scholarly journals Inference for the Exponential Distribution under Generalized Progressively Hybrid Censored Data from Partially Accelerated Life Tests with a Time Transformation Function

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1510
Author(s):  
Alaa H. Abdel-Hamid ◽  
Atef F. Hashem
Keyword(s):  
Exponential Distribution ◽  
Failure Rate ◽  
Censored Data ◽  
Sufficient Conditions ◽  
Transformation Function ◽  
Point Estimation ◽  
Estimation Methods ◽  
Time Transformation ◽  
Monte Carlo Simulation Study ◽  
Accelerated Life

In this article, the tampered failure rate model is used in partially accelerated life testing. A non-decreasing time function, often called a ‘‘time transformation function", is proposed to tamper the failure rate under design conditions. Different types of the proposed function, which have sufficient conditions in order to be accelerating functions, are investigated. A baseline failure rate of the exponential distribution is considered. Some point estimation methods, as well as approximate confidence intervals, for the parameters involved are discussed based on generalized progressively hybrid censored data. The determination of the optimal stress change time is discussed under two different criteria of optimality. A real dataset is employed to explain the theoretical outcomes discussed in this article. Finally, a Monte Carlo simulation study is carried out to examine the performance of the estimation methods and the optimality criteria.

scholarly journals Robust Estimation methods of Generalized Exponential Distribution with Outliers

2020 ◽  
pp. 545-559
Author(s):  
Hisham Mohamed Almongy ◽  
Ehab M. Almetwally
Keyword(s):  
Robust Estimation ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Point Estimation ◽  
Least Square ◽  
Estimation Methods ◽  
Monte Carlo Simulation Study ◽  
Least Absolute Deviations ◽  
Complete Dataset ◽  
M Estimation

This paper discussed robust estimation for point estimation of the shape and scale parameters for generalized exponential (GE) distribution using a complete dataset in the presence of various percentages of outliers. In the case of outliers, it is known that classical methods such as maximum likelihood estimation (MLE), least square (LS) and maximum product spacing (MPS) in case of outliers cannot reach the best estimator. To confirm this fact, these classical methods were applied to the data of this study and compared with non-classical estimation methods. The non-classical (Robust) methods such as least absolute deviations (LAD), and M-estimation (using M. Huber (MH) weight and M. Bisquare (MB) weight) had been introduced to obtain the best estimation method for the parameters of the GE distribution. The comparison was done numerically by using the Monte Carlo simulation study. The two real datasets application confirmed that the M-estimation method is very much suitable for estimating the GE parameters. We concluded that the M-estimation method using Huber object function is a suitable estimation method in estimating the parameters of the GE distribution for a complete dataset in the presence of various percentages of outliers.

scholarly journals Inferences for Exponentiated Gamma Constant-Stress Partially Accelerated Life Test Model Based on Generalized Type-I Hybrid Censored Data

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Abdalla Rabie ◽  
Abd-EL-Baset A. Ahmad ◽  
Thierno Souleymane Barry ◽  
Hassan M. Aljohani ◽  
Nada M. Alfaer ◽  
...  
Keyword(s):  
Censored Data ◽  
Constant Stress ◽  
Accelerated Life Test ◽  
Estimation Methods ◽  
Type I ◽  
Test Model ◽  
Life Test ◽  
Bayesian Estimates ◽  
Accelerated Life ◽  
Generalized Type

In this paper, the exponentiated gamma distribution (EGD) with generalized Type-I hybrid censored data under constant-stress partially accelerated life test (CSPALT) model is considered. The Bayesian and E-Bayesian estimation methods, as well as the maximum likelihood estimation method, are discussed for the parameter of the distribution and the acceleration factor. The E-Bayesian and Bayesian estimates are derived by using the squared error loss (SEL) and the LINEX loss functions. The MCMC method is applied for deriving the Bayesian and then E-Bayesian estimates. Moreover, a real data set is given for the illustrative purpose. After all, an evaluation is performed for the results of the proposed methods.

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.

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