scholarly journals The Logarithmic Burr-Hatke Exponential Distribution for Modeling Reliability and Medical Data

2018 ◽  
Vol 7 (5) ◽  
pp. 73
Author(s):  
T. H. M. Abouelmagd
Keyword(s):  
Exponential Distribution ◽  
Exponential Model ◽  
Likelihood Method ◽  
Model Parameters ◽  
Suitable Model ◽  
Monte Carlo Simulation Study ◽  
New Model ◽  
Weibull Models ◽  
Modified Weibull ◽  
Family Of Distributions

In this work, we introduced a new one-parameter exponential distribution. Some of its structural properties are derived% \textbf{.} The maximum likelihood method is used to estimate the model parameters by means of numerical Monte Carlo simulation study. The justification for the practicality of the new lifetime model is based on the wider use of the exponential model. The new model can be viewed as a mixtureof the exponentiated exponential distribution. It can also be considered as a suitable model for fitting right skewed data.\textbf{\ }We prove empirically the importance and flexibility of the new model in modelingcancer patients data, the new model provides adequate fits as compared to other related models with small values for $W^{\ast }$\ \ and $A^{\ast }$. The new model is much better than the Modified beta-Weibull, Weibull, exponentiated transmuted generalized Rayleig, the transmuted modified-Weibull, and transmuted additive Weibull models in modeling cancer patients data. We are also motivated to introduce this new model because it has only one parameter and we can generate some new families based on it such as the the odd Burr-Hatke exponential-G family of distributions, the logarithmic\textbf{\ }Burr-Hatke exponential-G family of distributions and the generalized\textbf{\ }Burr-Hatke exponential-G family of distributions, among others.

scholarly journals A Study on A New Type 1 Half-Logistic Family of Distributions and Its Applications

2020 ◽  
Vol 8 (4) ◽  
pp. 934-949
Author(s):  
Morad Alizadeh ◽  
Alireza Nematollahi ◽  
Emrah Altun ◽  
Mahdi Rasekhi
Keyword(s):  
Residual Life ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Mean Deviation ◽  
Model Parameters ◽  
Type I ◽  
Monte Carlo Simulation Study ◽  
New Type ◽  
Application Fields ◽  
Family Of Distributions

In this paper, we propose a new class of continuous distributions with two extra shape parameters called the a new type I half logistic-G family of distributions. Some of important properties including ordinary moments, quantiles, moment generating function, mean deviation, moment of residual life, moment of reversed residual life, order statistics and extreme value are obtained. To estimate the model parameters, the maximum likelihood method is also applied by means of Monte Carlo simulation study. A new location-scale regression model based on the new type I half logistic-Weibull distribution is then introduced. Applications of the proposed family is demonstrated in many fields such as survival analysis and univariate data fitting. Empirical results show that the proposed models provide better fits than other well-known classes of distributions in many application fields.

scholarly journals The Zubair-Inverse Lomax Distribution with Applications

2020 ◽  
pp. 1-14
Author(s):  
Jamilu Yunusa Falgore
Keyword(s):  
Maximum Likelihood ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Monte Carlo Simulation Study ◽  
New Model ◽  
Inverse Lomax Distribution ◽  
The Right ◽  
Decreasing Functions

In this article, an extension of Inverse Lomax (IL) distribution with the Zubair-G family is considered . Various statistical properties of the new model where derived, including moment generating function, R´enyi entropy, and order statistics. A Monte Carlo simulation study was presented to evaluate the performance of the maximum likelihood estimators. The new model can be skew to the right, constant, and decreasing functions depending on the parameter values.We discussed the estimation of the model parameters by maximum likelihood method. The application of the new model to the data sets indicates that the new model is better than the existing competitors as it has minimum value of statistics criteria.

scholarly journals Analysis of Type-II Censored Competing Risks’ Data under Reduced New Modified Weibull Distribution

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Saad J. Almalki ◽  
Tahani A. Abushal ◽  
M. D. Alsulami ◽  
G. A. Abd-Elmougod
Keyword(s):  
Competing Risks ◽  
Hazard Rate ◽  
Rate Function ◽  
Likelihood Method ◽  
Mcmc Methods ◽  
Model Parameters ◽  
Type Ii ◽  
Hazard Rate Function ◽  
Monte Carlo Simulation Study ◽  
Modified Weibull

Models with the bathtub-shaped hazard rate function are widely used in lifetime analysis and reliability engineering. In this paper, we adopted the reduced new modified Weibull (RNMW) distribution with a bathtub-shaped hazard rate function. Under consideration that the population units are failing with two independent causes of failure and the failure time is distributed with RNMW distribution, we formulate the model which is known as competing risks model. The model parameters under the type-II censoring scheme are estimated with the maximum likelihood method with the corresponding asymptotic confidence intervals. Also, the Bayes point and credible intervals with the help of MCMC methods are constructed. The real and simulated datasets are analyzed for illustrative purposes. Finally, the estimators are compared with the Monte Carlo simulation study.

scholarly journals The Burr X Exponentiated Weibull Model: Characterizations,Mathematical Properties and Applications to Failure and Survival Times Data

2019 ◽  
pp. 141-160 ◽  
Author(s):  
Mohamed G. Khalil ◽  
G. G. Hamedani ◽  
Haitham M. Yousof
Keyword(s):  
Weibull Model ◽  
Good Alternative ◽  
Likelihood Method ◽  
Model Parameters ◽  
Suitable Model ◽  
Survival Times ◽  
Exponentiated Weibull ◽  
Weibull Models ◽  
Lifetime Model ◽  
The Right

In this article, we introduce a new three-parameter lifetime model called the Burr X exponentiated Weibull model. The major justification for the practicality of the new lifetime model is based on the wider use of the exponentiated Weibull and Weibull models. We are motivated to propose this new lifetime model because it exhibits increasing, decreasing, bathtub, J shaped and constant hazard rates. The new lifetime model can be viewed as a mixture of the exponentiated Weibull distribution. It can also be viewed as a suitable model for fitting the right skewed, symmetric, left skewed and unimodal data. We provide a comprehensive account of some of its statistical properties. Some useful characterization results are presented. The maximum likelihood method is used to estimate the model parameters. We prove empirically the importance and flexibility of the new model in modeling two types of lifetime data. The proposed model is a better fit than the Poisson Topp Leone-Weibull, the Marshall Olkin extended-Weibull, gamma-Weibull , Kumaraswamy-Weibull , Weibull-Fréchet, beta-Weibull, transmuted modified-Weibull, Kumaraswamy transmuted- Weibull, modified beta-Weibull, Mcdonald-Weibull and transmuted exponentiated generalized-Weibull models so it is a good alternative to these models in modeling aircraft windshield data as well as the new lifetime model is much better than the Weibull-Weibull, odd Weibull-Weibull, Weibull Log-Weibull, the gamma exponentiated-exponential and exponential exponential-geometric models so it is a good alternative to these models in modeling the survival times of Guinea pigs. We hope that the new distribution will attract wider applications in reliability, engineering and other areas of research.

scholarly journals Truncated Cauchy Power Odd Fréchet-G Family of Distributions: Theory and Applications

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
M. Shrahili ◽  
I. Elbatal
Keyword(s):  
Maximum Likelihood Method ◽  
Exponential Model ◽  
Likelihood Method ◽  
Mean Deviation ◽  
Model Parameters ◽  
Lorenz Curves ◽  
New Family ◽  
The Family ◽  
Real World Datasets ◽  
Family Of Distributions

The truncated Cauchy power odd Fréchet-G family of distributions is presented in this article. This family’s unique models are launched. Statistical properties of the new family are proposed, such as density function expansion, moments, incomplete moments, mean deviation, Bonferroni and Lorenz curves, and entropy. We investigate the maximum likelihood method for predicting model parameters of the new family. Two real-world datasets are used to show the importance and flexibility of the new family by using the truncated Cauchy power odd Fréchet exponential model as example of the family and compare it with some known models, and this model proves the importance and the flexibility for the new family.

scholarly journals A New Generating Family of Distributions: Properties and Applications to the Weibull Exponential Model

2021 ◽  
Vol 19 (1) ◽  
Author(s):  
El-Sayed A. El-Sherpieny ◽  
Salwa Assar ◽  
Tamer Helal
Keyword(s):  
Hazard Rate ◽  
Survival Function ◽  
Real Data ◽  
Exponential Model ◽  
Rate Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Set ◽  
Rate Functions ◽  
Family Of Distributions

A new method for generating family of distributions was proposed. Some fundamental properties of the new proposed family include the quantile, survival function, hazard rate function, reversed hazard and cumulative hazard rate functions are provided. This family contains several new models as sub models, such as the Weibull exponential model which was defined and discussed its properties. The maximum likelihood method of estimation is using to estimate the model parameters of the new proposed family. The flexibility and the importance of the Weibull-exponential model is assessed by applying it to a real data set and comparing it with other known models.

scholarly journals The Alpha Power Transformation Family: Properties and Applications

2019 ◽  
pp. 525-545 ◽  
Author(s):  
Mohamed E. Mead ◽  
Gauss M. Cordeiro ◽  
Ahmed Z. Afify ◽  
Hazem Al Mofleh
Keyword(s):  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Power Transformation ◽  
Data Sets ◽  
Alpha Power ◽  
Weibull Distributions ◽  
Exponentiated Weibull ◽  
Rate Functions ◽  
Modified Weibull

Mahdavi A. and Kundu D. (2017) introduced a family for generating univariate distributions called the alpha power transformation. They studied as a special case the properties of the alpha power transformed exponential distribution. We provide some mathematical properties of this distribution and define a four-parameter lifetime model called the alpha power exponentiated Weibull distribution. It generalizes some well-known lifetime models such as the exponentiated exponential, exponentiated Rayleigh, exponentiated Weibull and Weibull distributions. The importance of the new distribution comes from its ability to model monotone and non-monotone failure rate functions, which are quite common in reliability studies. We derive some basic properties of the proposed distribution including quantile and generating functions, moments and order statistics. The maximum likelihood method is used to estimate the model parameters. Simulation results investigate the performance of the estimates. We illustrate the importance of the proposed distribution over the McDonald Weibull, beta Weibull, modified Weibull, transmuted Weibull and exponentiated Weibull distributions by means of two real data sets.

scholarly journals Generalized Exponentiated Weibull Linear Model in the Presence of Covariates

2017 ◽  
Vol 6 (3) ◽  
pp. 75
Author(s):  
Tiago V. F. Santana ◽  
Edwin M. M. Ortega ◽  
Gauss M. Cordeiro ◽  
Adriano K. Suzuki
Keyword(s):  
Regression Model ◽  
Linear Model ◽  
Goodness Of Fit ◽  
Likelihood Function ◽  
Confidence Bands ◽  
Model Parameters ◽  
Random Component ◽  
Monte Carlo Simulation Study ◽  
New Model ◽  
Exponentiated Weibull

A new regression model based on the exponentiated Weibull with the structure distribution and the structure of the generalized linear model, called the generalized exponentiated Weibull linear model (GEWLM), is proposed. The GEWLM is composed by three important structural parts: the random component, characterized by the distribution of the response variable; the systematic component, which includes the explanatory variables in the model by means of a linear structure; and a link function, which connects the systematic and random parts of the model. Explicit expressions for the logarithm of the likelihood function, score vector and observed and expected information matrices are presented. The method of maximum likelihood and a Bayesian procedure are adopted for estimating the model parameters. To detect influential observations in the new model, we use diagnostic measures based on the local influence and Bayesian case influence diagnostics. Also, we show that the estimates of the GEWLM are  robust to deal with the presence of outliers in the data. Additionally, to check whether the model supports its assumptions, to detect atypical observations and to verify the goodness-of-fit of the regression model, we define residuals based on the quantile function, and perform a Monte Carlo simulation study to construct confidence bands from the generated envelopes. We apply the new model to a dataset from the insurance area.

scholarly journals A New Flexible Version of the Lomax Distribution with Applications

2018 ◽  
Vol 7 (5) ◽  
pp. 120
Author(s):  
T. H. M. Abouelmagd
Keyword(s):  
Estimation Method ◽  
Good Alternative ◽  
Model Parameters ◽  
Data Sets ◽  
Suitable Model ◽  
Lifetime Data ◽  
New Model ◽  
The Right ◽  
New Distribution ◽  
Better Than

A new version of the Lomax model is introduced andstudied. The major justification for the practicality of the new model isbased on the wider use of the Lomax model. We are also motivated tointroduce the new model since the density of the new distribution exhibitsvarious important shapes such as the unimodal, the right skewed and the leftskewed. The new model can be viewed as a mixture of the exponentiated Lomaxdistribution. It can also be considered as a suitable model for fitting thesymmetric, left skewed, right skewed, and unimodal data sets. The maximumlikelihood estimation method is used to estimate the model parameters. Weprove empirically the importance and flexibility of the new model inmodeling two types of aircraft windshield lifetime data sets. The proposedlifetime model is much better than gamma Lomax, exponentiated Lomax, Lomaxand beta Lomax models so the new distribution is a good alternative to thesemodels in modeling aircraft windshield data.

scholarly journals A New Flexible Three-Parameter Model: Properties, Clayton Copula, and Modeling Real Data

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 440 ◽  
Author(s):  
Abdulhakim A. Al-babtain ◽  
I. Elbatal ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Simple Type ◽  
Data Sets ◽  
New Model ◽  
Clayton Copula ◽  
Mathematical Properties

In this article, we introduced a new extension of the binomial-exponential 2 distribution. We discussed some of its structural mathematical properties. A simple type Copula-based construction is also presented to construct the bivariate- and multivariate-type distributions. We estimated the model parameters via the maximum likelihood method. Finally, we illustrated the importance of the new model by the study of two real data applications to show the flexibility and potentiality of the new model in modeling skewed and symmetric data sets.

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