Bivariate Weibull Distribution: Properties and Different Methods of Estimation

Almetwally, Ehab M.; Muhammed, Hiba Z.; El-Sherpieny, El-Sayed A.

doi:10.1007/s40745-019-00197-5

Cited by 32 publications

(20 citation statements)

References 12 publications

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“…In the goodness-of-fit test for copulas, we use a parametric bootstrap N=10000 time and the empirical copula estimate. We compared the proposed Bivariate distributions by different Bivariate distributions as Bivariate FGM Gamma (BFGMG), which it is discussed by [5], Bivariate FGM Weibull (BFGMW), which it is discussed by [7] and Bivariate FGM generalized exponential (BFGMGE), which it is discussed by [25].…”

Section: The Medical Data Of Kidney Patientsmentioning

confidence: 99%

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Bivariate Weibull-G Family Based on Copula Function: Properties, Bayesian and non-Bayesian Estimation and Applications

El-Sherpieny

Muhammed

Almetwally

2021

Stat., optim. inf. comput.

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This paper aims to obtain a new flexible bivariate generalized family of distributions based on FGM copula, which is called bivariate FGM Weibull-G family. Some of its statistical properties are studied as marginal distributions, product moments, and moment generating functions. Some dependence measures as Kendall’s tau and median regression model are discussed. After introducing the general class, four special sub models of the new family are introduced by taking the baseline distributions as Pareto, inverted Topp-Leone, exponential, and Rayleigh distributions. Maximum likelihood and Bayesian approaches are used to estimate the model unknown parameters. Further, percentile bootstrap confidence interval and bootstrap-t confidence interval are estimated for the model’s parameters. A Monte-Carlo simulation study is carried out of the maximum likelihood and Bayesian estimators. Finally, we illustrate the importance of the proposed bivariate family using two real data sets in medical field.

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Section: The Medical Data Of Kidney Patientsmentioning

confidence: 99%

“…Almetwally and Muhammed [18] proposed a new bivariate Fréchet distribution based on FGM and AMH copula functions and discussed their statistical properties. Almetwally et al [7] introduced bivariate Weibull distribution by using the FGM copula function and some properties of this distribution are obtained. Samanthi and Sepanski [11]…”

Section: Introductionmentioning

confidence: 99%

Bivariate Weibull-G Family Based on Copula Function: Properties, Bayesian and non-Bayesian Estimation and Applications

El-Sherpieny

Muhammed

Almetwally

2021

Stat., optim. inf. comput.

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“…e mode value of the MOAPW distribution can be obtained by solving numerically equation (20). Also, from Figure 4, we can note that the MOAPW distribution has one mode in most cases.…”

Section: Complexitymentioning

confidence: 93%

“…e handled data from all such mentioned trials are called censored data. Censored test has many types and the most important and used schemes are Type-I censored and Type-II censored; see, for example, the works of Balakrishnan and Ng [18], El-Morshedy et al [19], and Almetwally et al [20]. is paper's aim is to introduce a new lifetime distribution defined as Marshall-Olkin alpha power Weibull (MOAPW) distribution, depending on the MOAP family.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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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.

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“…We plan to make a new extension bivariate OWITL based on copula in future studies, such as done in Almetwally et al [ 34 ], Muhammed and Almetwally [ 35 ] and Kim et al [ 36 ]. We plan to discuss a new application for the OWITL distribution quest based on a censored sample such as done in Almetwally et al [ 37 ] and Aslam et al [ 38 ].…”

Section: Introductionmentioning

confidence: 99%

The Odd Weibull Inverse Topp–Leone Distribution with Applications to COVID-19 Data

Almetwally

2021

Ann. Data. Sci.

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This paper aims at defining an optimal statistical model for the COVID-19 distribution in the United Kingdom, and Canada. A combining the inverted Topp–Leone distribution and the odd Weibull family introduces a new lifetime distribution with a three-parameter to formulate the odd Weibull inverted Topp–Leone (OWITL) distribution. As a simple linear representation, hazard rate function, and moment function, this new distribution has several nice properties. To estimate the unknown parameters of OWITL distribution, maximum likelihood, least-square, weighted least-squares, maximum product spacing, Cramér–von Mises estimators, and Anderson–Darling estimation methods are used. To evaluate the use of estimation techniques, a numerical outcome of the Monte Carlo simulation is obtained.

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Bivariate Weibull Distribution: Properties and Different Methods of Estimation

Cited by 32 publications

References 12 publications

Bivariate Weibull-G Family Based on Copula Function: Properties, Bayesian and non-Bayesian Estimation and Applications

Bivariate Weibull-G Family Based on Copula Function: Properties, Bayesian and non-Bayesian Estimation and Applications

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

The Odd Weibull Inverse Topp–Leone Distribution with Applications to COVID-19 Data

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