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Analysing autoregressive counts over time remains a relevant and evolving matter of interest, where oftentimes the assumption of normality is made for the error terms. In the case when data are discrete, the Poisson model may be assumed for the structure of the error terms. In order to address the equidispersion restriction of the Poisson distribution, various alternative considerations have been investigated in such an integer environment. This paper, inspired by the integer autoregressive process of order 1, incorporates negative binomial shape mixtures via a compound Poisson Lindley model for the error terms. The systematic construction of this model is offered and motivated, and is analysed comparatively against common alternate candidates with a number of simulation and data analyses. This work provides insight into noncentral-type behaviour in both the continuous Lindley model and in the discrete case for meaningful application and consideration in integer autoregressive environments. [ABSTRACT FROM AUTHOR]

Within statistical process control (SPC), normality is often assumed as the underlying probabilistic generator where the process variance is assumed equal for all rational subgroups. The parameters of the underlying process are usually assumed to be known—if this is not the case, some challenges arise in the estimation of unknown parameters in the SPC environment especially in the case of few observations. This paper proposes a bivariate beta type distribution to guide the user in the detection of a permanent upward or downward step shift in the process' variance that does not directly rely on parameter estimates, and as such presents itself as an attractive and intuitive approach for not only potentially identifying the magnitude of the shift, but also the position in time where this shift is most likely to occur. Certain statistical properties of this distribution are derived and simulation illustrates the theoretical results. In particular, some insights are gained by comparing the newly proposed model's performance with an existing approach. A multivariate extension is described, and useful relationships between the derived model and other bivariate beta distributions are also included. [ABSTRACT FROM AUTHOR]

Entropy indicates a measure of information contained in a complex system, and its estimation continues to receive ongoing focus in the case of multivariate data, particularly that on the unit simplex. Oftentimes the Dirichlet distribution is employed as choice of prior in a Bayesian framework conjugate to the popular multinomial likelihood with K distinct classes, where consideration of Shannon- and Tsallis entropy is of interest for insight detection within the data on the simplex. However, this prior choice only accounts for negatively correlated data, therefore this paper incorporates previously unconsidered mixtures of Dirichlet distributions as potential priors for the multinomial likelihood which addresses the drawback of negative correlation. The power sum functional, as the product moment of the mixture of Dirichlet distributions, is of direct interest in the multivariate case to conveniently access the Tsallis- and other generalized entropies that is incorporated within an estimation perspective of the posterior distribution using real economic data. A prior selection method is implemented to suggest a suitable prior for the consideration of the practitioner; empowering the user in future for consideration of suitable priors incorporating entropy within the estimation environment as well as having the option of certain mixture of Dirichlet distributions that may require positive correlation. [ABSTRACT FROM AUTHOR]

This research is inspired from monitoring the process covariance structure of q attributes where samples are independent, having been collected from a multivariate normal distribution with known mean vector and unknown covariance matrix. The focus is on two matrix random variables, constructed from different Wishart ratios, that describe the process for the two consecutive time periods before and immediately after the change in the covariance structure took place. The product moments of these constructed random variables are highlighted and set the scene for a proposed measure to enable the practitioner to calculate the run-length probability to detect a shift immediately after a change in the covariance matrix occurs. Our results open a new approach and provides insight for detecting the change in the parameter structure as soon as possible once the underlying process, described by a multivariate normal process, encounters a permanent/sustained upward or downward shift. [ABSTRACT FROM AUTHOR]

A cornerstone in the modeling of wireless communication is MIMO systems, where a complex matrix variate normal assumption is often made for the underlying distribution of the propagation matrix. A popular measure of information, namely capacity, is often investigated for the performance of MIMO designs. This paper derives upper bounds for this measure of information for the case of two transmitting antennae and an arbitrary number of receiving antennae when the propagation matrix is assumed to follow a scale mixture of complex matrix variate normal distribution. Furthermore, noncentrality is assumed to account for LOS scenarios within the MIMO environment. The insight of this paper illustrates the theoretical form of capacity under these key assumptions and paves the way for considerations of alternative distributional choices for the channel propagation matrix in potential cases of severe fading, when the assumption of normality may not be realistic. [ABSTRACT FROM AUTHOR]