scholarly journals Inference on a New Lifetime Distribution under Progressive Type II Censoring for a Parallel-Series Structure

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Atef F. Hashem ◽  
Salem A. Alyami
Keyword(s):  
Least Squares ◽  
Failure Time ◽  
Weighted Least Squares ◽  
Lifetime Distribution ◽  
Estimation Methods ◽  
Type Ii ◽  
Progressive Type ◽  
Type Ii Censored Data ◽  
Extensive Numerical Simulation ◽  
Parallel Series

A new lifetime distribution, called exponential doubly Poisson distribution, is proposed with decreasing, increasing, and upside-down bathtub-shaped hazard rates. One of the reasons for introducing the new distribution is that it can describe the failure time of a system connected in the form of a parallel-series structure. Some properties of the proposed distribution are addressed. Four methods of estimation for the involved parameters are considered based on progressively type II censored data. These methods are maximum likelihood, moments, least squares, and weighted least squares estimations. Through an extensive numerical simulation, the performance of the estimation methods is compared based on the average of mean squared errors and the average of absolute relative biases of the estimates. Two real datasets are used to compare the proposed distribution with some other well-known distributions. The comparison indicates that the proposed distribution is better than the other distributions to match the data provided.

scholarly journals Bayesian Estimation Based on Rayleigh Progressive Type II Censored Data with Binomial Removals

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Reza Azimi ◽  
Farhad Yaghmaei
Keyword(s):  
Censored Data ◽  
Failure Time ◽  
Simulation Method ◽  
Reliability Function ◽  
Rayleigh Distribution ◽  
Type Ii ◽  
Monte Carlo Simulation Method ◽  
Bayesian Procedures ◽  
Progressive Type ◽  
Type Ii Censored Data

This study considers the estimation problem for the parameter and reliability function of Rayleigh distribution under progressive type II censoring with random removals, where the number of units removed at each failure time has a binomial distribution. We use the maximum likelihood and Bayesian procedures to obtain the estimators of parameter and reliability function of Rayleigh distribution. We also construct the confidence intervals for the parameter of Rayleigh distribution. Monte Carlo simulation method is used to generate a progressive type II censored data with binomial removals from Rayleigh distribution, and then these data are used to compute the point and interval estimations of the parameter and compare both the methods used with different random schemes.

scholarly journals Parameter Estimation Based on the Frèchet Progressive Type II Censored Data with Binomial Removals

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
Mohamed Mubarak
Keyword(s):  
Censored Data ◽  
Time Distribution ◽  
Maximum Likelihood Method ◽  
Failure Time ◽  
Likelihood Method ◽  
Type Ii ◽  
Failure Time Distribution ◽  
Sampling Distributions ◽  
Progressive Type ◽  
Type Ii Censored Data

This paper considers the estimation problem for the Frèchet distribution under progressive Type II censoring with random removals, where the number of units removed at each failure time has a binomial distribution. We use the maximum likelihood method to obtain the estimators of parameters and derive the sampling distributions of the estimators, and we also construct the confidence intervals for the parameters and percentile of the failure time distribution.

scholarly journals Statistical Analysis of a Lifetime Distribution with a Bathtub-Shaped Failure Rate Function under Adaptive Progressive Type-II Censoring

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 670 ◽  
Author(s):  
Siyi Chen ◽  
Wenhao Gui
Keyword(s):  
Failure Rate ◽  
Estimation Method ◽  
Rate Function ◽  
Lifetime Distribution ◽  
Estimation Methods ◽  
Type Ii ◽  
Failure Rate Function ◽  
Data Set ◽  
Progressive Type ◽  
Two Parameters

In this paper, the estimation problem of two parameters of a lifetime distribution with a bathtub-shaped failure rate function based on adaptive progressive type-II censored data is discussed. This censoring scheme allows the experiment to be more efficient in the use of time and cost while ensuring the statistical inference efficiency based on the experimental results. Maximum likelihood estimators are proposed and the approximate confidence intervals for two parameters are computed using the asymptotic normality. Lindley approximation and Gibbs sampling are used to obtain Bayes point estimates and the latter is also used to generate Bayes two-sided credible intervals. Finally, the performance of various estimation methods is evaluated through simulation experiments, and the proposed estimation method is illustrated through the analysis of a real data set.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

scholarly journals A New Inverted Topp-Leone Distribution: Applications to the COVID-19 Mortality Rate in Two Different Countries

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 25 ◽  
Author(s):  
Ehab Almetwally ◽  
Randa Alharbi ◽  
Dalia Alnagar ◽  
Eslam Hafez
Keyword(s):  
Statistical Model ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Likelihood Estimation ◽  
Linear Representation ◽  
Rate Function ◽  
Estimation Methods ◽  
Unknown Parameters ◽  
Least Squares Estimators ◽  
New Distribution

This paper aims to find a statistical model for the COVID-19 spread in the United Kingdom and Canada. We used an efficient and superior model for fitting the COVID 19 mortality rates in these countries by specifying an optimal statistical model. A new lifetime distribution with two-parameter is introduced by a combination of inverted Topp-Leone distribution and modified Kies family to produce the modified Kies inverted Topp-Leone (MKITL) distribution, which covers a lot of application that both the traditional inverted Topp-Leone and the modified Kies provide poor fitting for them. This new distribution has many valuable properties as simple linear representation, hazard rate function, and moment function. We made several methods of estimations as maximum likelihood estimation, least squares estimators, weighted least-squares estimators, maximum product spacing, Crame´r-von Mises estimators, and Anderson-Darling estimators methods are applied to estimate the unknown parameters of MKITL distribution. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. also, we applied different data sets to the new distribution to assess its performance in modeling data.

scholarly journals Estimating the Parameters of the Exponential-Geometric distribution based on progressively type-II censored data

2018 ◽  
Vol 6 (1) ◽  
pp. 37
Author(s):  
Aisha Fayomi ◽  
Hamdah Al-Shammari
Keyword(s):  
Censored Data ◽  
Geometric Distribution ◽  
Asymptotic Variance ◽  
Parameters Estimation ◽  
Type Ii ◽  
Progressive Type ◽  
The Em Algorithm ◽  
Asymptotic Confidence Intervals ◽  
Distribution Parameters ◽  
Type Ii Censored Data

This paper deals with the problem of parameters estimation of the Exponential-Geometric (EG) distribution based on progressive type-II censored data. It turns out that the maximum likelihood estimators for the distribution parameters have no closed forms, therefore the EM algorithm are alternatively used. The asymptotic variance of the MLEs of the targeted parameters under progressive type-II censoring is computed along with the asymptotic confidence intervals. Finally, a simple numerical example is given to illustrate the obtained results.

scholarly journals Estimation of Multicomponent Reliability Based on Progressively Type II Censored Data from Unit Weibull Distribution

2021 ◽  
Vol 20 ◽  
pp. 288-299
Author(s):  
Refah Mohammed Alotaibi ◽  
Yogesh Mani Tripathi ◽  
Sanku Dey ◽  
Hoda Ragab Rezk
Keyword(s):  
Information Matrix ◽  
Credible Interval ◽  
Estimation Methods ◽  
Type Ii ◽  
Parametric Function ◽  
Data Set ◽  
Common Parameter ◽  
Bayesian Procedures ◽  
Mh Algorithm ◽  
Type Ii Censored Data

In this paper, inference upon stress-strength reliability is considered for unit-Weibull distributions with a common parameter under the assumption that data are observed using progressive type II censoring. We obtain di_erent estimators of system reliability using classical and Bayesian procedures. Asymptotic interval is constructed based on Fisher information matrix. Besides, boot-p and boot-t intervals are also obtained. We evaluate Bayes estimates using Lindley's technique and Metropolis-Hastings (MH) algorithm. The Bayes credible interval is evaluated using MH method. An unbiased estimator of this parametric function is also obtained under know common parameter case. Numerical simulations are performed to compare estimation methods. Finally, a data set is studied for illustration purposes.

Jaya algorithm in estimation of P[X > Y] for two parameter Weibull distribution

2022 ◽  
Vol 7 (2) ◽  
pp. 2820-2839
Author(s):  
Saurabh L. Raikar ◽  
◽  
Dr. Rajesh S. Prabhu Gaonkar ◽  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Real Life ◽  
Likelihood Estimation ◽  
Estimation Methods ◽  
Jaya Algorithm ◽  
Two Parameter

<abstract> <p>Jaya algorithm is a highly effective recent metaheuristic technique. This article presents a simple, precise, and faster method to estimate stress strength reliability for a two-parameter, Weibull distribution with common scale parameters but different shape parameters. The three most widely used estimation methods, namely the maximum likelihood estimation, least squares, and weighted least squares have been used, and their comparative analysis in estimating reliability has been presented. The simulation studies are carried out with different parameters and sample sizes to validate the proposed methodology. The technique is also applied to real-life data to demonstrate its implementation. The results show that the proposed methodology's reliability estimates are close to the actual values and proceeds closer as the sample size increases for all estimation methods. Jaya algorithm with maximum likelihood estimation outperforms the other methods regarding the bias and mean squared error.</p> </abstract>

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