A New Approach of Stochastic Dominance for Ranking Transformations on the Discrete Random Variable

We provide a simple way to visualize the variance and the mean absolute error of a random variable with finite mean. Some application to options theory and to second order stochastic dominance is given: we show, among other, that the "call-put parity" may be seen as a Taylor formula.

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A note on characteristic function for Bernstein polynomials involving special numbers and polynomials

Filomat ◽

10.2298/fil2002543s ◽

2020 ◽

Vol 34 (2) ◽

pp. 543-549

Author(s):

Buket Simsek

Keyword(s):

Characteristic Function ◽

Binomial Distribution ◽

Bernstein Polynomials ◽

Random Variable ◽

Stirling Numbers ◽

Bernoulli Numbers ◽

Discrete Random Variable ◽

Euler Numbers ◽

Negative Order ◽

Special Numbers And Polynomials

The aim of this present paper is to establish and study generating function associated with a characteristic function for the Bernstein polynomials. By this function, we derive many identities, relations and formulas relevant to moments of discrete random variable for the Bernstein polynomials (binomial distribution), Bernoulli numbers of negative order, Euler numbers of negative order and the Stirling numbers.

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Modified Mixed Generalized Ordered Response Model to Handle Misclassification in Injury Severity Data

Transportation Research Record Journal of the Transportation Research Board ◽

10.1177/0361198118796352 ◽

2018 ◽

Vol 2672 (30) ◽

pp. 53-63 ◽

Cited By ~ 4

Author(s):

Lacramioara Balan ◽

Rajesh Paleti

Keyword(s):

Injury Severity ◽

Random Variable ◽

Parameter Estimates ◽

Discrete Random Variable ◽

Response Models ◽

Ordinal Response ◽

Proposed Model ◽

Misclassification Errors ◽

Misclassification Rates ◽

Ordered Response

Traditional crash databases that record police-reported injury severity data are prone to misclassification errors. Ignoring these errors in discrete ordered response models used for analyzing injury severity can lead to biased and inconsistent parameter estimates. In this study, a mixed generalized ordered response (MGOR) model that quantifies misclassification rates in the injury severity variable and adjusts the bias in parameter estimates associated with misclassification was developed. The proposed model does this by considering the observed injury severity outcome as a realization from a discrete random variable that depends on true latent injury severity that is unobservable to the analyst. The model was used to analyze misclassification rates in police-reported injury severity in the 2014 General Estimates System (GES) data. The model found that only 68.23% and 62.75% of possible and non-incapacitating injuries were correctly recorded in the GES data. Moreover, comparative analysis with the MGOR model that ignores misclassification not only has lower data fit but also considerable bias in both the parameter and elasticity estimates. The model developed in this study can be used to analyze misclassification errors in ordinal response variables in other empirical contexts.

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Convergence of Spanish Regions, 1990-2003. A New Approach Using Stochastic Dominance Techniques

Journal of Income Distribution ◽

10.25071/1874-6322.11362 ◽

2010 ◽

Author(s):

Carmelo García ◽

Ismael Ahamdanech ◽

Mercedes Prieto

Keyword(s):

Stochastic Dominance ◽

Capita Income ◽

Economic Convergence ◽

Per Capita Income ◽

New Approach ◽

Spanish Regions ◽

Income Data ◽

Per Capita ◽

New Statistics ◽

Empirical Methodology

The traditional analysis of economic convergence between countries or regions is usually performed by comparing distribution means, such as per-capita income. This kind of analysis, which is intimately related to the economic welfare of a society, presents, however, only a partial approach to measuring economic convergence, given that the disparities within regions or countries are not considered. The empirical methodology used in this article complements the traditional convergence approach, introducing efficiency and inequality aspects of income distribution. Using first and second stochastic dominance, the convergence among Spanish regions from 1990 to 2003 is studied by means of two new statistics developed here. Per-capita income data taken from the Encuesta de Presupuestos Familiares (EPF [the Spanish Household Budget Survey]) of 1990-1991 and the Spanish Survey on Income and Living Conditions (SILC) of 2003 are employed to make the comparisons. We find that a divergence process is taking place in Spain between rich and poor regions

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Expectation of a Discrete Random Variable

An Introduction to the Theory of Probability ◽

10.1142/9789814313438_0005 ◽

2011 ◽

pp. 125-138

Keyword(s):

Random Variable ◽

Discrete Random Variable

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Uniform discrete random-variable generator

Medical & Biological Engineering ◽

10.1007/bf02475550 ◽

1973 ◽

Vol 11 (3) ◽

pp. 362-364 ◽

Cited By ~ 1

Author(s):

P. A. Parker ◽

R. N. Scott

Keyword(s):

Random Variable ◽

Discrete Random Variable

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On certain coloring parameters of Mycielski graphs of some graphs

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830918500301 ◽

2018 ◽

Vol 10 (03) ◽

pp. 1850030

Author(s):

N. K. Sudev ◽

K. P. Chithra ◽

K. A. Germina ◽

S. Satheesh ◽

Johan Kok

Keyword(s):

Graph Coloring ◽

Random Variable ◽

Proper Coloring ◽

Discrete Random Variable ◽

Variable Formula ◽

Statistical Measures ◽

Random Experiment ◽

Mean And Variance

Coloring the vertices of a graph [Formula: see text] according to certain conditions can be considered as a random experiment and a discrete random variable [Formula: see text] can be defined as the number of vertices having a particular color in the proper coloring of [Formula: see text]. The concepts of mean and variance, two important statistical measures, have also been introduced to the theory of graph coloring and determined the values of these parameters for a number of standard graphs. In this paper, we discuss the coloring parameters of the Mycielskian of certain standard graphs.

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Exact cash-account deflator for the G2++ model

International Journal of Financial Engineering ◽

10.1142/s2424786320500097 ◽

2020 ◽

Vol 07 (01) ◽

pp. 2050009

Author(s):

Francesco Strati ◽

Luca G. Trussoni

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Insurance Industry ◽

Random Variable ◽

Time Span ◽

Discrete Random Variable ◽

Variable Formula ◽

Monte Carlo Simulation Technique ◽

Insurance Contracts ◽

Embedded Options

In this paper, we shall propose a Monte Carlo simulation technique applied to a G2++ model: even when the number of simulated paths is small, our technique allows to find a precise simulated deflator. In particular, we shall study the transition law of the discrete random variable :[Formula: see text] in the time span [Formula: see text] conditional on the observation at time [Formula: see text], and we apply it in a recursive way to build the different paths of the simulation. We shall apply the proposed technique to the insurance industry, and in particular to the issue of pricing insurance contracts with embedded options and guarantees.

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Asymptotic properties of the number of replications of a paired comparison

Journal of Applied Probability ◽

10.2307/3212581 ◽

1974 ◽

Vol 11 (1) ◽

pp. 43-52 ◽

Cited By ~ 8

Author(s):

V. R. R. Uppuluri ◽

W. J. Blot

Keyword(s):

Paired Comparison ◽

Beta Function ◽

Asymptotic Properties ◽

Random Variable ◽

Incomplete Beta Function ◽

Discrete Random Variable ◽

World Series ◽

Mean And Variance ◽

The Mean ◽

Made In

A discrete random variable describing the number of comparisons made in a sequence of comparisons between two opponents which terminates as soon as one opponent wins m comparisons is studied. By equating two different expressions for the mean of the variable, a closed form for the incomplete beta function with equal arguments is obtained. This expression is used in deriving asymptotic (m-large) expressions for the mean and variance. The standardized variate is shown to converge to the Gaussian distribution as m→ ∞. A result corresponding to the DeMoivre-Laplace limit theorem is proved. Finally applications are made to the genetic code problem, to Banach's Match Box Problem, and to the World Series of baseball.

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A Portfolio Optimality Test Based on the First-Order Stochastic Dominance Criterion

Journal of Financial and Quantitative Analysis ◽

10.1017/s0022109009990251 ◽

2009 ◽

Vol 44 (5) ◽

pp. 1103-1124 ◽

Cited By ~ 31

Author(s):

Miloš Kopa ◽

Thierry Post

Keyword(s):

Stochastic Dominance ◽

New Approach ◽

First Order ◽

Value Stocks ◽

Order Stochastic Dominance ◽

Market Portfolio ◽

The Face ◽

Binary Choices ◽

Return Distributions ◽

Optimality Test

AbstractExisting approaches to testing for the efficiency of a given portfolio make strong parametric assumptions about investor preferences and return distributions. Stochastic dominance-based procedures promise a useful nonparametric alternative. However, these procedures have been limited to considering binary choices. In this paper we take a new approach that considers all diversified portfolios and thereby introduce a new concept of first-order stochastic dominance (FSD) optimality of a given portfolio relative to all possible portfolios. Using our new test, we show that the U.S. stock market portfolio is significantly FSD nonoptimal relative to benchmark portfolios formed on market capitalization and book-to-market equity ratios. Without appealing to parametric assumptions about the return distribution, we conclude that no nonsatiable investor would hold the market portfolio in the face of the attractive premia of small caps and value stocks.

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