Acyclic phase-type distributions form a versatile model, serving as approximations to many probability distributions in various circumstances. They exhibit special properties and characteristics that usually make their applications attractive. Compared to acyclic continuous phase-type (ACPH) distributions, acyclic discrete phase-type (ADPH) distributions and their subclasses (ADPH family) have ...

In applications there occur different forms of uncertainty. The twomost important types are randomness (stochastic variability) and imprecision(fuzziness). In modelling, the dominating concept to describe uncertainty isusing stochastic models which are based on probability. However, fuzzinessis not stochastic in nature and therefore it is not considered in probabilisticmodels.Since many years t...

We propose a dynamic program to find the shortest path in a network having gamma probability distributions as arc lengths. Two operators of sum and comparison need to be adapted for the proposed dynamic program. Convolution approach is used to sum two gamma probability distributions being employed in the dynamic program.

In this paper we consider a location model based on the threshold concept. We find the best location such that the probability of revenues falling short of the threshold is minimized. This objective is appropriate when a firm will not survive if its revenues fall below a known threshold. A new store is to be located. Demand is not deterministic but rather has a statistical distribution. We seek...

A cumulative distribution function (CDF) states the probability that a sample of a random variable will be no greater than a value x, where x is a real value. Closed form expressions for important CDFs have parameters, such as mean and variance. If these parameters are not point values but rather intervals, sharp or fuzzy, then a single CDF is not specified. Instead, a family of CDFs is specifi...

In this journal, a “hybrid method” was proposed for the joint propagation of probability distributions (expressing variability) and possibility distributions (i.e., fuzzy numbers, expressing imprecision or partial ignorance) in the computation of risk. In order to compare the results of the hybrid computation (a random fuzzy set) to a tolerance threshold (a tolerable level of risk), a post-proc...

In this paper, fuzzy quantitative models of language statistics are constructed. All suggested models are based on the assumption about a superposition of two kinds of uncertainties: probabilistic and possibilistic. The realization of this superposition in statistical distributions is achieved by the probability measure splitting procedure. In this way, the fuzzy versions of generalized binomia...

In this paper, the reconcilability between the P-value and the posterior probability in testing a point null hypothesis against the one-sided hypothesis is considered. Two essential families, non regular and exponential family of distributions, are studied. It was shown in a non regular family of distributions; in some cases, it is possible to find a prior distribution function under which P-va...

Traditional statistical data processing techniques (such as Least Squares) assume that we know the probability distributions of measurement errors. Often, we do not have full information about these distributions. In some cases, all we know is the bound of the measurement error; in such cases, we can use known interval data processing techniques. Sometimes, this bound is fuzzy; in such cases, w...

For modelling imprecise data the literature offers two different methods: either the use of probability distributions or the use of fuzzy sets. In our opinion these two concepts should be used parallel or combined, dependent on the real situation. Moreover, in many economic problems the well-known probabilistic or fuzzy solution procedures are not suitable methods because neither the stochastic...