Methodology and Applications of Statistics
A Volume in Honor of C.R. Rao on the Occasion of his 100th Birthday
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Article
Correction to: A general near-exact distribution theory for the most common likelihood ratio test statistics used in Multivariate Analysis
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Article
Bivariate distributions with equi-dispersed normal conditionals and related models
A random variable is equi-dispersed if its mean equals its variance. A Poisson distribution is a classical example of this phenomenon. However, a less well-known fact is that the class of normal densities that...
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Article
Open AccessCharacterization of the Geometric Distribution Via Linear Combinations of Observations and of Records
In a sequence of independent identically distributed geometric random variables, the sum of the first two record values is distributed as a simple linear combination of geometric variables. It is verified that...
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Article
Preservation of distributional properties of component lifetimes by system lifetimes
We analyze reliability systems with components whose lifetimes are identically distributed, and whose joint distribution admits a Samaniego signature representation of the system lifetime distribution. Our mai...
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Article
All Conditional Distributions for Y Given X that are Compatible with a Given Conditional Distribution for X Given Y
For a given conditional distribution for X given Y, it is important to identify the class of all conditional distributions for Y given X such that there exists at least one bivariate distribution with the given p...
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Chapter
Some Bivariate and Multivariate Models Involving Independent Gamma Distributed Components
Several multivariate models involving independent gamma distributed components (three of which are new) are described. The flexible bivariate beta(2) model introduced by Arnold and Ng (2011) provides the template...
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Book
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Article
Commentary on “From unidimensional to multidimensional inequality: a review”
Some commentary related to Andreoli and Zoli’s interesting survey article is presented.
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Chapter
Setting the Scene
Although the Fox H and Meijer G functions yield very handy representations for the probability density functions and cumulative distribution functions of several distributions and distributions of products of ind...
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Chapter
Multiple Products of Independent Beta Random Variables with Finite Form Representations for Their Distributions
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....
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Chapter
Application of the Finite Form Representations of Meijer G and Fox H Functions to the Distribution of Several Likelihood Ratio Test Statistics
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 in...
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Chapter
Approximate Finite Forms for the Cases Not Covered by the Finite Representation Approach
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 d...
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Chapter
The Meijer G and Fox H Functions
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 ...
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Chapter
Finite Form Representations for Extended Instances of Meijer G and Fox H Functions
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 Me...
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Chapter
MathematicaⓇ, Maxima, and R Packages to Implement the Likelihood Ratio Tests and Compute the Distributions in the Previous Chapter
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 ...
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Article
Analytic Expressions for Multivariate Lorenz Surfaces
The Lorenz curve is a much used instrument in economic analysis. It is typically used for measuring inequality and concentration. In insurance, it is used to compare the riskiness of portfolios, to order reins...
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Chapter
Transformations and Their Effects
We may most easily motivate the material in the present chapter by setting it in the context of income distributions. Income distributions which exhibit a high degree of inequality (as indicated by their Lore...
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Chapter
Introduction
The theory of majorization is perhaps most remarkable for its simplicity. How can such a simple concept be useful in so many diverse fields? The plethora of synonyms or quasi-synonyms for variability (diversit...
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Chapter
Some Related Orderings
In Sect. 6.4, we encountered some alternative inequality curves and the corresponding orderings that they can be used to define (they were Bonferroni, Leimkuhler, and Zenga-I and II). In this chapter we consid...
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Chapter
Families of Lorenz Curves
The Lorenz curve is an important instrument for analyzing the size distributions of income, wealth and inequality . The problem of finding an appropriate functional form for a given data set or class of data s...
