Bivariate distributions with conditionals satisfying the proportional generalized odds rate model

Abstract

New bivariate models are obtained with conditional distributions (in two different senses) satisfying the proportional generalized odds rate (PGOR) model. The PGOR semi-parametric model includes as particular cases the Cox proportional hazard rate (PHR) model and the proportional odds rate (POR) model. Thus the new bivariate models are very flexible and include, as particular cases, the bivariate extensions of PHR and POR models. Moreover, some well known parametric bivariate models are also included in these general models. The basic theoretical properties of the new models are obtained. An application to fit a real data set is also provided.

Likelihood ratio comparisons and logconvexity properties ofp-spacings from generalized order statistics

“…, 𝛼 𝑛 lead to the model of GOS with parameters 𝑘 = 𝛼 𝑛 and 𝑚 𝑖 = (𝑛 −𝑖 +1)𝛼 𝑖 − (𝑛 −𝑖)𝛼 𝑖+1 −1 (and hence 𝛾 𝑖 = (𝑛 −𝑖 +1)𝛼 𝑖 ). In the literature, (1) is usually referred to the proportional hazard rate assumption (see [17,31] for new extensions of the proportional hazard rate model). We refer the reader to Table 1 of Kamps [23] for complete information on various submodels.…”

“…Indeed, the specific choice of distribution functions with a cdf and positive real numbers lead to the model of GOS with parameters and (and hence ). In the literature, (1) is usually referred to the proportional hazard rate assumption (see [17,31] for new extensions of the proportional hazard rate model). We refer the reader to Table 1 of Kamps [23] for complete information on various submodels.…”