Suppose that N is a Z+-valued random variable and that X,X1, X2, . . . is a sequence of independent and identically distributed Z+ random variables independent of N . In this paper we are interested in properties of the conditional variable Nk D =(N | ∑Nj=1 Xj = k). In particular, we want to know the asymptotic behavior of the conditional mean ENk or the conditional variance var Nk as k → ∞. We...

we prove that the limit of a sequence of pettis integrable bounded scalarly measurable weak random elements, of finite weak norm, with values in the dual of a non-separable banach space is pettis integrable. then we provide basic properties for the pettis conditional expectation, and prove that it is continuous. calculus of pettis conditional expectations in general is very different from the c...

Contents 1. Introduction. 2. The distribution function of a random variable. 3. Classification of random variables. 4. Some special discrete probability distributions. 5. Some special continuous probability distributions. 6. Location characteristics of a real-valued random variable. 7. Dispersion characteristics of a real-valued random variable. 8. Joint distribution functions. 9. Independence ...

In this paper, the two parameter ADK entropy, as a generalized of Re'nyi entropy, is considered and some properties of it, are investigated. We will see that the ADK entropy for continuous random variables is invariant under a location and is not invariant under a scale transformation of the random variable. Furthermore, the joint ADK entropy, conditional ADK entropy, and chain rule of this ent...

Given a probability space (Ω,F , P ), a F -measurable random variable X , and a sub-σ-algebra G ⊂ F , it is well known that the conditional expectation E[X|G] is the optimal L-predictor (also known as “the least mean square error” predictor) of X among all the G-measurable random variables [8, 11]. In this paper, we provide necessary and sufficient conditions under which the conditional expecta...

We show that analogously to classical probability theory the conditional expectation E ( ? ~ X ) of a fuzzy random variable Y w.r.t. a fuzzy random variable X is w.r.t. a suitable metric the best approximation o f ? by measurable functions ofX. Furthermore, several linear regression functions, i.e. best approximation of ? by linear functions o f z and examples for random LR-fuzzy numbers and Ga...

Conditional Random Fields have been successfully applied to a number of NLP tasks like concept tagging, named entity tagging, or grapheme-to-phoneme conversion. When no alignment between source and target side is provided with the training data, it is challenging to build a CRF system with state-of-the-art performance. In this work, we present an approach incorporating an Mto-N alignment as a h...

The task of suggesting recipients for an email has recently received attention as it has potential to enhance the flow of knowledge and information within an organization or social network. We investigate two transfer learning techniques to improve recipient prediction performance through considering predictions for multiple users. We present a novel continuous hidden variable conditional rando...

We present a discriminative latent variable model for classification problems in structured domains where inputs can be represented by a graph of local observations. A hidden-state Conditional Random Field framework learns a set of latent variables conditioned on local features. Observations need not be independent and may overlap in space and time. We evaluate our model on object detection and...