The first step is to ensure that the given distribution actually is a valid probability distribution. As mentioned earlier, this involves checking two key properties: non-negativity and summation to ...

Probability theory forms the mathematical backbone for quantifying uncertainty and random events, providing a rigorous language with which to describe both everyday phenomena and complex scientific ...

The world is full of uncertainty: accidents, storms, unruly financial markets, noisy communications. The world is also full of data. Probabilistic modeling and the related field of statistical ...

We consider functions φ having the following properties: φ(0)=1, φ(-t) = φ(t) φ is continuable to a function analytic in the upper halfplane. We discuss the problem under which conditions such a ...

The estimator proposed by Brunk for the indefinite integral of a regression function defined on the unit cube in β dimensional Euclidean space is studied. It is shown to be strongly uniformly ...