Conditioning relation reduces the variability domain of bivariate probability law by one dimension and identifies a sub-domain L of existence of a couple of possible values for parameters based on TRT measures.
We illustrate the methodology developed by examples, obtaining two extended versions of the bivariate Gumbel's law.
The I-PCM method employs a simple modification of bivariate integrals based on the additive law of probability.
Using (3.23) and (3.24) we can show that the order statistics of the components of a random vector from a bivariate t distribution obey the skew t law.
In their Theorem 1, Arnold and Lin (2004) showed that the order statistics of the components of a random vector from a bivariate normal distribution obey the skew-normal law.
The study of the rule of law index subfactors showed that in bivariate regressions, all eight subindices were significantly associated with IMR, MMR, CVMR+DMR and LE (table 3).
We used bivariate pair correlation functions (Illian et al. 2008; Law et al. 2009), with associated confidence envelopes, to quantify the spatial positioning of sets of points (two sets at a time), relative to each other.
All other rule of law measures were associated with all the health outcomes in bivariate analysis, but not all of these associations were robust when possible confounders (GDP per capita, health expenditure, freedom, Gini coefficient and status of women) were introduced (table 4).
Fourth, bivariate and multivariate regression models of the health outcomes on the rule of law subindices were completed.
If a woman had negative reactions to the infant from her husband (p = 0.05), the woman's own mother (p = 0.02) and her mother in law (p = 0.01) were all associated with higher EPDS score in bivariate analysis, as were intimate partner violence, and being frightened of your husband or family (p < 0.001).
