scholarly journals Statistical Inference under Censored Data for the New Exponential-X Fréchet Distribution: Simulation and Application to Leukemia Data

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Omar Alzeley ◽  
Ehab M. Almetwally ◽  
Ahmed M. Gemeay ◽  
Huda M. Alshanbari ◽  
E. H. Hafez ◽  
...  
Keyword(s):  
Censored Data ◽  
Real Life ◽  
Estimation Methods ◽  
Type I ◽  
Hazard Functions ◽  
Type I Censoring ◽  
Fréchet Distribution ◽  
Statistical Measures ◽  
Frechet Distribution ◽  
Leukemia Data

In reliability studies, the best fitting of lifetime models leads to accurate estimates and predictions, especially when these models have nonmonotone hazard functions. For this purpose, the new Exponential-X Fréchet (NEXF) distribution that belongs to the new exponential-X (NEX) family of distributions is proposed to be a superior fitting model for some reliability models with nonmonotone hazard functions and beat the competitive distribution such as the exponential distribution and Frechet distribution with two and three parameters. So, we concentrated our effort to introduce a new novel model. Throughout this research, we have studied the properties of its statistical measures of the NEXF distribution. The process of parameter estimation has been studied under a complete sample and Type-I censoring scheme. The numerical simulation is detailed to asses the proposed techniques of estimation. Finally, a Type-I censoring real-life application on leukaemia patient’s survival with a new treatment has been studied to illustrate the estimation methods, which are well fitted by the NEXF distribution among all its competitors. We used for the fitting test the novel modified Kolmogorov–Smirnov (KS) algorithm for fitting Type-I censored data.

scholarly journals A New Three-parameter Xgamma Fréchet Distribution with Different Methods of Estimation and Applications

2021 ◽  
pp. 291-308
Author(s):  
Mohamed Ibrahim Mohamed ◽  
Laba Handique ◽  
Subrata Chakraborty ◽  
Nadeem Shafique Butt ◽  
Haitham M. Yousof
Keyword(s):  
Real Life ◽  
Estimation Methods ◽  
Data Sets ◽  
Clear Preference ◽  
Life Data ◽  
Fréchet Distribution ◽  
Real Life Data ◽  
Proposed Model ◽  
Frechet Distribution

In this article an attempt is made to introduce a new extension of the Fréchet model called the Xgamma Fréchet model. Some of its properties are derived. The estimation of the parameters via different estimation methods are discussed. The performances of the proposed estimation methods are investigated through simulations as well as real life data sets. The potentiality of the proposed model is established through modelling of two real life data sets. The results have shown clear preference for the proposed model compared to several know competing ones.

scholarly journals Estimation of Constant Stress Partially Accelerated Life Test for Fréchet Distribution with Type-I Censoring

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Abdullah Ali H. Ahmadini ◽  
Wali Khan Mashwani ◽  
Rehman Ahmad Khan Sherwani ◽  
Shokrya S. Alshqaq ◽  
Farrukh Jamal ◽  
...  
Keyword(s):  
Constant Stress ◽  
Accelerated Life Test ◽  
Likelihood Method ◽  
Type I ◽  
Type I Censoring ◽  
Fréchet Distribution ◽  
Accelerated Life Tests ◽  
Accelerated Life ◽  
Life Tests ◽  
Frechet Distribution

Modern reliability engineering accelerated life tests (ALT) and partially accelerated life tests (PALT) are widely used to obtain the timely information on the reliability of objects, products, elements, and materials as well as to save time and cost. The ALTs or PALTs are useful in determining the failed manners of the items at routine conditions by using the information of the data generated from the experiment. PALT is the most sensible method to be used for estimating both ordinary and ALTs. In this research, constant stress PALT design for the Fréchet distribution with type-I censoring has been investigated due to a wide applicability of the Fréchet distribution in engineering problems especially in hydrology. The distribution parameters and acceleration factor are obtained by using the maximum likelihood method. Fisher's information matrix is used to develop the asymptotic confidence interval estimates of the model parameters. A simulation study is conducted to illustrate the statistical properties of the parameters and the confidence intervals by using the R software. The results indicated that the constant stress PALT plan works well. Moreover, a numerical example is given to exemplify the performance of the proposed methods.

Properties and methods of estimation for a bivariate exponentiated Fréchet distribution

2020 ◽  
Vol 70 (5) ◽  
pp. 1211-1230
Author(s):  
Abdus Saboor ◽  
Hassan S. Bakouch ◽  
Fernando A. Moala ◽  
Sheraz Hussain
Keyword(s):  
Maximum Likelihood ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Superior Performance ◽  
Estimation Methods ◽  
Conditional Probability Density ◽  
Data Set ◽  
Fréchet Distribution ◽  
Frechet Distribution

AbstractIn this paper, a bivariate extension of exponentiated Fréchet distribution is introduced, namely a bivariate exponentiated Fréchet (BvEF) distribution whose marginals are univariate exponentiated Fréchet distribution. Several properties of the proposed distribution are discussed, such as the joint survival function, joint probability density function, marginal probability density function, conditional probability density function, moments, marginal and bivariate moment generating functions. Moreover, the proposed distribution is obtained by the Marshall-Olkin survival copula. Estimation of the parameters is investigated by the maximum likelihood with the observed information matrix. In addition to the maximum likelihood estimation method, we consider the Bayesian inference and least square estimation and compare these three methodologies for the BvEF. A simulation study is carried out to compare the performance of the estimators by the presented estimation methods. The proposed bivariate distribution with other related bivariate distributions are fitted to a real-life paired data set. It is shown that, the BvEF distribution has a superior performance among the compared distributions using several tests of goodness–of–fit.

scholarly journals The extended Weibull–Fréchet distribution: properties, inference, and applications in medicine and engineering

2021 ◽  
Vol 7 (1) ◽  
pp. 225-246
Author(s):  
Ekramy A. Hussein ◽  
◽  
Hassan M. Aljohani ◽  
Ahmed Z. Afify ◽  
◽  
...  
Keyword(s):  
Density Function ◽  
Failure Rate ◽  
Real Life ◽  
Fréchet Distribution ◽  
Bathtub Shape ◽  
Mathematical Properties ◽  
Engineering Sciences ◽  
Asymmetric Shape ◽  
Frechet Distribution ◽  
Symmetric Shape

<abstract><p>In this paper, a flexible version of the Fréchet distribution called the extended Weibull–Fréchet (EWFr) distribution is proposed. Its failure rate has a decreasing shape, an increasing shape, and an upside-down bathtub shape. Its density function can be a symmetric shape, an asymmetric shape, a reversed-J shape and J shape. Some mathematical properties of the EWFr distribution are explored. The EWFr parameters are estimated using several frequentist estimation approaches. The performance of these methods is addressed using detailed simulations. Furthermore, the best approach for estimating the EWFr parameters is determined based on partial and overall ranks. Finally, the performance of the EWFr distribution is studied using two real-life datasets from the medicine and engineering sciences. The EWFr distribution provides a superior fit over other competing Fréchet distributions such as the exponentiated-Fréchet, beta-Fréchet, Lomax–Fréchet, and Kumaraswamy Marshall–Olkin Fréchet.</p></abstract>

scholarly journals The Generalized Gamma Shared Frailty Model under Different Baseline Distributions

2019 ◽  
Vol 4 (1) ◽  
pp. 219-231
Author(s):  
Sukhmani Sidhu ◽  
Kanchan Jain ◽  
Suresh K. Sharma Sharma
Keyword(s):  
Survival Data ◽  
Bayes Factor ◽  
Real Life ◽  
Frailty Model ◽  
Information Criteria ◽  
Estimation Methods ◽  
Hazard Functions ◽  
Generalized Gamma ◽  
Shared Frailty ◽  
Event Times

In the analysis of clustered survival data, shared frailty models are often used when observations in the same group share common unknown risk factors or frailty. There is dependence in the event times belonging to the same group, while event times from different groups are conditionally independent given their covariates. In such models, the known effect on survival time is described using the baseline distribution and regression coefficients while the unknown effect is described through a frailty distribution. In this paper, the Gompertz, log-logistic, and generalized exponential distributions are studied as baseline distributions, under a shared frailty effect described by the generalized gamma distribution. Their hazard functions have been compared and their applicability under different settings and performance with generalized gamma frailty has been explored. These models are fitted to three real life datasets using Bayesian estimation methods and compared using the Bayesian Information Criteria (AIC, BIC, and DIC) and the Bayes Factor.

scholarly journals MCMC Method for Exponentiated Lomax Distribution based on Accelerated Life Testing with Type I Censoring

2021 ◽  
Vol 20 ◽  
pp. 319-334
Author(s):  
Refah Alotaibi ◽  
H. Rezk ◽  
Sanku Dey
Keyword(s):  
Accelerated Life Testing ◽  
Constant Stress ◽  
Estimation Methods ◽  
Model Parameters ◽  
Type I ◽  
Life Testing ◽  
Informative Priors ◽  
Lomax Distribution ◽  
Type I Censoring ◽  
Accelerated Life

Accelerated Life Testing (ALT) is an effective technique which has been used in different fields to obtain more failures in a shorter period of time. It is more economical than traditional reliability testing. In this article, we propose Bayesian inference approach for planning optimal constant stress ALT with Type I censoring. The lifetime of a test unit follows an exponentiated Lomax distribution. Bayes point estimates of the model parameters and credible intervals under uniform and log-normal priors are obtained. Besides, optimum test plan based on constant stress ALT under Type I censoring is developed by minimizing the pre-posterior variance of a specified low percentile of the lifetime distribution at use condition. Gibbs sampling method is used to find the optimal stress with changing time. The performance of the estimation methods is demonstrated for both simulated and real data sets. Results indicate that both the priors and the sample size affect the optimal Bayesian plans. Further, informative priors provide better results than non-informative priors.

scholarly journals Bayesian Analysis of a Shape Parameter of the Weibull-Frechet Distribution

2018 ◽  
pp. 1-19
Author(s):  
Terna Godfrey Ieren ◽  
Angela Unna Chukwu
Keyword(s):  
Loss Function ◽  
Shape Parameter ◽  
Real Life ◽  
Loss Functions ◽  
Quadratic Loss ◽  
Bayes Estimators ◽  
Informative Priors ◽  
Fréchet Distribution ◽  
Minimum Bayes Risk ◽  
Frechet Distribution

In this paper, we estimate a shape parameter of the Weibull-Frechet distribution by considering the Bayesian approach under two non-informative priors using three different loss functions. We derive the corresponding posterior distributions for the shape parameter of the Weibull-Frechet distribution assuming that the other three parameters are known. The Bayes estimators and associated posterior               risks have also been derived using the three different loss functions. The performance of the Bayes estimators are evaluated and compared using a comprehensive simulation study and a real life application to find out the combination of a loss function and a prior having the minimum Bayes risk and hence producing the best results. In conclusion, this study reveals that in order to estimate the parameter in question, we should use quadratic loss function under either of the two non-informative priors used in this study.  

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