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