parameters for asymmetric distribution and some lifetime indices such as reliability and hazard rate functions based on progressive first-failure censoring. Maximum likelihood, bootstrap and Bayesian approaches of the distribution parameters and reliability characteristics are investigated. Furthermore, the approximate confidence intervals and highest posterior density credible intervals of the parameters are constructed based on the asymptotic distribution of the maximum likelihood estimators and Markov chain Monte Carlo technique, respectively. In addition, the delta method is implemented to obtain the variances of the reliability and hazard functions. Moreover, we apply two methods of bootstrap to construct the confidence intervals. The Bayes inference based on the squared error and LINEX loss functions is obtained. Extensive simulation studies are conducted to evaluate the behavior of the proposed methods. Finally, a real data set of the COVID-19 mortality rate is analyzed to illustrate the estimation methods developed here.

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“…In the last couple of decades, statisticians have much attention to study this distribution. Abushal [1] applied the maximum likelihood and Bayes approaches to estimate parameters, reliability and hazard functions of the CR distribution based on progressive first-failure censoed data. Shajaee et al [2] obtained the empirical Bayes estimates for parameter and reliability function associated with the CR distribution under record data.…”

Section: Introductionmentioning

confidence: 99%

The beta compound Rayleigh distribution : Properties and applications

Reyad

Ibrahim

2017

IJASP

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In this paper, we introduce a new four parameter continuous model, called the beta compound Rayleigh (BCR) distribution that extends the compound Rayleigh distribution. Basic properties of the proposed distribution such as; mean, variance, coefficient of variation, raw and incomplete moments, skewness, kurtosis, moment and probability generating functions, reliability analysis, Lorenz, Bonferroni and Zenga curves, Rényi of entropy, order statistics and record statistics are investigated. We obtain the maximum likelihood estimates and the observed information matrix for the model parameters. Two real data sets are used to illustrate the usefulness of the new model.

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Estimation of the Unknown Parameters for the Compound Rayleigh Distribution Based on Progressive First-Failure-Censored Sampling

Cited by 12 publications

References 29 publications

A New Exponential Family of Distributions with Applications to Engineering and Medical Data

A New Exponential Family of Distributions with Applications to Engineering and Medical Data

Bayesian Inferential Approaches and Bootstrap for the Reliability and Hazard Rate Functions under Progressive First-Failure Censoring for Coronavirus Data from Asymmetric Model

The beta compound Rayleigh distribution : Properties and applications

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