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

Abstract

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.

The modified Bagdonavičius-Nikulin goodness-of-fit test statistic for the right censored distributional validation with applications in medicine and reliability

“…For the purpose of examining the distributional validity, four right censored data sets are examined using the new modified test statistic. For more details, information, applications, and new extensions of this test in the case of censored data from the right, see: Yousof et al (2021b) (for a new parametric lifetime model along with modified Chi-square type test for right censored distributional validation, characteristics and many estimation methods), Ibrahim et al (2021) (for a new exponential generalized log-logistic model with the Bagdonavičius and Nikulin testing for distribution validation and some non-Bayesian estimation methods), see also Ibrahim et al (2019 and and Yadav et al (2022) for some related details about the Nikulin-Rao-Robson goodness-of-fit test.…”

Chi-squared type test for distributional censored and uncensored validity with numerical assessments and real data applications

“…For the purpose of examining the distributional validity, four right censored data sets are examined using the new modified test statistic. For more details, information, applications, and new extensions of this test in the case of censored data from the right, see: Yousof et al (2021a) (for a new parametric lifetime model along with modified chi-squared type test for right censored distributional validation, characterizations and many estimation methods), Ibrahim et al (2021) (for a new exponential generalized log-logistic model with the Bagdonavičius and Nikulin testing for distribution validation and some non-Bayesian estimation methods), see also Ibrahim et al (2019Ibrahim et al ( , 2020 and Yadav et al (2022) for some related details about the Nikulin-Rao-Robson goodness-of-fit test.…”