Clearly, there is a delicate balance that must be struck between the formulation of the probability axioms, and the understanding of 'bets' and 'sure loss' for the Dutch Book theorem and its converse to hold.
In this article, a general formulation of the probability weighted moments of the Weibull Distribution is presented in order to estimate the parameters mentioned above.
Model uncertainty is also acknowledged through numerical stabilisation measures by including a nugget term in the formulation of the probability model.
Similarly, the independent random variables are used in the formulation of the probability of detecting a crack, described in Eq. (3).
The former method combines a logistic formulation for the probability of occurrence of an event with a proportional hazards specification for the time of occurrence of the event [ 7- 13], so that the effects of the treatment and other factors can be interpreted separately into those on the proportion of cured patients and the failure time of uncured patients.
In this paper, to analyse data including such a long-term censored relapse-free time, we discuss a semi-parametric cure regression (Cox cure regression), which combines a logistic formulation for the probability of occurrence of an event with a Cox proportional hazards specification for the time of occurrence of the event.
Two alternative formulations of the total suicide probability can be considered: on the one hand, if AI-dependent cell death is not affected by the maximum suicide efficacy, then pCD total = pCD + q * pAI * (1 − pCD); on the other hand, if the maximum suicide efficacy CD max also limits AI-dependent cell death, then pCD total = pCD + q * pAI * (CD max − pCD).
The proposed formulation of the classic Probability Density Evolution Method reduces the corresponding Generalized Density Evolution equations, which are partial differential equations, to a system of ordinary differential equations, that can be efficiently solved with the method of characteristics.
Moreover, the analytical formulation of these probabilities is practically confirmed by using an importance sampling method, a Monte Carlo strategy of numerical simulation that can be used to compute rare events.
