Goodness-of-fit tests for the weighted exponential distribution

Authors

Department of Statistics, University of Isfahan, Isfahan, Iran

Abstract

In the new class of weighted exponential distributions was presented by Gupta and Kundu [1], the skewness  parameter has been added to the exponential distribution. Therefore the weighted exponential distribution has the skewness and scale parameters. In this paper, we first study Anderson and Kolmogorov-Smirnov goodness of fit tests for this class with unknown parameters. Then, we apply bootstrap method for estimation of Anderson’s quantile and another method for Kolmogorov-Smirnov. We use the maximum likelihood method for estimation of parameters. Finally, we compare Kolmogorov-Smirnov and Anderson tests in a Monte Carlo simulation study. The results show that the Kolmogorov–Smirnov test has greater power than Anderson test.

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References

[1] Gupta, R. D. and Kundu, D. (2009), A new class of weighted exponential distributions, Statistics, 43, 621 - 643. [2] Azzalini, A. (1985), A class of distributions which includes the normal ones, Scandinavian Journal of Statistics, 12, 171–178.
[3] Gupta, R.D. and Kundu, D. (1999), Generalized exponential distributions, Australian and New Zealand Journal of Statistics, 41(2), 173-188. [4] Arnold, B.C. and Beaver, R.J. (2000), The skew-Cauchy distribution, Statistics and probability letters, 49, 285−290.
[5] Gupta, R.D. and Kundu, D. (2007), Skew-Logistic distribution, Tech. Rep., Indian Institute of Technology Kanpur, Kanpur, India.
[6] Genton, M.G. (2004), Skew-elliptical distributions and their applications: a journey beyond normality, Chapman and Hall/CRC. [7] Stephens, M.A. (1986), Tests based on EDF statistics, Goodness-of-fit Techniques, 68, 97-193.

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History

  • Receive Date: 10 June 2013
  • Accept Date: 10 June 2013

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