Goodness-of-fit tests for progressively Type-II censored data from location–scale distributions

In this article, we propose several goodness-of-fit methods for location–scale families of distributions under progressively Type-II censored data. The new tests are based on order statistics and sample spacings. We assess the performance of the proposed tests for the normal and Gumbel models against several alternatives by means of Monte Carlo simulations. It has been observed that the proposed tests are quite powerful in comparison with an existing goodness-of-fit test proposed for progressively Type-II censored data by Balakrishnan et al. [Goodness-of-fit tests based on spacings for progressively Type-II censored data from a general location–scale distribution, IEEE Trans. Reliab. 53 (2004), pp. 349–356]. Finally, we illustrate the proposed goodness-of-fit tests using two real data from reliability literature.

[1]  A. Pettitt,et al.  Modified Cramér-von Mises statistics for censored data , 1976 .

[2]  N. Balakrishnan,et al.  Goodness-of-fit tests based on spacings for progressively type-II censored data from a general location-scale distribution , 2004, IEEE Transactions on Reliability.

[3]  D. Barr,et al.  A Kolmogorov-Smirnov Test for Censored Samples , 1973 .

[4]  Narayanaswamy Balakrishnan,et al.  Interval Estimation of Parameters of Life From Progressively Censored Data , 1994 .

[5]  M GREENWOOD,et al.  The statistical study of infectious diseases. , 1946, Journal of the Royal Statistical Society. Series A.

[6]  Bingxing Wang.  Goodness-of-fit test for the exponential distribution based on progressively Type-II censored sample , 2008 .

[7]  James Durbin,et al.  Tests for serial correlation in regression analysis based on the periodogram of least-squares residuals , 1969 .

[8]  P. Moran,et al.  Random division of an interval , 1951, Mathematical Proceedings of the Cambridge Philosophical Society.

[9]  C. Huber-Carol.  Goodness-of-Fit Tests and Model Validity , 2012 .

[10]  H. D. Brunk.  On the Range of the Difference between Hypothetical Distribution Function and Pyke's Modified Empirical Distribution Function , 1962 .

[11]  Charles P. Quesenberry,et al.  Power studies of some tests for uniformity , 1977 .

[12]  N. Balakrishnan,et al.  A General Purpose Approximate Goodness-of-Fit Test for Progressively Type-II Censored Data , 2012, IEEE Transactions on Reliability.

[13]  Narayanaswamy Balakrishnan,et al.  Testing Exponentiality Based on Kullback-Leibler Information With Progressively Type-II Censored Data , 2007, IEEE Transactions on Reliability.

[14]  Narayanaswamy Balakrishnan,et al.  A Simple Simulational Algorithm for Generating Progressive Type-II Censored Samples , 1995 .

[15]  Asymptotic Results on the Greenwood Statistic and Some of its Generalizations , 1984 .

[16]  Ralph B. D'Agostino,et al.  Goodness-of-Fit-Techniques , 2020 .

[17]  Wayne Nelson,et al.  Applied life data analysis , 1983 .

[18]  THE RANDOM DIVISION OF AN INTERVAL-PART III , 1951 .

[19]  Narayanaswamy Balakrishnan,et al.  A Test of Exponentiality Based on Spacings for Progressively Type-II Censored Data , 2002 .

[20]  H. O. Hartley,et al.  Quadratic forms in order statistics used as goodness-of-fit criteria , 1972 .

[21]  Wayne B. Nelson,et al.  Applied Life Data Analysis: Nelson/Applied Life Data Analysis , 2005 .

[22]  James R. King,et al.  Probability Charts for Decision Making , 1981 .

[23]  N. Balakrishnan,et al.  A New Method for Goodness-of-Fit Testing Based on Type-II Right Censored Samples , 2008, IEEE Transactions on Reliability.

[24]  Michael A. Stephens,et al.  Results from the Relation Between Two Statistics of the Kolmogorov-Smirnov Type , 1969 .

[25]  L. J. Bain,et al.  Goodness‐of‐fit tests for the weibull dictribution with unknown parameters and censored sampling , 1983 .

[26]  H. O. Hartley,et al.  A goodness of pit test for censored data , 1974 .

[27]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[28]  N. Balakrishnan,et al.  Progressive Censoring: Theory, Methods, and Applications , 2000 .

[29]  Y. A. Hegazy,et al.  Some New Goodness‐Of‐Fit Tests Using Order Statistics , 1975 .

[30]  Narayanaswamy Balakrishnan,et al.  Progressive censoring methodology: an appraisal , 2007 .

[31]  Lee J. Bain,et al.  Correlation type gogdness-of-fit statistics with censored sampling , 1976 .