Independence with Lower and Upper Probabilities

Stochastic independence with respect to upper and lower conditional probabilities deined by Hausdorff outer and inner measures

A new model of coherent upper conditional prevision is proposed in a metric space. It is defined by the Choquet integral with respect to the s-dimensional Hausdorff outer measure if the conditioning event has positive and finite Hausdorff outer measure in its dimension s. Otherwise if the conditioning event has Hausdorff outer measure in its dimension equal to zero or infinity it is defined by ...

Independence with Respect to Upper and Lower Conditional Probabilities Assigned by Hausdorff Outer and Inner Measures

In this paper the notion of s-irrelevance with respect to upper and lower conditional probabilities assigned by Hausdorff outer and inner measures is proved to be a sufficient condition for strong independence introduced for credal sets. An example is given to show that the converse is not true. Moreover the definition of sconditional irrelevance is given and a generalized factorization propert...

Stochastic independence with respect to upper and lower conditional probabilities defined by Hausdorff outer and inner measures

The Concept of Sub-independence and Its Application in Statistics and Probabilities

 Many Limit Theorems, Convergence Theorems and Characterization Theorems in Probability and Statistics, in particular those related to normal distribution , are based on the assumption of independence of two or more random variables. However, the full power of independence is not used in the proofs of these Theorems, since it is the distribution of summation of the random variables whic...

Exact maximum coverage probabilities of confidence intervals with increasing bounds for Poisson distribution mean

 ‎A Poisson distribution is well used as a standard model for analyzing count data‎. ‎So the Poisson distribution parameter estimation is widely applied in practice‎. ‎Providing accurate confidence intervals for the discrete distribution parameters is very difficult‎. ‎So far‎, ‎many asymptotic confidence intervals for the mean of Poisson distribution is provided‎. ‎It is known that the coverag...

Independence and 2-Monotonicity: Nice to Have, Hard to Keep

When using lower probabilities to model uncertainty about the value assumed by a variable, 2-monotonicity is an interesting property to satisfy, as it greatly facilitates further treatments (such as the computation of lower/upper expectation bounds). In this paper, we show that multivariate joint models induced from marginal ones by strong independence, epistemic independence or epistemic irrel...