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.

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.

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.

scholarly journals Validation of the Topp-Leone-Lomax Model via a Modified Nikulin-Rao-Robson Goodness-of-Fit Test with Different Methods of Estimation

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 57 ◽  
Author(s):  
Abhimanyu Singh Yadav ◽  
Hafida Goual ◽  
Refah Mohammed Alotaibi ◽  
Rezk H ◽  
M. Masoom Ali ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Rate Function ◽  
Estimation Methods ◽  
Model Parameters ◽  
Simple Type ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Failure Rate Function ◽  
New Model

In this paper, we introduce a new univariate version of the Lomax model as well as a simple type copula-based construction via Morgenstern family and via Clayton copula for introducing a new bivariate and a multivariate type extension of the new model. The new density has a strong physical interpretation and can be a symmetric function and unimodal with a heavy tail with positive skewness. The new failure rate function can be “upside-down”, “decreasing” with many different shapes and “decreasing-constant”. Some mathematical and statistical properties of the new model are derived. The model parameters are estimated using different estimation methods. For comparing the estimation methods, Markov Chain Monte Carlo (MCMC) simulations are performed. The applicability of the new model is illustrated via four real data applications, these data sets are symmetric and right skewed. We constructed a modified Chi-Square goodness-of-fit test based on Nikulin-Rao-Robson test in the case of complete and censored sample for the new model. Different simulation studies are performed along applications on real data for validation propose.

scholarly journals Expanded Fréchet Model: Mathematical Properties, Copula, Different Estimation Methods, Applications and Validation Testing

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1949
Author(s):  
Mukhtar M. Salah ◽  
M. El-Morshedy ◽  
M. S. Eliwa ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Estimation Method ◽  
Least Square ◽  
Estimation Methods ◽  
Goodness Of Fit Test ◽  
Least Square Estimation ◽  
Chi Square ◽  
Anderson Darling ◽  
The Right

The extreme value theory is expanded by proposing and studying a new version of the Fréchet model. Some new bivariate type extensions using Farlie–Gumbel–Morgenstern copula, modified Farlie–Gumbel–Morgenstern copula, Clayton copula, and Renyi’s entropy copula are derived. After a quick study for its properties, different non-Bayesian estimation methods under uncensored schemes are considered, such as the maximum likelihood estimation method, Anderson–Darling estimation method, ordinary least square estimation method, Cramér–von-Mises estimation method, weighted least square estimation method, left-tail Anderson–Darling estimation method, and right-tail Anderson–Darling estimation method. Numerical simulations were performed for comparing the estimation methods using different sample sizes for three different combinations of parameters. The Barzilai–Borwein algorithm was employed via a simulation study. Three applications were presented for measuring the flexibility and the importance of the new model for comparing the competitive distributions under the uncensored scheme. Using the approach of the Bagdonavicius–Nikulin 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. The modified goodness-of-fit statistic test was applied for the right censored real data set, called leukemia free-survival times for autologous transplants. Based on the maximum likelihood estimators on initial data, the modified goodness-of-fit test recovered the loss in information while the grouping data and followed chi-square distributions. All elements of the modified goodness-of-fit criteria tests are explicitly derived and given.

scholarly journals Clinical Application of Mathematical Long Bone Ratios to Calculate Appropriate Donor Limb Lengths in Bilateral Upper Limb Transplantation

Hand ◽  
2018 ◽  
Vol 14 (4) ◽  
pp. 523-529
Author(s):  
Justyn Lutfy ◽  
Alexis Pietak ◽  
Shaun D. Mendenhall ◽  
Michael W. Neumeister
Keyword(s):  
Clinical Application ◽  
Upper Limb ◽  
Goodness Of Fit ◽  
Linear Regression Analysis ◽  
Limb Length ◽  
Long Bone ◽  
Multivariate Linear Regression Analysis ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Data Set

Background: Limited methods exist to aid in deciding the appropriate donor limb lengths in bilateral upper limb amputees qualifying for vascularized composite allotransplantation. We hypothesized mathematical equations could be created using long bone length ratios, and applied to radiographs, to approximate the patient’s limb length prior to amputation. Methods: A data set of 30 skeletons’ unilateral upper limb long bones measured using osteometric board and calipers was used. Anatomic segment ratios were calculated based on humerus length after multivariate linear regression analysis. For clinical application testing, 5 cadavers’ upper limbs were radiographed. Radiographic bone lengths were then measured along the long axis of each long bone. These measured radiographic lengths were then compared with the predicted bone lengths, generated from the skeleton data set ratios, for each cadaver. Results: The chi-square goodness-of-fit test showed excellent fit ( P < .01) between the predicted and radiographically measured lengths for the 5 cadavers, and interobserver measurements showed no statistical difference. Depending on the cadaver, percent error in total limb length predicted to measure ranged from 0.9% to 2.7%. The variables to multiply an individual humerus length to calculate a given anatomic segment thus proved to be effective. Conclusions: If a bilateral upper limb amputee has 1 intact humerus, ratios to the humerus length can be reliably applied to calculate the preamputation limb length based on the patient’s radiographic humerus length. These formulas are indicated for finding the appropriate limb lengths, and smaller anatomic segments, for donor-recipient matching in upper limb transplantation.

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 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.

Sign in / Sign up

Export Citation Format

Share Document