Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study

El-Raheem, A. M. Abd; Abu‐Moussa, Mahmoud H.; El-Din, M. M. Mohie; Hussam, Eslam

doi:10.3390/math8101786

Cited by 12 publications

(5 citation statements)

References 45 publications

(46 reference statements)

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“…where in Type-I censoring ℘ � T and in Type-II censoring ℘ � x r: n . For more information, see the work of Balakrishnan [21], El-Sherpieny et al [22], Hassan and Abd-Allah [23], Abd El-Raheem et al [24], Hafez et al [25], and Hassan and Mohamed [26].…”

Section: Mle Based On Censoredmentioning

confidence: 99%

Marshall–Olkin Alpha Power Weibull Distribution: Different Methods of Estimation Based on Type‐I and Type‐II Censoring

et al. 2021

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This paper introduces the new novel four-parameter Weibull distribution named as the Marshall–Olkin alpha power Weibull (MOAPW) distribution. Some statistical properties of the distribution are examined. Based on Type-I censored and Type-II censored samples, maximum likelihood estimation (MLE), maximum product spacing (MPS), and Bayesian estimation for the MOAPW distribution parameters are discussed. Numerical analysis using real data sets and Monte Carlo simulation are accomplished to compare various estimation methods. This novel model’s supremacy upon some famous distributions is explained using two real data sets and it is shown that the MOAPW model can achieve better fits than other competitive distributions.

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Section: Mle Based On Censoredmentioning

confidence: 99%

Marshall–Olkin Alpha Power Weibull Distribution: Different Methods of Estimation Based on Type‐I and Type‐II Censoring

et al. 2021

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“…This method is formulated by making a mixture from two or three distributions to formulate a new superior that can model all the data that the traditional ones failed to model. Many authors worked on the Pareto distribution; see [ 1 ], where the authors worked on the Pareto-IV distribution and estimated its parameters under accelerated life test, when the items were under type-II censored sample. Also, as an example for authors that worked on the Fréchet distribution, see [ 2 ], where the authors estimated the parameters of the Fréchet distribution under type -II censoring scheme using classical and Bayesian estimation methods.…”

Section: Introductionmentioning

confidence: 99%

“…Fréchet and Weibull distributions are the most important models for extreme values, and many statisticians have studied these models in many published papers according to their importance in many fields such as earthquakes, floods, engineering, physics, quality control, and medicine. For more information about Fréchet and Weibull distributions, see [ 1 , 2 , 9 , 10 ].…”

Section: Introductionmentioning

confidence: 99%

A Flexible Extension of Pareto Distribution: Properties and Applications

Alshanbari

El-Bagoury

Gemeay

et al. 2021

Computational Intelligence and Neuroscience

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This paper introduced a relatively new mixture distribution that results from a mixture of Fréchet–Weibull and Pareto distributions. Some properties of the new statistical model were derived, such as moments with their related measures, moment generating function, mean residual life function, and mean deviation. Furthermore , different estimation methods were introduced for determining the unknown parameters of the proposed model. Finally, we introduced three real data sets which were applied to our distribution and compared them with other well-known statistical competitive models to show the superiority of our model for fitting the three real data sets, and we can clearly see that our distribution outperforms its competitors. Also, to verify our results, we carried out the existence and uniqueness test to the log-likelihood to determine whether the roots are global maximum or not.

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“…, R m . For more extensive reading about this subject, see the works done by alBalakrishnan [5], Fathi [6], and Abd El-Raheem [7] .…”

Section: Introductionmentioning

confidence: 99%

Study on Lindley Distribution Accelerated Life Tests: Application and Numerical Simulation

Hussam¹,

Riad

Mubarak

et al. 2020

Symmetry

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Saving money and time are very important in any research project, so we must find a way to decrease the time of the experiment. This method is called the accelerated life tests (ALT) under censored samples, which is a very efficient method to reduce time, which leads to a decrease in the cost of the experiment. This research project includes inference on Lindley distribution in a simple step-stress ALT for the Type II progressive censored sample. The paper contains two major sections, which are a simulation study and a real-data application on the experimental design of an industry experiment on lamps. These sections are used to conduct results on the study of the distribution. The simulation was done using Mathematica 11 program. To use real data in the censored sample, we fitted them to be compatible with the Lindley distribution using the modified Kolmogorov–Smirnov (KS) goodness of fit test for progressive Type II censored data. We used the tampered random variable (TRV) acceleration model to generate early failures of items under stress. We also found the values of the distribution parameter and the accelerating factor using the maximum likelihood estimation of (MLEs) and Bayes estimates (BEs) using symmetric loss function for both simulated data and real data. Next, we estimated the upper and lower bounds of the parameters using three methods, namely approximate confidence intervals (CIs), Bootstrap CIs, and credible CIs, for both parameters of the distribution, ψ and ζ. Finally, we found the value of the parameter for the real data set under normal use conditions and stress conditions and graphed the reliability functions under normal and accelerated use.

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Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study

Cited by 12 publications

References 45 publications

Marshall–Olkin Alpha Power Weibull Distribution: Different Methods of Estimation Based on Type‐I and Type‐II Censoring

Marshall–Olkin Alpha Power Weibull Distribution: Different Methods of Estimation Based on Type‐I and Type‐II Censoring

A Flexible Extension of Pareto Distribution: Properties and Applications

Study on Lindley Distribution Accelerated Life Tests: Application and Numerical Simulation

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