Sampling Distribution for the K-Th Order Statistics from the Generalized Gumbel Distribution | ||||
| The Egyptian Statistical Journal | ||||
| Article 1, Volume 48, Issue 1, June 2004, Page 1-11 PDF (4.75 MB) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/esju.2004.313568 | ||||
 View on SCiNiTO | ||||
| Author | ||||
Amal S. Hassan  
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| Institute of Statistical Studies & Research, Cairo University | ||||
| Abstract | ||||
| This article is concerned with the sampling distribution of the k-th order statistics of the generalized Gumbel distribution with one shape parameter 2 suggested by Adeyemi (2002). Focusing on the moments for the k-th order statistics numerical solutions we obtained for different values of the shape parameter and different sample sizes (small, moderate and large) using Mathcad statistical package (2001). Pearson system technique is used to fit a suitable distribution for the k-th order statistics. Regardless of the values of the shape parameter and the sample sizes, the fitting distributions for the smallest and the largest order statistics are Pearson type I and IV respectively, while if k = n-1 the best fit is a Pearson type VI. Part of the numerical results and some graphs for some sampling distributions are displayed at the appendix. | ||||
| Keywords | ||||
| Generalized Gumbel Distribution - Order Statistics; Moments - Pearson Curve | ||||
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