A useful discrete distribution (the Conway–Maxwell–Poisson distribution) is revived and its statistical and probabilistic properties are introduced and explored. This distribution is a two-parameter extension of the Poisson distribution that generalizes some well-known discrete distributions (Poisson, Bernoulli and geometric). It also leads to the generalization of distributions derived from th...

The relationship between the norm square of the standardized cumulative distribution and the chi-square statistic is examined using the form of the covariance matrix as well as the projection perspective. This investigation enables us to give uncorrelated components of the chi-square statistic and provide interpretation of these components as innovations standardizing the cumulative distributio...

In this paper, we propose and study fitting algorithms for MMPP(2) and CMPP ATM traffic models, which are special cases of Markov Modulated Poisson Processes (MMPP). Two fitting algorithms, both based on the cell interarrival times, are considered for the MMPP(2) model: one fits the cumulative distribution and auto-covariance functions and other fits the first three moments and auto-covariance ...

This paper describes a visual interactive procedure for fitting beta distributions to activity times in a simulation model when sample data are not available for statistical analysis of the model's input processes. Using subjective information about a given activity time the modeler specifies the activity's minimum and maximum times together with two of the following characteristics: mode, mean...

In the resonance theory, the radial dilatation is emphasized, and the blood pressure wave is transmitted in the form of “moving windkessel”. Based on this conjecture, we developed a semi-empirical procedure to describe the pressure distribution in a complex simulated model composed of a main tube and attached organs. Now we try to apply this fitting method to hemodynamics in vivo, and we tested...

Identifying the underlying models in a set of data points contaminated by noise and outliers, leads to a highly complex multi-model fitting problem. This problem can be posed as a clustering problem by the projection of higher order affinities between data points into a graph, which can then be clustered using spectral clustering. Calculating all possible higher order affinities is computationa...

Material models are essential to the production of photo-realistic images. Measured BRDFs provide accurate representation with complex visual appearance, but have larger storage cost. Analytical BRDFs such as CookTorrance provide a compact representation but fail to represent the effects we observe with measured appearance. Accurately fitting an analytical BRDF to measured data remains a challe...

Because the application of surface fitting algorithms exerts a considerable fuzzy influence on the mathematical features of kinetic energy distribution, their relation mechanism in different external conditional parameters must be quantitatively analyzed. Through determining the kinetic energy value of each selected representative position coordinate point by calculating kinetic energy paramete...

The paper presents the results of a case study fitting the generalized Pareto distribution to insurance industry claims data. Besides classical parametric procedures, robust statistical concepts are considered. The latter provide instruments to assess the characteristics of estimators also in the neighborhood of parametric models. A demand for robust methods may arise in cases of fitting distri...