In those cases, the likelihood function no longer approximates a normal distribution, especially in the case of relatively small sample size.
Despite the title, our algebras are often allowed to have no approximate identity.
No approximating assumptions are needed other than the usual assumption of a linear elastic system modelled by finite elements.
( q ̃ i, q ̃ j ) is the best matched point pair of (p i, p j ) with the best similarity score in Equation 3. Notice that if no approximate congruent match ( q ̃ i, q ̃ j ) is found, we set the probability value to zero, i.e., S p (p i, p j ) = 0.
The driver variables studied were: tobacco consumption (yes, no), approximate age (18 34, 35 64, and ≥65 years) and sex (male, female).
Therefore, no approximate heuristics are necessary to efficiently apply the ME principle by evaluating all possible topological locations for read r.
It was found that the forecast uncertainties increased for greater earthquakes (e.g., M w > 8) because the tsunami source was no longer approximated as a point source for such earthquakes.
It is also found that the forecast uncertainties become larger for greater earthquakes because the tsunami source is no longer approximated as a point source for greater earthquakes (e.g., M w > 8).
Because the percentage of people using a denture/bridge was high (males: 68.1%, females: 67.6%), adjusted odds ratio derived from the logistic regression could no longer approximate PR [ 21].
When the outcome of interest, such as the percentage of fatal cases in the AMI case fatality rate, exceeds 10%, or if the odds ratio is greater than 2.5 or less than 0.5, the estimation of the relative risk by the adjusted odds ratios, derived from the logistic regression no longer adequately approximates the relative risk, which may become heavily biased.
