In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function P(x, t) of finding the walker at position x at time t is completely determined by the Lapla...

A vector-valued random variable X = X 1 · · · X n T is said to have a multivariate normal (or Gaussian) distribution with mean µ ∈ R n and covariance matrix Σ ∈ S n ++ 1 if its probability density function 2 is given by p(x; µ, Σ) = 1 (2π) n/2 |Σ| 1/2 exp − 1 2 (x − µ) T Σ −1 (x − µ). We write this as X ∼ N (µ, Σ). In these notes, we describe multivariate Gaussians and some of their basic prope...

Randomisation schemes are rules that assign patients to treatments in a clinical trial. Many of these schemes have the common aim of maintaining balance in the numbers of patients across treatment groups. The properties of imbalance that have been investigated in the literature are based on two treatment groups. In this paper, their properties for K > 2 treatments are studied for two randomisat...

In this paper, we consider admissible estimation of the parameter ?r in the gamma distribution with truncated parameter space under entropy loss function. We obtain the classes of admissible estimators. The result can be applied to estimation of parameters in the normal, lognormal, pareto, generalized gamma, generalized Laplace and other distributions.

This study compares the classification ability of various fusion algorithms (average, majority vote, median, max/min) when individual classifiers are potentially correlated. A logistic transformation of multivariate normal distribution (MVN) is used to generate the posterior probability estimates, assuring that the probability exists between 0 and 1. With varying parameters of MVN and number of...