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On the power of Gini index-based goodness-of-fit test for the Inverse Gaussian distribution | ||
| Journal of Mahani Mathematical Research | ||
| دوره 14، شماره 1 - شماره پیاپی 31، فروردین 2025، صفحه 1-22 اصل مقاله (616.21 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2023.22215.1513 | ||
| نویسندگان | ||
| Hadi Alizadeh Noughabi* 1؛ Mohammad Shafaei Noughabi2 | ||
| 1Department of Statistics, University of Birjand, Birjand, Iran | ||
| 2Department of Mathematics and Statistics, University of Gonabad, Gonabad, Iran | ||
| چکیده | ||
| The Inverse Gaussian distribution finds application in various fields, such as finance, survival analysis, psychology, engineering, physics, and quality control. Its capability to model skewed distributions and non-constant hazard rates makes it a valuable tool for understanding a wide range of phenomena. In this paper, we present a goodness-of-fit test specifically designed for the Inverse Gaussian distribution. Our test uses an estimate of the Gini index, a statistical measure of inequality. We provide comprehensive details on the exact and asymptotic distributions of the newly developed test statistic. To facilitate the application of the test, we estimate the unknown parameters of the Inverse Gaussian distribution using maximum likelihood estimators. Monte Carlo methods are utilized to determine the critical points and assess the actual sizes of the test. A power comparison study is conducted to evaluate the performance of existing tests. Comparing its powers with those of other tests, we demonstrate that the Gini index-based test performs favorably. Finally, we present a real data analysis for illustrative purposes. | ||
| کلیدواژهها | ||
| Gini index؛ Type-I error؛ Critical points؛ Test power؛ Monte Carlo simulation | ||
| مراجع | ||
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