The foundations of models of dependence in probabilistic safety assessment

Flexible bivariate beta distributions

“…Indeed, it is possible by judicious choices of values for the α i 's to obtain a correlation equal to any number in the intervals (0, 1) and (−1, 0). This fact can also be seen from the construction of the proposed bivariate beta distribution in (1). For positive correlations, we can consider α 3 = α 4 = 0, i.e., the bivariate beta distribution studied by Olkin and Liu [9], which gives correlations ranging from 0 to 1.…”

“…In particular they are natural choices for use as prior distributions for the parameters of correlated binomial random variables in Bayesian analysis (see, for example, [1]). There are several bivariate beta distributions that have been proposed in the statistics literature, see, for example, [4,5,9,8,7,2,3].…”

Detecting Diagnostic Accuracy of Biomarkers Through a Bivariate Beta Distribution

“…It is most suitable to be assumed as a prior distribution for the correlated binomial variable in Bayesian setup. 39 The prior information of two correlated random variables applied in clinical trials. 40,41…”

Analysis of incomplete data in the presence of dependent competing risks from Marshall–Olkin bivariate Weibull distribution under progressive hybrid censoring

“…For example, in a study of diabetic retinopathy for which the causes of failure (competing risks) were treated, untreated, or both eyes, it was obvious that such causes were dependent (Lin et al, 1999). The dependent characteristic between competing risks is of great importance, and should not be neglected (Apostolakis and Moieni, 1987). Furthermore, independent is a special case of the dependent.…”