ITM Web Conf.
Volume 20, 2018International Conference on Mathematics (ICM 2018) Recent Advances in Algebra, Numerical Analysis, Applied Analysis and Statistics
|Number of page(s)||22|
|Published online||12 October 2018|
Hypothesis Testing on the Location Parameter of a Skew-Normal Distribution (SND) with Application
Department of Mathematics and Statistics, Faculty of Science, Prince of Songkla University, Hatyai, Songkhla, 90110, Thailand
2 Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504, USA
This work deals with testing a hypothesis on the location parameter (μ) of a skew-normal distribution (SND) based on a random sample of size n. The details of this work can be summarized in four major components: (a) First we review some useful results on SND, including the approximate probability distribution of the sample average. (b) Next, we develop several tests to test a hypothesis on μ based on the sample mean when the scale (σ) and shape (λ) parameters are known. (c) The tests for the known scale and shape are then extended for unknown scale and shape. (d) Finally, the test methods have been used for a real-life data set.
Key words: Fisher information / Likelihood ratio test / Neyman-Pearson Lemma / Power function / Size of a test
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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