85.76 Another Discrete Random Variable Having the Property 'Mean = Variance'

2001 ◽  
Vol 85 (504) ◽  
pp. 516 ◽  
Author(s):  
M. N. Deshpande
Keyword(s):  
Random Variable ◽  
Discrete Random Variable ◽  
Mean Variance

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

Filomat ◽  
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.

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

2018 ◽  
Vol 2672 (30) ◽  
pp. 53-63 ◽  
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.

A MEAN–VARIANCE BOUND FOR A THREE-PIECE LINEAR FUNCTION

2007 ◽  
Vol 21 (4) ◽  
pp. 611-621 ◽  
Author(s):  
Karthik Natarajan ◽  
Zhou Linyi
Keyword(s):  
Convex Function ◽  
Closed Form ◽  
Linear Function ◽  
Upper Bound ◽  
Random Variable ◽  
Expected Value ◽  
Variance Bound ◽  
The Mean ◽  
Mean Variance

In this article, we derive a tight closed-form upper bound on the expected value of a three-piece linear convex function E[max(0, X, mX − z)] given the mean μ and the variance σ2 of the random variable X. The bound is an extension of the well-known mean–variance bound for E[max(0, X)]. An application of the bound to price the strangle option in finance is provided.

scholarly journals Mean-Variance Hedging and Forward-Backward Stochastic Differential Filtering Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Guangchen Wang ◽  
Zhen Wu
Keyword(s):  
Control Systems ◽  
Partial Information ◽  
Random Variable ◽  
Contingent Claim ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Quadratic Optimal Control ◽  
Hedging Problem ◽  
Mean Variance ◽  
Markov Control

This paper is concerned with a mean-variance hedging problem with partial information, where the initial endowment of an agent may be a decision and the contingent claim is a random variable. This problem is explicitly solved by studying a linear-quadratic optimal control problem with non-Markov control systems and partial information. Then, we use the result as well as filtering to solve some examples in stochastic control and finance. Also, we establishbackwardandforward-backwardstochastic differential filtering equations which aredifferentfrom the classical filtering theory introduced by Liptser and Shiryayev (1977), Xiong (2008), and so forth.

Uniform discrete random-variable generator

1973 ◽  
Vol 11 (3) ◽  
pp. 362-364 ◽  
Author(s):  
P. A. Parker ◽  
R. N. Scott
Keyword(s):  
Random Variable ◽  
Discrete Random Variable

On certain coloring parameters of Mycielski graphs of some graphs

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.

Exact cash-account deflator for the G2++ model

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.

scholarly journals Numerical Modelling of Squeeze Film Performance between Rotating Transversely Rough Curved Circular Plates under the Presence of a Magnetic Fluid Lubricant

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Nikhilkumar D. Abhangi ◽  
G. M. Deheri
Keyword(s):  
Magnetic Fluid ◽  
Random Variable ◽  
Squeeze Film ◽  
Circular Plates ◽  
Random Roughness ◽  
Load Carrying ◽  
Nonzero Mean ◽  
Mean Variance ◽  
Positive Effect ◽  
Bearing System

An endeavour has been made to study and analyze the behaviour of a magnetic fluid-based squeeze film between curved transversely rough rotating circular plates when the curved upper plate lying along a surface determined by an exponential function approaches the curved lower plate along the surface governed by a secant function. A magnetic fluid is used as the lubricant in the presence of an external magnetic field oblique to the radial axis. The random roughness of the bearing surfaces is characterised by a stochastic random variable with nonzero mean, variance, and skewness. The associated nondimensional averaged Reynolds equation is solved with suitable boundary conditions in dimensionless form to obtain the pressure distribution, leading to the expression for the load carrying capacity. The results establish that the bearing system registers an enhanced performance as compared to that of the bearing system dealing with a conventional lubricant. This investigation proves that albeit the bearing suffers due to transverse surface roughness, there exist sufficient scopes for obtaining a relatively better performance in the case of negatively skewed roughness by properly choosing curvature parameters and the rotation ratio. It is appealing to note that the negative variance further enhances this positive effect.

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