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 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.

Goodness-of-fit test for skew normality based on energy statistics

2020 ◽  
Vol 28 (3) ◽  
pp. 227-236
Author(s):  
Logan Opperman ◽  
Wei Ning
Keyword(s):  
Goodness Of Fit ◽  
Type I Error ◽  
Real Data ◽  
Testing Procedure ◽  
Data Sets ◽  
Type I ◽  
Goodness Of Fit Test ◽  
Power Comparisons

AbstractIn this paper, we propose a goodness-of-fit test based on the energy statistic for skew normality. Simulations indicate that the Type-I error of the proposed test can be controlled reasonably well for given nominal levels. Power comparisons to other existing methods under different settings show the advantage of the proposed test. Such a test is applied to two real data sets to illustrate the testing procedure.

scholarly journals A Modified Chi-square Type Test for Distributional Validity with Applications to Right Censored Reliability and Medical Data

2021 ◽  
pp. 1113-1121 ◽  
Author(s):  
Haitham M. Yousof ◽  
Abdullah H. Al-nefaie ◽  
Khaoula Aidi ◽  
M. Masoom Ali ◽  
Mohamed ibrahim Mohamed
Keyword(s):  
Censored Data ◽  
Goodness Of Fit ◽  
Data Sets ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Right Censored Data ◽  
Type Test ◽  
The Right ◽  
New Distribution

In this paper, a modified Chi-square goodness-of-fit test called the modified Bagdonavičius-Nikulin goodness-of-fit test statistic is investigated and the applied for distributional validation under the right censored case. The new modified goodness-of-fit test is presented and applied for the right censored data sets. The algorithm of the censored Barzilai-Borwein is employed via a comprehensive simulation study for assessing validity of the new test. The modified Bagdonavičius-Nikulin test is applied to four real and right censored data sets. A new distribution is compared with many other competitive distributions under the new modified Bagdonavičius-Nikulin goodness-of-fit test statistic.

The exponentiated exponential burr XII distribution: Theory and application to lifetime data

2020 ◽  
pp. 1-14
Author(s):  
Majdah M. Badr
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Significant Heterogeneity ◽  
Lifetime Data ◽  
Fit Statistics ◽  
Mathematical Properties ◽  
New Distribution

Lifetime data collected from reliability tests are among data that often exhibit significant heterogeneity caused by variations in manufacturing which make standard lifetime models inadequate. In this paper we introduce a new lifetime distribution derived from T-X family technique called exponentiated exponential Burr XII (EE-BXII) distribution. We establish various mathematical properties. The maximum likelihood estimates (MLE) for the EE-BXII parameters are derived. We estimate the precision of the maximum likelihood estimators via simulation study. Some numerical illustrations are performed to study the behavior of the obtained estimators. Finally the model is applied to a real dataset. We apply goodness of fit statistics and graphical tools to examine the adequacy of the EE-BXII distribution. The importance of this research lies in deriving a new distribution under the name EE-BXII, which is considered the best distributions in analyzing data of life times at present if compared to many distributions in analysis real data.

scholarly journals Applying the Multivariate Time-Rescaling Theorem to Neural Population Models

2011 ◽  
Vol 23 (6) ◽  
pp. 1452-1483 ◽  
Author(s):  
Felipe Gerhard ◽  
Robert Haslinger ◽  
Gordon Pipa
Keyword(s):  
Statistical Models ◽  
Goodness Of Fit ◽  
Real Data ◽  
Spike Trains ◽  
Population Models ◽  
Neural Population ◽  
Data Sets ◽  
Goodness Of Fit Test ◽  
Population Activity ◽  
Neural Information

Statistical models of neural activity are integral to modern neuroscience. Recently interest has grown in modeling the spiking activity of populations of simultaneously recorded neurons to study the effects of correlations and functional connectivity on neural information processing. However, any statistical model must be validated by an appropriate goodness-of-fit test. Kolmogorov-Smirnov tests based on the time-rescaling theorem have proven to be useful for evaluating point-process-based statistical models of single-neuron spike trains. Here we discuss the extension of the time-rescaling theorem to the multivariate (neural population) case. We show that even in the presence of strong correlations between spike trains, models that neglect couplings between neurons can be erroneously passed by the univariate time-rescaling test. We present the multivariate version of the time-rescaling theorem and provide a practical step-by-step procedure for applying it to testing the sufficiency of neural population models. Using several simple analytically tractable models and more complex simulated and real data sets, we demonstrate that important features of the population activity can be detected only using the multivariate extension of the test.

scholarly journals A New Goodness of Fit Test for Multivariate Normality and Comparative Simulation Study

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3003
Author(s):  
Jurgita Arnastauskaitė ◽  
Tomas Ruzgas ◽  
Mindaugas Bražėnas
Keyword(s):  
Goodness Of Fit ◽  
Distribution Density ◽  
Empirical Distribution ◽  
Real Data ◽  
Multivariate Normality ◽  
Data Sets ◽  
Goodness Of Fit Test ◽  
Absolute Deviation ◽  
Test For Multivariate Normality ◽  
The Mean

The testing of multivariate normality remains a significant scientific problem. Although it is being extensively researched, it is still unclear how to choose the best test based on the sample size, variance, covariance matrix and others. In order to contribute to this field, a new goodness of fit test for multivariate normality is introduced. This test is based on the mean absolute deviation of the empirical distribution density from the theoretical distribution density. A new test was compared with the most popular tests in terms of empirical power. The power of the tests was estimated for the selected alternative distributions and examined by the Monte Carlo modeling method for the chosen sample sizes and dimensions. Based on the modeling results, it can be concluded that a new test is one of the most powerful tests for checking multivariate normality, especially for smaller samples. In addition, the assumption of normality of two real data sets was checked.

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 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 Goodness-of-Fit Tests for Bivariate Time Series of Counts

Econometrics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 10
Author(s):  
Šárka Hudecová ◽  
Marie Hušková ◽  
Simos G. Meintanis
Keyword(s):  
Goodness Of Fit ◽  
Probability Generating Function ◽  
Parametric Bootstrap ◽  
Real Data ◽  
Data Sets ◽  
Test Statistics ◽  
Finite Sample ◽  
Generalized Poisson ◽  
Goodness Of Fit Tests ◽  
Monte Carlo Experiments

This article considers goodness-of-fit tests for bivariate INAR and bivariate Poisson autoregression models. The test statistics are based on an L2-type distance between two estimators of the probability generating function of the observations: one being entirely nonparametric and the second one being semiparametric computed under the corresponding null hypothesis. The asymptotic distribution of the proposed tests statistics both under the null hypotheses as well as under alternatives is derived and consistency is proved. The case of testing bivariate generalized Poisson autoregression and extension of the methods to dimension higher than two are also discussed. The finite-sample performance of a parametric bootstrap version of the tests is illustrated via a series of Monte Carlo experiments. The article concludes with applications on real data sets and discussion.

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