Scaling up the number of base stations per unit area and augmenting the heterogeneity of networks are two major trends in mobile cellular systems of the fourth (4G)- and fifth generation (5G), making it increasingly difficult to characterize aggregate interference statistics with system models that are characterized by a low number of parameters. This paper proposes a new circular interference model that aggregates given interferer topologies to power profiles along circles. We introduce a mapping procedure that preserves the aggregate interference statistics at arbitrary user locations within the associated cell with a certain desired accuracy. At the same time, our method identifies the amount of nodes in a given interferer topology that principally determine the shape of the interference distribution. To further refine the analysis of given power profiles, a new finite sum representation for the sum of Gamma random variables with integer-valued shape parameter is introduced. The approach allows decomposing the distribution of the aggregate interference into the contributions of the individual interferers. Such knowledge is particularly expedient for the application of base station coordination- and cooperation schemes. Moreover, the proposed method enables accurate prediction of the corresponding signal-to-interference-ratio- and rate statistics.

A Circular Interference Model for Heterogeneous Cellular Networks

Exact posterior computation in non-conjugate Gaussian location-scale parameters models

In general, data measurements of continuous data such as volume, time, and length are always imprecise real numbers (Viertl (2011)). More specifically, quantities related to environment such as amounts of chemicals released to the environment, flood levels and Snowfall precipitation are always imprecise data. In this paper, we are interested in conducting statistical analysis for a flood data set taking in consideration that the data is imprecise and using the generalized inverse Lindley distribution. The analysis includes both maximum likelihood and Bayesian estimation. The maximum likelihood estimates are found by utilizing two algorithms; the Newton-Raphson and expectation maximization algorithms. The three proposed methods for estimating the parameters of the generalized Lindley distribution are applied then to the flood dataset where approximately equal estimates are obtained.

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Statistical analysis for an imprecise flood dataset using the generalized inverse Lindley distribution

A new generalized extended inverse Gaussian density function involving a confluent hypergeometric function is defined. Closed form representations of a generalized extended inverse Gaussian density function and the corresponding moment generating function are provided in terms of Meijer’s G-function. Some other statistical functions which are associated with the proposed distribution are also derived. Many distributions can be obtained as limiting cases of the proposed density function. This density is utilized to model an actual data set. The new distribution provides a better fit than related distributions as measured by the Anderson-Darling and Cramer-von Mises statistics. The proposed distribution could, for instance, find applications in the physical and biological sciences and in particular be helpful to researchers working in special functions as well as reliability analysis, survival models and diffraction theory.

A confluent hypergeometric generalized inverse gaussian distribution

A lot of work has been done on products and ratios of random variables by Provost and his co-workers, see, for example, Provost [S.B. Provost, The exact distribution of the ratio of a linear combination of chi-square variables over the root of a product of chi-square variables, Canad. J. Statist. 14 (1986), pp. 61–67; S.B. Provost, The distribution function of a statistic for testing the equality of scale parameters in two gamma populations, Metrika 36 (1989), pp. 337–345]. Here, we extend this idea by introducing a pathway model. The exact density functions of the products of pathway random variables are obtained using the Mellin transform technique. Their computable series forms are derived. The particular cases of the derived results are shown to be associated with the thermonuclear functions and reaction rate probability integral in the theory of nuclear reaction rate, Kratzel integral in applied analyses and inverse Gaussian density in stochastic processes. Graphical representations of the density fu...

Distribution of products of independently distributed pathway random variables

Sums of gamma random variables have been utilized for modeling purposes in connection with problems arising in engineering, queueing theory and communication theory, among other areas of application. Particular attention is paid in this paper to linear combinations of chi-square random variables, as quadratic forms in central normal vectors possess such a structure and several test statistics encountered in multivariate analysis are asymptotically so distributed. The inverse Mellin transform technique is employed to derive the exact density function of a weighted sum of independently distributed chi-square random variables. Three numerical examples attest to the validity and applicability of the resulting representation of the density function.

The Exact Density Function of a Sum of Independent Gamma Random Variables as an Inverse Mellin Transform

This article proposes a five-parameter exponential-type distribution whose exact moments and normalizing constant are obtained as inverse Mellin transforms and expressed as generalized hypergeometric functions. Several commonly used statistical distributions such as the gamma, Weibull and half-normal turn out to be particular cases of this generalized distribution. It is shown in a numerical example that the proposed distribution produces a better fit than the Weibull or inverse Gaussian distributions when used for modeling a data set consisting of maximum flood levels over a certain time period.

A generalized exponential-type distribution

The generalized inverse Gaussian distribution which was popularized in the late seventies by Ole Barndorff-Neilsen is extended in this paper by incorporating an additional parameter in its density function. A reduced version of the resulting model is also being considered. The effects of the parameters are described for both distributions. Additionally, several of their statistical functions are provided. Data sets pertaining to maximum flood levels and snowfall precipitations were fitted with several statistical models for comparison purposes.

Iman Mabrouk

Papers

The Exact Density Function of a Sum of Independent Gamma Random Variables as an Inverse Mellin Transform

A generalized exponential-type distribution

An Extended Inverse Gaussian Model