scholarly journals A New Log-Logistic Lifetime Model with Mathematical Properties, Copula, Modified Goodness-of-Fit Test for Validation and Real Data Modeling

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1508 ◽  
Author(s):  
Mahmoud M. Mansour ◽  
Mohamed Ibrahim ◽  
Khaoula Aidi ◽  
Nadeem Shafique Butt ◽  
Mir Masoom Ali ◽  
...  
Keyword(s):  
Logistic Model ◽  
Goodness Of Fit ◽  
Real Data ◽  
Survival Times ◽  
Goodness Of Fit Test ◽  
Clayton Copula ◽  
Mathematical Properties ◽  
Renyi’S Entropy ◽  
The Right ◽  
Modified Test

After defining a new log-logistic model and studying its properties, some new bivariate type versions using “Farlie-Gumbel-Morgenstern Copula”, “modified Farlie-Gumbel-Morgenstern Copula”, “Clayton Copula”, and “Renyi’s entropy Copula” are derived. Then, using the Bagdonavicius-Nikulin goodness-of-fit (BN-GOF) test for validation, we proposed a goodness-of-fit test for a new log-logistic model. The modified test is applied for the “right censored” real dataset of survival times. All elements of the modified test are explicitly derived and given. Three real data applications are presented for measuring the flexibility and the importance of the new model under the uncensored scheme. Two other real datasets are analyzed for censored validation.

scholarly journals The four-parameter exponentiated Weibull model with Copula, properties and real data modeling.

2021 ◽  
pp. 649-667
Author(s):  
Wahid Shehata ◽  
Haitham M. Yousof
Keyword(s):  
Estimation Method ◽  
Real Data ◽  
Weibull Model ◽  
Hazard Rates ◽  
Survival Times ◽  
New Model ◽  
Clayton Copula ◽  
Failure Times ◽  
Mathematical Properties ◽  
Exponentiated Weibull

A new four-parameter lifetime model is introduced and studied. The new model derives its flexibility and wide applicability from the well-known exponentiated Weibull model. Many bivariate and the multivariate type versions are derived using the Morgenstern family and Clayton copula. The new density can exhibit many important shapes with different skewness and kurtosis which can be unimodal and bimodal. The new hazard rate can be decreasing, J-shape, U-shape, constant, increasing, upside down and increasing-constant hazard rates. Various of its structural mathematical properties are derived. Graphical simulations are used in assessing the performance of the estimation method. We proved empirically the importance and flexibility of the new model in modeling various types of data such as failure times, remission times, survival times and strengths data.

scholarly journals Validation of the Odd Lindley Exponentiated Exponential by a ModiÖed Goodness of Fit Test with Applications to Censored and Complete Data

2019 ◽  
pp. 745-771 ◽  
Author(s):  
Hafida Goual ◽  
Haitham M. Yousof ◽  
Mir Masoom Ali
Keyword(s):  
Goodness Of Fit ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Complete Data ◽  
Data Sets ◽  
Grouped Data ◽  
Goodness Of Fit Test ◽  
Right Censored Data ◽  
Mathematical Properties ◽  
Chi Squared

In this paper, we Örst introduse a new extension of the exponentiated exponential distribution along with its several mathematical properties. Second, we construct a modiÖed Chi-squared goodness-of-Öt test based on the Nikulin-Rao-Robson statistic in presence of censored and complete data. We describe the theory and the mechanism of the Y 2 n statistic test which can be used in survival and reliability data analysis. We use the maximum likelihood estimators based on the initial non grouped data sets. Then, we conduct numerical simulations to reinforce the results. For showing the applicability of our model in various Öelds, we illustrate it and the proposed test by applications to two real data sets for complete data case and two other right censored data sets.

scholarly journals A new parametric lifetime model with modified chi-square type test for right censored validation, characterizations and different estimation methods

2021 ◽  
pp. 399-425
Author(s):  
Haitham Yousof ◽  
Khaoula Aidi ◽  
G.G. Hamedani ◽  
Mohamed Ibrahim
Keyword(s):  
Censored Data ◽  
Goodness Of Fit ◽  
Real Data ◽  
Estimation Methods ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Data Set ◽  
Right Censored Data ◽  
New Model ◽  
The Right

A new three-parameter extension of the generalized Nadarajah-Haghighi model is introduced and studied. Some of its statistical properties are derived. Characterization results are presented. The failure rate can be "increasing", "decreasing", "bathtub", "upside-down", "upside-down-constant", "increasing-constant" or "constant". Different non-Bayesian estimation methods under uncensored scheme are considered. Numerical simulations are performed for comparing the estimation methods using different sample sizes. The censored Barzilai-Borwein algorithm is employed via a simulation study. Using the approach of the Bagdonavicius-Nikulin chi-square goodness-of-fit test for validation under the right censored data, we propose a modified chi-square goodness-of-fit test for the new model. Based on the maximum likelihood estimators on initial data, the modified Bagdonavicius-Nikulin chi-square goodness-of-fit test recovers the loss in information. The modified Bagdonavicius-Nikulin test for validation under the right censored data is applied to four real and right censored data sets. The new model is compared with many other competitive models by means of a real data set.

scholarly journals A New Parametric Life Distribution with Modified Bagdonavičius–Nikulin Goodness-of-Fit Test for Censored Validation, Properties, Applications, and Different Estimation Methods

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 592 ◽  
Author(s):  
Mahmoud Mansour ◽  
Mahdi Rasekhi ◽  
Mohamed Ibrahim ◽  
Khaoula Aidi ◽  
Haitham M. Yousof ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Real Data ◽  
Weibull Model ◽  
Estimation Methods ◽  
Model Parameters ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Data Set ◽  
The Right

In this paper, we first study a new two parameter lifetime distribution. This distribution includes “monotone” and “non-monotone” hazard rate functions which are useful in lifetime data analysis and reliability. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Renyi entropy, δ-entropy, order statistics and probability weighted moments are derived. Non-Bayesian estimation methods such as the maximum likelihood, Cramer-Von-Mises, percentile estimation, and L-moments are used for estimating the model parameters. The importance and flexibility of the new distribution are illustrated by means of two applications to real data sets. Using the approach of the Bagdonavicius–Nikulin goodness-of-fit test for the right censored validation, we then propose and apply a modified chi-square goodness-of-fit test for the Burr X Weibull model. The modified goodness-of-fit statistics test is applied for the right censored real data set. Based on the censored maximum likelihood estimators on initial data, the modified goodness-of-fit test recovers the loss in information while the grouped data follows the chi-square distribution. The elements of the modified criteria tests are derived. A real data application is for validation under the uncensored scheme.

A Goodness of Fit Test for the Multilevel Logistic Model

2015 ◽  
Vol 45 (2) ◽  
pp. 643-659 ◽  
Author(s):  
A. A. P. N. M. Perera ◽  
M. R. Sooriyarachchi ◽  
S. L. Wickramasuriya
Keyword(s):  
Logistic Model ◽  
Goodness Of Fit ◽  
Goodness Of Fit Test ◽  
Multilevel Logistic Model

A test for fuzzy exponentiality based on Kullback-Leibler information

2021 ◽  
pp. 1-8
Author(s):  
Lingtao Kong
Keyword(s):  
Biological Sciences ◽  
Monte Carlo ◽  
Goodness Of Fit ◽  
Experimental Studies ◽  
Real Data ◽  
Test Statistics ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Higher Power ◽  
Leibler Information

The exponential distribution has been widely used in engineering, social and biological sciences. In this paper, we propose a new goodness-of-fit test for fuzzy exponentiality using α-pessimistic value. The test statistics is established based on Kullback-Leibler information. By using Monte Carlo method, we obtain the empirical critical points of the test statistic at four different significant levels. To evaluate the performance of the proposed test, we compare it with four commonly used tests through some simulations. Experimental studies show that the proposed test has higher power than other tests in most cases. In particular, for the uniform and linear failure rate alternatives, our method has the best performance. A real data example is investigated to show the application of our test.

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.

scholarly journals A Modified Chi-square Type Test Statistic for the Double Burr X Model with Applications to Right Censored Medical and Reliability Data

2021 ◽  
pp. 615-623
Author(s):  
Khaoula Aidi ◽  
Nadeem Shafique Butt ◽  
Mir Masoom Ali ◽  
Mohamed Ibrahim ◽  
Haitham M. Yousof ◽  
...  
Keyword(s):  
Censored Data ◽  
Goodness Of Fit ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Right Censored Data ◽  
The Right

A new modified version of the Bagdonavičius-Nikulin goodness-of-fit test statistic is presented for validity for the right censor case under the double Burr type X distribution. The maximum likelihood estimation method in censored data case is used and applied. Simulations via the algorithm of Barzilai-Borwein is performed for assessing the right censored estimation method. Another simulation study is presented for testing the null hypothesis under the modified version of the Bagdonavičius and Nikulin goodness-of-fit statistical test. Four right censored data sets are analyzed under the new modified test statistic for checking the distributional validation.

Alpha Power-Kumaraswamy Distribution with An Application on Survival Times of Cancer Patients

2020 ◽  
Vol 2 (2) ◽  
Author(s):  
Fatima Ulubekova ◽  
Gamze Ozel
Keyword(s):  
Hazard Rate ◽  
Real Data ◽  
Rate Function ◽  
Data Sets ◽  
Alpha Power ◽  
Survival Times ◽  
Kumaraswamy Distribution ◽  
Data Application ◽  
The Right ◽  
Better Than

The aim of the study is to obtain the alpha power Kumaraswamy (APK) distribution. Some main statistical properties of the APK distribution are investigated including survival, hazard rate and quantile functions, skewness, kurtosis, order statistics. The hazard rate function of the proposed distribution could be useful to model data sets with bathtub hazard rates. We provide a real data application and show that the APK distribution is better than the other compared distributions fort the right-skewed data sets.

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