This paper gives a PDE for multi-time joint probability of the Airy process, which generalizes Adler and van Moerbeke’s result on the 2-time case. As an intermediate step, the PDE for the multi-time joint probability of the Dyson Brownian motion is also given.

Following [9] some properties of Q-probability and Q-states are studied. Representation theorem of Q-probabilities and Q-states, the existence of the joint observable and The central limit theorem are proved. Keywords—Q-probability, Q-state, representation theorem, intuitionistic fuzzy events, joint Q-observable, Central limit theorem.

The Lower Rhine Delta, a transitional area between the River Rhine and Meuse and the North Sea, is at risk of flooding induced by infrequent events of a storm surge or upstream flooding, or by more infrequent events of a combination of both. A joint probability analysis of the astronomical tide, the wind induced storm surge, the Rhine flow and the Meuse flow at the boundaries is established in ...

Joint quantum measurements of non-commuting observables are possible, if one accepts an increase in the measured variances. A necessary condition for a joint measurement to be possible is that a joint probability distribution exists for the measurement. This fact suggests that there may be a link with Bell inequalities, as these will be satisfied if and only if a joint probability distribution ...

This chapter is a brief introduction to two important statistical methods— maximum likelihood estimation and hypothesis testing. We shall show how to use these methods to test the biological sequence models developed in previous chapters against experimental data. We shall also show how hypothesis testing ideas inspire scoring methods for sequence alignment. denote the outcome of an experiment ...

Modeling of a large joint probability table is problematic when its variables have a large number of categories. In such a case, a mixture of simpler probability tables could be a good model. And the estimation of such a large probability table frequently has another problem of data sparseness. When constructing mixture models with sparse data, EM estimators based on the β-likelihood are expect...

Prediction of the performance of international joint ventures remains a relatively underresearched area, yet its importance is well recognized due to the tremendous surge in joint venture activities in the past decade. Data on 1,463 Sino–Hong Kong joint ventures were gathered and those that appeared on the Honor Roll of the China Association of Enterprises with Foreign Investment are identified...

This chapter is a brief introduction to two important statistical methods— maximum likelihood estimation and hypothesis testing. We shall show how to use these methods to test the biological sequence models developed in previous chapters against experimental data. We shall also show how hypothesis testing ideas inspire scoring methods for sequence alignment. denote the outcome of an experiment ...

Axiomatically, the definition of the joint prob­ ability of several continuous variables is based on a cumulative distribution function, F(x, y, z, K), whose properties are analogous to the case of a single variable, and the probability density function derives from it. However, in practice, the probability P is never defined from a cumulative function, F, but from a density function, f, assum­...