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Table 1 Estimators of the components of the variance of the generalized waring distribution

From: On the distribution theory of over-dispersion

Component due to

Marginal variance ofX

Marginal variance ofY

Variance ofX  + Yentire period

Random factors

a ^ k ^ ρ ^ 1

% a ^ m ^ ρ ^ 1

% a ^ k ^ + m ^ ρ ^ 1

Proneness

% k ^ 2 a ^ a ^ + ρ ^ 1 ρ ^ 1 2 ρ ^ 2

% m ^ 2 a ^ a ^ + ρ ^ 1 ρ ^ 1 2 ρ ^ 2

% k ^ + m ^ 2 a ^ a ^ + ρ ^ 1 ρ ^ 1 2 ρ ^ 2

Liability

% a ^ k ^ a ^ + 1 ρ ^ 1 ρ ^ 2

% a ^ m ^ a ^ + 1 ρ ^ 1 ρ ^ 2

% a ^ k ^ + m ^ a ^ + 1 ρ ^ 1 ρ ^ 2

Total

% a ^ k ^ ρ ^ + k ^ 1 ρ ^ + a ^ 1 ρ ^ 1 2 ρ ^ 2

% a ^ m ^ ρ ^ + m ^ 1 ρ ^ + a ^ 1 ρ ^ 1 2 ρ ^ 2

% a ^ k ^ + m ^ ρ ^ + k ^ + m ^ 1 ρ ^ + a ^ 1 ρ ^ 1 2 ρ ^ 2