The exponential generalized log-logistic model: Bagdonavičius-Nikulin test for validation and non-Bayesian estimation methods

A modified Bagdonaviˇcius-Nikulin chi-square goodness-of-fit is defined and studied. The lymphoma data is analyzed using the modified goodness-of-fit test statistic. Di ff erent non-Bayesian estimation methods under complete samples schemes are considered, discussed and compared such as the maximum likelihood least square estimation method, the Cramer-von Mises estimation method, the weighted least square estimation method, the left tail-Anderson Darling estimation method and the right tail Anderson Darling estimation method. Numerical simulation studies are performed for comparing these estimation methods. The potentiality of the new model is illustrated using three real data sets and compared with many other well-known generalizations. Cram´er-von-Mises estimation, the weighted least square estimation, the left tail-Anderson Darling estimation, and the right tail Anderson Darling estimation methods. Numerical simulation studies were performed for comparing these estimation methods using di ff erent sample sizes and three di ff erent combinations of parameters. The potentiality of the EG-LL model is illustrated using three real data sets and the model is compared with many other well-known generalizations. The new model was proven worthy in modeling breaking stress, survival times and medical data sets. The Barzilai-Borwein algorithm is employed via a simulation study for assessing the performance of the estimators with di ff erent sample sizes as sample size tends to ∞ . Using the Bagdonaviˇcius-Nikulin goodness-of-fit test for validation, we propose a modified chi-square GOF tests for the EG-LL model. We have analyzed a lymphoma data set consisting of times (in months) from diagnosis to death for 31 individuals with advanced non Hodgkin’s lymphoma clinical symptoms by using our model under the modified Bagdonaviˇcius-Nikulin goodness-of-fit test statistic. Based on the MLEs, the modified Bagdon-aviˇcius-Nikulin goodness-of-fit test recovered the loss of information for the grouping data and fol-24

[1]  Khaoula Aidi,et al.  A new parametric lifetime model with modified chi-square type test for right censored validation, characterizations and different estimation methods , 2021 .

[2]  G. Hamedani,et al.  A New Parametric Lifetime Distribution with Modified Chi-square Type Test for Right Censored Validation, Characterizations and Different Estimation Methods , 2021 .

[3]  M. S. Eliwa,et al.  Expanded Fréchet Model: Mathematical Properties, Copula, Different Estimation Methods, Applications and Validation Testing , 2020, Mathematics.

[4]  H. Yousof,et al.  A New Log-Logistic Lifetime Model with Mathematical Properties, Copula, Modified Goodness-of-Fit Test for Validation and Real Data Modeling , 2020 .

[5]  Haitham M. Yousof,et al.  A New Parametric Life Distribution with Modified Bagdonavičius–Nikulin Goodness-of-Fit Test for Censored Validation, Properties, Applications, and Different Estimation Methods , 2020, Entropy.

[6]  Haitham M. Yousof,et al.  Validation of the Topp-Leone-Lomax Model via a Modified Nikulin-Rao-Robson Goodness-of-Fit Test with Different Methods of Estimation , 2019, Symmetry.

[7]  H. Yousof,et al.  Validation of Burr XII inverse Rayleigh model via a modified chi-squared goodness-of-fit test , 2019, Journal of applied statistics.

[8]  G. Hamedani,et al.  A new extension of Lindley distribution: modified validation test, characterizations and different methods of estimation , 2019, Communications for Statistical Applications and Methods.

[9]  M. M. Ali,et al.  Validation of the Odd Lindley Exponentiated Exponential by a ModiÖed Goodness of Fit Test with Applications to Censored and Complete Data , 2019, Pakistan Journal of Statistics and Operation Research.

[10]  M. M. Ali,et al.  Extended Weibull log-logistic distribution , 2019, Journal of Nonlinear Sciences and Applications.

[11]  G. G. Hamedani,et al.  A new lifetime model with regression models, characterizations and applications , 2019, Commun. Stat. Simul. Comput..

[12]  H. Yousof,et al.  A NEW LOMAX DISTRIBUTION FOR MODELING SURVIVAL TIMES AND TAXES REVENUE DATA SETS , 2019 .

[13]  Ahmed M. Gad,et al.  The Burr XII-Burr XII Distribution: Mathematical Properties and Characterizations , 2019 .

[14]  E. Altun,et al.  A New Log-location Regression Model with Influence Diagnostics and Residual Analysis , 2018, Facta Universitatis, Series: Mathematics and Informatics.

[15]  H. Yousof,et al.  Zografos–Balakrishnan Burr XII Distribution: Regression Modeling and Applications , 2018 .

[16]  E. Altun,et al.  A new family of distributions with properties, regression models and applications , 2018 .

[17]  M. Nikulin,et al.  Chi-Squared Goodness-of-Fit Tests for Parametric Accelerated Failure Time Models , 2013 .

[18]  Mikhail Nikulin,et al.  Chi-Squared Goodness of Fit Tests with Applications , 2013 .

[19]  Mikhail Nikulin,et al.  Chi-squared goodness-of-fit test for right censored data , 2011 .

[20]  W. J. Padgett,et al.  A Bootstrap Control Chart for Weibull Percentiles , 2006, Qual. Reliab. Eng. Int..

[21]  I. Gijbels,et al.  Estimation of a Change Point in a Hazard Function Based on Censored Data , 2003, Lifetime data analysis.

[22]  Magne Vollan Aarset,et al.  How to Identify a Bathtub Hazard Rate , 1987, IEEE Transactions on Reliability.

[23]  Pandu R. Tadikamalla,et al.  A Look at the Burr and Related Distributioni , 1980 .

[24]  Robert N. Rodriguez.  A guide to the Burr type XII distributions , 1977 .

[25]  Irving W. Burr,et al.  Pameters for a general system of distributions to match a grid of α3 and α4 , 1973 .

[26]  Irving W. Burr,et al.  On A General System of Distributions III. The Sample Range , 1968 .

[27]  T. Bjerkedal.  Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli. , 1960, American journal of hygiene.

[28]  I. W. Burr.  Cumulative Frequency Functions , 1942 .