On goodness-of-fit testing for Burr type X distribution under progressively type-II censoring

• Published in: Computational statistics Vol. 37; no. 5; pp. 2249 - 2265
• Main Authors: Pakyari, Reza, Baklizi, Ayman
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2022; Springer Nature B.V
• Subjects: Correlation coefficients; Economic Theory/Quantitative Economics/Mathematical Methods; Goodness of fit; Mathematics and Statistics; Maximum likelihood estimators; Monte Carlo simulation; Original Paper; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Statistical tests; Statistics; Survival analysis; Correlation coefficient; Nelson-Aalen estimate; Progressive Type-II censoring; Exponential distribution; Kalpan–Meier estimate; Burr distribution; Cumulative hazard function; Goodness-of-fit testing; Monte Carlo simulation
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-022-01197-5

In this article, we propose two goodness-of-fit test statistics for the Burr Type X distribution when the available data are subject to progressively Type-II censoring. The proposed test statistics are based on the sample correlation coefficient between the Kaplan-Meier estimator of the survival function and the lifetime data and also based on the correlation between the Nelson-Aalen estimator of the cumulative hazard function and the lifetime data. The new tests exhibit good performance in terms of power in compare to the EDF-based test statistics of Pakyari and Balakrishnan (IEEE Trans Reliab 61:238–242, 2012). The maximum likelihood estimator of the unknown Burr Type X model is also studied and an approximate estimator is given. Finally, two real datasets are analyzed for illustrative purposes.