Testing the Validity of the Exponential Model Based on Type II Censored Data Using Transformed Sample Data

Authors

  • Hadi Alizadeh Noughabi University of Birjand, Birjand

DOI:

https://doi.org/10.6092/issn.1973-2201/6194

Keywords:

Testing exponentiality, Type-II censoring, Power study, Monte Carlo simulation

Abstract

In this article, we propose a new approach to testing exponentiality for Type-II censored samples. Our method converts the original observations into transformed data which follow from a special distribution. It is shown that the proposed tests do not depend on the scale parameter of the exponential distribution and hence the tests are exact. Power performance of the proposed tests is compared with the existing tests against various alternatives. The results are impressive and the proposed tests have higher power than the competing tests. Finally, two real data from reliability literature as illustrate examples are presented.

References

H. ALIZADEH NOUGHABI N. R. ARGHAMI (2011a). Testing exponentiality using transformed data. Journal of Statistical Computation and Simulation, 81, 511-516.

H. ALIZADEH NOUGHABI N. R. ARGHAMI (2011b). Testing exponentiality based on characterizations of the exponential distribution. Journal of Statistical Computation and Simulation, 81, 1641{1651.

H. ALIZADEH NOUGHABI N. R. ARGHAMI (2012). General treatment of goodness-of-t tests based on Kullback-Leibler information. Journal of Statistical Computation and Simulation, 83, 1556{1569.

H. ALIZADEH NOUGHABI N. R. ARGHAMI (2013). Testing normality using transformed data. Communication in Statistics: Theory and Methods, 42, 3065{3075.

H. ALIZADEH NOUGHABI A goodness of t test for Laplace distribution against symmetric alternatives, using transformed data. (Submitted).

T. W. ANDERSON, D. A. DARLING (1954). A test of goodness of fit. Journal of American Statistical Association, 49, 765{769.

N. BALAKRISHNAN, W. CHEN (1999). Handbook of tables for order statistics from Lognormal distributions with applications. Springer.

N. BALAKRISHNAN, A. HABIBI RAD, N. R. ARGHAMI (2007). Testing exponentiality based on KullbackLeibler information with progressively type-II censored data. IEEE Transactions on Reliability, 56, 301{307.

N. BALAKRISHNAN, H.K.T. NG, N. KANNAN (2004). Goodness-of-fit tests based on spacings for progressively Type-II censored data from a general location-scale distribution. IEEE Transactions on Reliability, 53, 349{356.

C. W. BRAIN, S. S. SHAPIRO (1983). A regression test for exponentiality: censored, complete samples. Technometrics, 25, 69{76.

R.B. D'AGOSTINO, M. A. STEPHENS (1986). Goodness-of-Fit Techniques. New York, Marcel Dekker.

B. R. DHUMAL, D. T. SHIRKE (2012). A modified test for testing exponentiality using transformed data. Journal of Statistical Computation and Simulation, 84, 397{403.

A. HABIBI RAD, F. YOUSEFZADEH, N. BALAKRISHNAN (2011). Goodness-of-fit test based on KullbackLeibler information for progressively Type-II censored data. IEEE Transactions on Reliability, 60, 570{579.

C. HUBER-CAROL, N. BALAKRISHNAN, M. S. NIKULIN, M. MESBAH (2002). Goodness-of-fit tests and model validity. Boston, Basel, Berlin: Birkhuser.

A. N. KOLMOGOROV (1933). Sulla Determinazione Empirica di une legge di Distribuzione. Giornale dellIntituto Italiano degli Attuari, 4, 83{91.

J. LIM, S. PARK (2007). Censored Kullback-Leibler information and goodness-of-fit test with type II censored data. Journal of Applied Statistics, 34, 1051{1064.

C-T. LIN, Y-L. HUANG, N. BALAKRISHNAN (2008). A new method for goodness-of-fit testing based on Type-II right censored samples. IEEE Transactions on Reliability, 57, 633{642.

R. PAKYARI, N. BALAKRISHNAN (2012). A general purpose approximate goodness-of-fit test for progressively Type-II censored data. IEEE Transactions on Reliability, 61, 238{244.

R. PAKYARI, N. BALAKRISHNAN (2013). Goodness-of-fit tests for progressively Type-II censored data from location-scale distributions. Journal of Statistical Computation and Simulation, 83, 167{178.

S. PARK (2005). Testing exponentiality based on the Kullback-Leibler information. IEEE Transactions on Reliability, 54, 22{26.

S. PARK, D. PARK (2003). Correcting moments for goodness of fit tests based on two entropy estimates. Journal of Statistical Computation and Simulation, 73, 685{694.

M. SAMANTA, C. J. SCHWARZ (1998). The Shapiro-Wilk test for exponentiality based on censored data. Journal of American Statistical Association, 83, 528-531.

C. VON MISES (1931). Wahrscheinlichkeitsrechnung und ihre Anwendung in der Statistik und theoretischen Physik. Deuticke, Leipzig and Vienna.

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Published

2016-09-30

How to Cite

Alizadeh Noughabi, H. (2016). Testing the Validity of the Exponential Model Based on Type II Censored Data Using Transformed Sample Data. Statistica, 76(3), 221–232. https://doi.org/10.6092/issn.1973-2201/6194

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Articles