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>

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 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 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.  

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 Two-Parameter Burr-Hatke Distribution: Properties and Bayesian and Non-Bayesian Inference with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Ahmed Z. Afify ◽  
Hassan M. Aljohani ◽  
Abdulaziz S. Alghamdi ◽  
Ahmed M. Gemeay ◽  
Abdullah M. Sarg
Keyword(s):  
Real Life ◽  
Estimation Methods ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Bayesian Techniques ◽  
Bathtub Shape ◽  
Mathematical Properties ◽  
Squared Error ◽  
And Behavior ◽  
Two Parameter

This article introduces a two-parameter flexible extension of the Burr-Hatke distribution using the inverse-power transformation. The failure rate of the new distribution can be an increasing shape, a decreasing shape, or an upside-down bathtub shape. Some of its mathematical properties are calculated. Ten estimation methods, including classical and Bayesian techniques, are discussed to estimate the model parameters. The Bayes estimators for the unknown parameters, based on the squared error, general entropy, and linear exponential loss functions, are provided. The ranking and behavior of these methods are assessed by simulation results with their partial and overall ranks. Finally, the flexibility of the proposed distribution is illustrated empirically using two real-life datasets. The analyzed data shows that the introduced distribution provides a superior fit than some important competing distributions such as the Weibull, Fréchet, gamma, exponential, inverse log-logistic, inverse weighted Lindley, inverse Pareto, inverse Nakagami-M, and Burr-Hatke distributions.

scholarly journals The four-parameter Fréchet distribution: Properties and applications

2020 ◽  
pp. 249-264
Author(s):  
Mohamed Hamed ◽  
Fahad Aldossary ◽  
Ahmed Z. Afify
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Model Parameters ◽  
Fréchet Distribution ◽  
Mathematical Properties ◽  
Modeling Data ◽  
Frechet Distribution

In this article, we propose a new four-parameter Fréchet distribution called the odd Lomax Fréchet distribution. The new model can be expressed as a linear mixture of Fréchet densities. We provide some of its mathematical properties. The estimation of the model parameters is performed by the maximum likelihood method. We illustrate the good performance of the maximum likelihood estimates via a detailed numerical simulation study. The importance and usefulness of the proposed distribution for modeling data are illustrated using two real data applications.

New Acceptance Sampling Plans Based on Percentiles for Exponentiated Fréchet Distribution

2016 ◽  
Vol 31 (1) ◽  
Author(s):  
Gadde Srinivasa Rao ◽  
Kanaparthi Rosaiah ◽  
Mothukuri Sridhar Babu ◽  
Devireddy Charanaudaya Sivakumar
Keyword(s):  
Operating Characteristic ◽  
Real Data ◽  
Acceptance Sampling ◽  
Producer’S Risk ◽  
Data Set ◽  
Sampling Plans ◽  
Fréchet Distribution ◽  
Acceptance Sampling Plans ◽  
Characteristic Values ◽  
Frechet Distribution

AbstractIn this article, acceptance sampling plans are developed for the exponentiated Fréchet distribution based on percentiles when the life test is truncated at a pre-specified time. The minimum sample size necessary to ensure the specified life percentile is obtained under a given customer's risk and producer's risk simultaneously. The operating characteristic values of the sampling plans are presented. One example with real data set is also given as an illustration.

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