scholarly journals A new inverse Weibull distribution: properties, classical and Bayesian estimation with applications

2021 ◽  
Vol 48 (3) ◽  
Author(s):  
Ahmed Z. Afify ◽  
◽  
Ahmed I. Shawky ◽  
Mazen Nassar ◽  
◽  
...  
Keyword(s):  
Weibull Distribution ◽  
Bayesian Estimation ◽  
Real Data ◽  
Estimation Methods ◽  
Data Sets ◽  
Exponential Distributions ◽  
Unknown Parameters ◽  
Large Samples ◽  
Mathematical Properties ◽  
Inverse Weibull Distribution

This article proposes a new extension of the inverse Weibull distribution called, logarithmic transformed inverse Weibull distribution which can provide better fits than some of its well-known extensions. The proposed distribution contains inverse Weibull, inverse Rayleigh, inverse exponential, logarithmic transformed inverse Rayleigh and logarithmic transformed inverse exponential distributions as special sub-models. Our main focus is to derive some of its mathematical properties along with the estimation of its unknown parameters using frequentist and Bayesian estimation methods. We compare the performances of the proposed estimators using extensive numerical simulations for both small and large samples. The importance and potentiality of this distribution is analyzed via two real data sets.

scholarly journals Extended Poisson Inverse Weibull Distribution: Theoretical and Computational Aspects

2019 ◽  
Vol 8 (2) ◽  
pp. 146
Author(s):  
Saeed Al-mualim
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Mathematical Properties ◽  
Inverse Weibull Distribution ◽  
Computational Aspects

A new extension of the Poisson Inverse Weibull distribution is derived and studied in details. Number of structural mathematical properties are derived. We used the well-known maximum likelihood method for estimating the model parameters. The new model is applied for modeling some real data sets to prove its importance and flexibility empirically.

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

2020 ◽  
Vol 70 (4) ◽  
pp. 953-978
Author(s):  
Mustafa Ç. Korkmaz ◽  
G. G. Hamedani
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Lorenz Curves ◽  
Proposed Model ◽  
New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

scholarly journals A New Family of Discrete Distributions with Mathematical Properties, Characterizations, Bayesian and Non-Bayesian Estimation Methods

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1648
Author(s):  
Mohamed Aboraya ◽  
Haitham M. Yousof ◽  
G.G. Hamedani ◽  
Mohamed Ibrahim
Keyword(s):  
Bayesian Estimation ◽  
Generating Function ◽  
Bayesian Methods ◽  
Probability Generating Function ◽  
Real Data ◽  
Discrete Distributions ◽  
Estimation Methods ◽  
Squared Error Loss Function ◽  
New Family ◽  
Mathematical Properties

In this work, we propose and study a new family of discrete distributions. Many useful mathematical properties, such as ordinary moments, moment generating function, cumulant generating function, probability generating function, central moment, and dispersion index are derived. Some special discrete versions are presented. A certain special case is discussed graphically and numerically. The hazard rate function of the new class can be “decreasing”, “upside down”, “increasing”, and “decreasing-constant-increasing (U-shape)”. Some useful characterization results based on the conditional expectation of certain function of the random variable and in terms of the hazard function are derived and presented. Bayesian and non-Bayesian methods of estimation are considered. The Bayesian estimation procedure under the squared error loss function is discussed. Markov chain Monte Carlo simulation studies for comparing non-Bayesian and Bayesian estimations are performed using the Gibbs sampler and Metropolis–Hastings algorithm. Four applications to real data sets are employed for comparing the Bayesian and non-Bayesian methods. The importance and flexibility of the new discrete class is illustrated by means of four real data applications.

scholarly journals Bayesian Estimation for Inverse Weibull Distribution Under Progressive Type-II Censored Data With Beta-Binomial Removals

2018 ◽  
Vol 47 (1) ◽  
pp. 77-94
Author(s):  
Pradeep Kumar Vishwakarma ◽  
Arun Kaushik ◽  
Aakriti Pandey ◽  
Umesh Singh ◽  
Sanjay Kumar Singh
Keyword(s):  
Weibull Distribution ◽  
Real Data ◽  
Estimation Procedure ◽  
Type Ii ◽  
Unknown Parameters ◽  
Data Set ◽  
Progressive Type ◽  
Inverse Weibull Distribution ◽  
Type Ii Censored Data ◽  
Censoring Scheme

This paper deals with the estimation procedure for inverse Weibull distribution under progressive type-II censored samples when removals follow Beta-binomial probability law. To estimate the unknown parameters, the maximum likelihood and Bayes estimators are obtained under progressive censoring scheme mentioned above. Bayes estimates are obtained using Markov chain Monte Carlo (MCMC) technique considering square error loss function and compared with the corresponding MLE's. Further, the expected total time on test is obtained under considered censoring scheme.  Finally, a real data set has been analysed to check the validity of the study.

scholarly journals Binomial-exponential 2 Distribution: Different Estimation Methods and Weather Applications

2017 ◽  
Vol 18 (2) ◽  
pp. 0233 ◽  
Author(s):  
Hassan S Bakouch ◽  
Sanku Dey ◽  
Pedro Luiz Ramos ◽  
Francisco Louzada
Keyword(s):  
Method Of Moments ◽  
Minimum Distance ◽  
Real Data ◽  
Ordinary Least Squares ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Anderson Darling ◽  
Von Mises ◽  
Modified Moments

In this paper, we have considered different estimation methods of the unknown parameters of a binomial-exponential 2 distribution. First, we briefly describe different frequentist approaches such as the method of moments, modified moments, ordinary least-squares estimation, weightedleast-squares estimation, percentile, maximum product of spacings, Cramer-von Mises type minimum distance, Anderson-Darling and Right-tail Anderson-Darling, and compare them using extensive numerical simulations. We apply our proposed methodology to three real data sets related to the total monthly rainfall during April, May and September at Sao Carlos, Brazil.

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

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Ehab M. Almetwally ◽  
Mohamed A. H. Sabry ◽  
Randa Alharbi ◽  
Dalia Alnagar ◽  
Sh. A. M. Mubarak ◽  
...  
Keyword(s):  
Weibull Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Methods ◽  
Data Sets ◽  
Type I ◽  
Alpha Power ◽  
Type Ii ◽  
Censored Samples ◽  
Distribution Parameters

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.

scholarly journals Bayesian and non-Bayesian estimation of four-parameter of bivariate discrete inverse Weibull distribution with applications to model failure times, football and biological data

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2511-2531 ◽  
Author(s):  
M.S. Eliwa ◽  
M. El-Morshedy
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Real Data ◽  
Discrete Analogue ◽  
Biological Data ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model ◽  
Inverse Weibull Distribution ◽  
Detailed Simulation

In this paper we have considered one model, namely the bivariate discrete inverse Weibull distribution, which has not been considered in the statistical literature yet. The proposed model is a discrete analogue of Marshall-Olkin inverse Weibull distribution. Some of its important statistical properties are studied. Maximum likelihood and Bayesian methods are used to estimate the model parameters. A detailed simulation study is carried out to examine the bias and mean square error of maximum likelihood and Bayesian estimators. Finally, three real data sets are analyzed to illustrate the importance of the proposedmodel.

scholarly journals On Progressive Censored Competing Risks Data: Real Data Application and Simulation Study

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1805
Author(s):  
Abd M. Abd El-Raheem ◽  
Mona Hosny ◽  
Mahmoud H. Abu-Moussa
Keyword(s):  
Competing Risks ◽  
Simulation Study ◽  
Expectation Maximization Algorithm ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Competing Risks Data ◽  
Competing Risk Models

Competing risks are frequently overlooked, and the event of interest is analyzed with conventional statistical techniques. In this article, we consider the analysis of bi-causes of failure in the context of competing risk models using the extension of the exponential distribution under progressive Type-II censoring. Maximum likelihood estimates for the unknown parameters via the expectation-maximization algorithm are obtained. Moreover, the Bayes estimates of the unknown parameters are approximated using Tierney-Kadane and MCMC techniques. Interval estimates using Bayesian and classical techniques are also considered. Two real data sets are investigated to illustrate the different estimation methods, and to compare the suggested model with Weibull distribution. Furthermore, the estimation methods are compared through a comprehensive simulation study.

scholarly journals Parameter Estimation and Applications of the Weibull Distribution for Strength Data of Glass Fiber

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Yuxuan Wu ◽  
Hanyang Xie ◽  
Jyun-You Chiang ◽  
Gang Peng ◽  
Yan Qin
Keyword(s):  
Parameter Estimation ◽  
Weibull Distribution ◽  
Glass Fiber ◽  
Fiber Strength ◽  
Estimation Method ◽  
Real Data ◽  
Estimation Methods ◽  
Data Sets ◽  
Strength Data ◽  
Parameter Estimation Method

Glass fiber is a good substitute for metal materials. However, in the process of manufacturing, it is necessary to carry out sampling inspection on its tensile strength to infer its quality. According to previous literatures, the strength data can be well fitted by the Weibull distribution, while the poor parameter estimation method cannot obtain reliable analysis results. Therefore, a new parameter estimation method is proposed. Based on the simulation results, it is found that the proposed parameter estimation method outperforms the other competitors to obtain reliable estimates of the Weibull parameters. Finally, the proposed parameter estimation method is applied to two real data sets of glass fiber strength for illustration. The results of data analysis show that our proposed parameter estimation method is more suitable for these data sets than other estimation methods.

scholarly journals A Flexible Extension of Pareto Distribution: Properties and Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Huda M. Alshanbari ◽  
Abd Al-Aziz Hosni El-Bagoury ◽  
Ahmed M. Gemeay ◽  
E. H. Hafez ◽  
Ahmed Sedky Eldeeb
Keyword(s):  
Residual Life ◽  
Mixture Distribution ◽  
Real Data ◽  
Moment Generating Function ◽  
Estimation Methods ◽  
Global Maximum ◽  
Mean Deviation ◽  
Mean Residual Life ◽  
Data Sets ◽  
Unknown Parameters

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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