In this paper, we discuss a new stochastic diffusion process in which the trend function is proportional to Lomax density function. This distribution arises naturally studies of frequency extremely rare events. We first consider probabilistic characteristics proposed model, including its analytic expression as unique solution differential equation, transition probability together with condition...

For a large class of additive random utility discrete choice models with income effects, we compute the probability distribution of the compensating variation. We show that the cumulative distribution function only depends on the choice probabilities. Our results are used to compute the distribution of equivalent variation. The moments of the compensating variation are a onedimensional integral...

We describe a Gröbner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely conditional case, and other special cases. We also investigate the connection to generalized permutohedra and describe a “conditional probability simplex.” 1 Relations...

Although the random sum distribution has been well-studied in probability theory, inference for the mean of such distribution is very limited in the literature. In this paper, two approaches are proposed to obtain inference for the mean of the Poisson-Exponential distribution. Both proposed approaches require the log-likelihood function of the Poisson-Exponential distribution, but the exact for...

The AIS-BN algorithm [2] is a successful importance sampling-based algorithm for Bayesian networks that relies on two heuristic methods to obtain an initial importance function: 2-cutoff , replacing small probabilities in the conditional probability tables by a larger 2, and setting the probability distributions of the parents of evidence nodes to uniform. However, why the simple heuristics are...

Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation. A novel description of normalisation is given as a mathematically well-behaved total function. The output of this ‘hyper’ normalisation operation is a distr...

Abstract In this paper, we introduce the newly generated Ristić–Balakrishnan–Topp–Leone–Gompertz-G family of distributions. Statistical and mathematical properties new including moments, moment generating function, incomplete conditional probability weighted distribution order statistics, stochastic ordering, Rényi entropy are derived. The unknown parameters inferred using maximum likelihood es...

We consider the characterization of muscle fatigue through noninvasive sensing mechanism such as surface electromyography (SEMG). While changes in the properties of SEMG signals with respect to muscle fatigue have been reported in the literature, the large variation in these signals across different individuals makes the task of modeling and classification of SEMG signals challenging. Indeed, t...