scholarly journals Multivariate Classes of GB2 Distributions with Applications

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 72
Author(s):  
José María Sarabia ◽  
Vanesa Jordá ◽  
Faustino Prieto ◽  
Montserrat Guillén
Keyword(s):  
Order Statistics ◽  
Random Variables ◽  
Multivariate Distributions ◽  
Empirical Application ◽  
Income Distributions ◽  
Flexible Distribution ◽  
Parametric Families ◽  
Wind Events

The general beta of the second kind distribution (GB2) is a flexible distribution which includes several relevant parametric families of distributions. This distribution has important applications in earnings and income distributions, finance and insurance. In this paper, several multivariate classes of the GB2 distribution are proposed. The different multivariate versions are based on two simple univariate representations of the GB2 distribution. The first type of multivariate distributions are constructed from a stochastic dependent representations defined in terms of gamma random variables. Using this representation and beginning by two particular multivariate GB2 distributions, multivariate Singh–Maddala and Dagum income distributions are presented and several properties are obtained. Then, a general multivariate GB2 distribution is introduced. The second type of multivariate distributions are based on a generalization of the distribution of the order statistics, which gives place to multivariate GB2 distribution with support above the diagonal. We discuss the role of these families in modeling bivariate income distributions. Finally, an empirical application is given, where we show that a multivariate GB2 distribution can be useful for modeling compound precipitation and wind events in the whole range.

scholarly journals On the Increasing Convex Order of Relative Spacings of Order Statistics

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 618
Author(s):  
Antonia Castaño-Martínez ◽  
Gema Pigueiras ◽  
Miguel A. Sordo
Keyword(s):  
Order Statistics ◽  
Relative Deprivation ◽  
Sufficient Conditions ◽  
Convex Order ◽  
Increasing Convex Order ◽  
Income Distributions ◽  
Parametric Families ◽  
Relative Differences

Relative spacings are relative differences between order statistics. In this context, we extend previous results concerning the increasing convex order of relative spacings of two distributions from the case of consecutive spacings to general spacings. The sufficient conditions are given in terms of the expected proportional shortfall order. As an application, we compare relative deprivation within some parametric families of income distributions.

Stochastic comparisons of order statistics under multivariate imperfect repair

1996 ◽  
Vol 33 (1) ◽  
pp. 156-163 ◽  
Author(s):  
Taizhong Hu
Keyword(s):  
Order Statistics ◽  
Probability Space ◽  
Random Variables ◽  
Stochastic Comparisons ◽  
Special Model ◽  
Imperfect Repair ◽  
Monotone Coupling ◽  
Common Probability

A monotone coupling of order statistics from two sets of independent non-negative random variables Xi, i = 1, ···, n, and Yi, i = 1, ···, n, means that there exist random variables X′i, Y′i, i = 1, ···, n, on a common probability space such that , and a.s. j = 1, ···, n, where X(1) ≦ X(2) ≦ ·· ·≦ X(n) are the order statistics of Xi, i = 1, ···, n (with the corresponding notations for the X′, Y, Y′ sample). In this paper, we study the monotone coupling of order statistics of lifetimes in two multi-unit systems under multivariate imperfect repair. Similar results for a special model due to Ross are also given.

scholarly journals Education and Energy Intensity: Simple Economic Modelling and Preliminary Empirical Results

2018 ◽  
Vol 10 (8) ◽  
pp. 2625 ◽  
Author(s):  
Tiago Sequeira ◽  
Marcelo Santos
Keyword(s):  
Gross Domestic Product ◽  
Economic Model ◽  
Energy Use ◽  
Energy Intensity ◽  
The Other ◽  
Economic Modelling ◽  
Empirical Application ◽  
Primary Schooling ◽  
Simple Economic

The ratio of energy use to Gross Domestic Product (defined as energy intensity) is a major determinant of environmental hazard and an indicator of eco-efficiency. This paper explains why education can have an effect in reducing the energy intensity thus affecting eco-efficiency. We devise a stylized economic model with simple and widely accepted assumptions that highlights the role of education in decreasing energy intensity worldwide. In an empirical application that is robust to the features of the data, we show that primary schooling contributes to a decrease in energy intensity which has a very significant effect, even accounting for the other well-known determinants of energy intensity. Additionally, when schooling is taken into account, income is no longer a negative determinant of energy intensity.

A clustering law for some discrete order statistics

2003 ◽  
Vol 40 (01) ◽  
pp. 226-241 ◽  
Author(s):  
Sunder Sethuraman
Keyword(s):  
Distribution Function ◽  
Positive Integer ◽  
Order Statistics ◽  
Law Of Large Numbers ◽  
Asymptotic Properties ◽  
Random Variables ◽  
Large Numbers ◽  
The Law ◽  
Sample Maximum ◽  
Independent Identically Distributed

Let X 1, X 2, …, X n be a sequence of independent, identically distributed positive integer random variables with distribution function F. Anderson (1970) proved a variant of the law of large numbers by showing that the sample maximum moves asymptotically on two values if and only if F satisfies a ‘clustering’ condition, In this article, we generalize Anderson's result and show that it is robust by proving that, for any r ≥ 0, the sample maximum and other extremes asymptotically cluster on r + 2 values if and only if Together with previous work which considered other asymptotic properties of these sample extremes, a more detailed asymptotic clustering structure for discrete order statistics is presented.

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