# Classical Tests of Hypotheses for the Skewness Parameter of Two-Piece Double Exponential Distribution

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## Abstract

In this paper, we derive uniformly most powerful and uniformly most powerful unbiased tests for the skewness parameter of the two-piece double exponential distribution when the location and scale parameters are known. Neyman structure and likelihood ratio tests are derived in the case of known location parameter but unknown scale parameter. Test for symmetry of the distribution can be deduced as a special case. All the tests are exact and the cut-off points and power of the test can be obtained easily. The tests derived are applied to daily percentage change in the price of gold quoted in Mumbai market for the years 2015 and 2016. It has been deduced that the long term distribution is Laplace while the short term distribution is at times two-piece double exponential. These results can be advantageously used for speculative trading in the metal by short and long term investors.

## Keywords

Asymmetric Laplace distribution Likelihood ratio test Neyman structure test Two-piece distribution Uniformly most powerful test Uniformly most powerful unbiased test## Notes

### Acknowledgements

The authors would like to place on record their sincere thanks to the anonymous referees and the editor for their most valuable comments and suggestions that have improved the presentation of this manuscript.

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