Showing papers by "Barry C. Arnold published in 2019"
01 Jan 2019
11 citations
TL;DR: A stochastic representation of the epsilon–skew–Cauchy distribution is considered, viewed as a member of the family of skewed distributions discussed in Arellano-Valle et al. (2005).
Abstract: In this paper, we consider a stochastic representation of the epsilon–skew–Cauchy distribution, viewed as a member of the family of skewed distributions discussed in Arellano-Valle et al. (2005). The stochastic representation facilitates derivation of distributional properties of the model. In addition, we introduce symmetric and asymmetric extensions of the Cauchy distribution, together with an extension of the epsilon–skew–Cauchy distribution. Multivariate versions of these distributions can be envisioned. Bivariate examples are discussed in some detail.
2 citations
01 Jan 2019
TL;DR: In this article, the authors present a number of l.r.t.v.d. statistics used in multivariate analysis, both for real and complex random variables, whose exact distributions are particular cases of the products of independent Beta r.f.
Abstract: In this chapter the authors present a number of l.r.t. statistics used in Multivariate Analysis, both for real and complex random variables, whose exact distributions are particular cases of the products of independent Beta r.v.’s in Theorems 3.1– 3.3 in Chap. 3, and whose p.d.f.’s and c.d.f.’s have thus their expressions given by Corollaries 4.1– 4.5 in the previous chapter.
1 citations
01 Jan 2019
TL;DR: In this chapter details are given on the packages programmed in MathematicaⓇ, Maxima, and R for the implementation of all the tests addressed in Chap.
Abstract: In this chapter details are given on the packages programmed in MathematicaⓇ, Maxima, and R for the implementation of all the tests addressed in Chap. 5. Functions and modules were developed for several tasks such as the computation of p-values and quantiles for each test and to obtain the computed value of the statistics and corresponding p-values from data stored in a data file. As such, also functions and modules used to read these data files, which may have several different internal structures, were programmed. Details are given on the use of all functions and modules, and comparisons are established among the three packages. The full content of all three packages is available on the book’s supplementary material web site.
01 Jan 2019
TL;DR: In this paper, the authors consider three multiple products of independent Beta random variables which are shown to have equivalent representations as the exponential of sums of independent integer Gamma r.v. distributions, and as such have finite form representations for their distributions.
Abstract: In this chapter the authors consider three multiple products of independent Beta random variables which are shown to have equivalent representations as the exponential of sums of independent integer Gamma r.v.’s, and as such have finite form representations for their distributions.
01 Jan 2019
TL;DR: In this chapter the authors use the results in the three theorems in the previous chapter to obtain the p.d.f. and c.v.f’s of all the products of independent Beta r.c.f., this way obtaining theences among several instances of the Meijer G and the Fox H functions and their finite representations through the EGIG p.
Abstract: In this chapter the authors use the results in the three theorems in the previous chapter to obtain the p.d.f.’s and c.d.f.’s of all the products of independent Beta r.v.’s in those theorems in terms of the Meijer G and the Fox H functions as well as their finite forms based on the EGIG (Exponentiated Generalized Integer Gamma) p.d.f. and c.d.f., this way obtaining the equivalences among several instances of the Meijer G and Fox H functions and their finite representations through the EGIG p.d.f. and c.d.f..
01 Jan 2019
TL;DR: In this article, the authors give new Mellin inversion formulas for both the p.d. and the c.d., and develop sharp upper bounds on the difference between the exact and approximate representations for the Meijer G functions.
Abstract: In this chapter the authors set the guidelines to approach cases not covered by the finite form representations studied in the book, give new Mellin inversion formulas for both the p.d.f. and the c.d.f., and develop sharp upper bounds on the difference between the exact and approximate representations for the Meijer G functions as well as for the differences between the exact and approximate p.d.f.’s and c.d.f.’s of the product of independent Beta r.v.’s.
01 Jan 2019
TL;DR: In this article, the Meijer G and Fox H functions are introduced and the authors open the way to the establishment of several cases where there are finite representations for these functions which have not been previously identified and that as such are not recognized by any of the available software.
Abstract: In this chapter besides briefly introducing the Meijer G and Fox H functions through their usual definitions, the authors open the way to the establishment of several cases where there are finite representations for these functions which have not been previously identified and that as such are not recognized by any of the available software. These cases are related to the distribution of three extended products of independent Beta random variables, which are treated in Chap. 3.