Limit Theorems for Lower-Upper Extreme Values from Two-Dimensional Distribution Function
Barakat, H. (1988). Limit Theorems for Lower-Upper Extreme Values from Two-Dimensional Distribution Function. EKB Journal Management System, 32(2), 153-167. doi: 10.21608/esju.1988.316570
H. M. Barakat. "Limit Theorems for Lower-Upper Extreme Values from Two-Dimensional Distribution Function". EKB Journal Management System, 32, 2, 1988, 153-167. doi: 10.21608/esju.1988.316570
Barakat, H. (1988). 'Limit Theorems for Lower-Upper Extreme Values from Two-Dimensional Distribution Function', EKB Journal Management System, 32(2), pp. 153-167. doi: 10.21608/esju.1988.316570
Barakat, H. Limit Theorems for Lower-Upper Extreme Values from Two-Dimensional Distribution Function. EKB Journal Management System, 1988; 32(2): 153-167. doi: 10.21608/esju.1988.316570

Limit Theorems for Lower-Upper Extreme Values from Two-Dimensional Distribution Function

The Egyptian Statistical Journal
Article 6, Volume 32, Issue 2, December 1988, Page 153-167  XML
Document Type: Original Article
DOI: 10.21608/esju.1988.316570
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Author
H. M. Barakat
Abstract
The limiting distribution of the random vector
(V̅_(k,k^':n) - b̅_n) / a̅_n = (X_(1,k:n) - b₁ₙ) / a₁ₙ, (X_(2,n-k^'+1:n) - b₂ₙ) / a₂ₙ
 
k and k' being constants, are investigated, necessary and sufficient conditions for waking convergence of the distribution of the above vector are obtained. The conditions under which the components of the vector (V̅_(k,k^':n) - b̅_n) / a̅_n  are asymptotically independent are also obtained. Some cases are examined when the number of observations is a random variable.
Keywords
Convergence; Extreme Values; Limit Theorems; Necessary and Sufficient Conditions; Two; Dimensional Distribution Function
Statistics
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