An Enriched α − μ Model as Fading Candidate

Abstract

This paper introduces an enriched α − μ distribution which may act as fading model with its origins via the scale mixture construction. The distribution’s characteristics are visited and its feasibility as a fading candidate in wireless communications systems is investigated. The analysis of the system reliability and some performance measures of wireless communications systems over this enriched α − μ fading candidate are illustrated. Computable representations of the Laplace transform for this scale mixture construction are also provided. The derived expressions are explored via numerical investigations. Tractable results are computed in terms of the Meijer G-function. This unified scale mixture approach allows access to previously unconsidered underlying models that may yield improved fits to experimental data in practice.

A Bivariate Beta from Gamma Ratios for Determining a Potential Variance Change Point: Inspired from a Process Control Scenario

“…The proposed model compares favourably with the Q chart model studied by [5] in most situations; especially when the number of samples is small, and when the process variance experiences a change early on in the series of samples. Future work can include focus on (i) when a shift occurs within a sample, (ii) expanding underlying distributional assumptions to that of the class of scale mixtures to consider departures from normality (see [11]), and (iii) the multivariate setup, of which we propose the probability density function in the following theorem and a proof outlined in the Appendices A and B. Theorem 4. Let W i be independent gamma random variables with parameters (α i > 0,…”

“…197.8, to (A4), the result in (12) follows. From (11), by rearranging the terms, and applying [6] p. 25, Equations (1).110 and 1.111 twice, it follows that…”

“…In this section a shape analysis is conducted for the joint probability density function (11). A standard set of parameters has been chosen as a baseline.…”

“…Theorem 2. Assume that (U 1 , U 2 ) has the joint probability density function in (11), then the marginal probability density function of U 1 is given by…”

“…Assume that (U 1 , U 2 ) has the joint probability density function (11), then the maximum order statistic of U 1 and U 2 can be determined either by…”