For each distribution, I give the name of the distribution along with one or two parameters and indicate whether it is a discrete distribution or a continuous one. Then I describe an example interpretation for a random variable X having that distribution. Each discrete distribution is determined by a probability mass function f which gives the probabilities for the various outcomes, so that f(x...

In this paper, we present an overview of basic parametric probability distributions which are frequently used in reliability. We present some main characteristics of these distributions, and briefly discuss underlying assumptions related to their suitability as models for specific reliability scenarios.

In this paper, we attempt to answer the three questions about the invariant probability distribution for stochastic matrices: (1) does every stochastic matrix have an invariant probability distribution?; (2) is the invariant probability distribution unique?; and (3) when can we conclude that the power of a stochastic matrix converges? To answer these questions, we present the Perron-Frobenius T...

In this current paper the following problems are addressed: (1) extending the knowledge of a partially known probability distribution function to any point of a continuous sample space, (2) constructing an imprecise probability distribution based on the knowledge of a set of credible or confidence intervals, and (3) computing the lower and upper expected values of a random continuous variable. ...

Manipulating probability distributions is central to data compression, so it is natural to ask how well we can compress probability distributions themselves. For example, this is useful for probabilistic reasoning [2] and query optimization [6]. Our interest in it stems from designing single-round asymmetric communication protocols [1,4]. Suppose a server with high bandwidth wants to help a cli...

The conflation of a finite number of probability distributions P1, . . . , Pn is a consolidation of those distributions into a single probability distribution Q = Q(P1, . . . , Pn), where intuitively Q is the conditional distribution of independent random variables X1, . . . ,Xn with distributions P1, . . . , Pn, respectively, given that X1 = · · · = Xn. Thus, in large classes of distributions ...

This paper combines the novel concept of Fuzzy Gaussian Inference(FGI) with Genetic Programming (GP) in order to accurately classify real natural 3d human Motion Capture data. FGI builds Fuzzy Membership Functions that map to hidden Probability Distributions underlying human motions, providing a suitable modelling paradigm for such noisy data. Genetic Programming (GP) is used to make a time dep...

The validity of the normal distribution as an error model is commonly tested with a (half) normal probability plot. Real data often contain outliers. The use of t-distributions in a probability plot to model such data more realistically is described. It is shown how a suitable value of the parameter nu of the t-distribution can be determined from the data. The results suggest that even data tha...

The volume of cold tap water consumed is an essential element in quantitative microbial risk assessment. This paper presents a review of tap water consumption studies. Study designs were evaluated and statistical distributions were fitted to water consumption data from The Netherlands, Great Britain, Germany and Australia. We conclude that the diary is to be preferred for collecting water consu...

Dubois and Prade introduced the mean value of a fuzzy number as a closed interval bounded by the expectations calculated from its upper and lower distribution functions. In this paper introducing the notations of lower possibilistic and upper possibilistic mean values we definine the interval-valued possibilistic mean and investigate its relationship to the interval-valued probabilistic mean. W...