scholarly journals Redukcja efektu brzegowego w estymacji jądrowej wybranych charakterystyk funkcyjnych zmiennej losowej

2016 ◽  
Vol 16 (3) ◽  
pp. 111 ◽  
Author(s):  
Aleksandra Katarzyna Baszczyńska
Keyword(s):  
Density Function ◽  
Gross National Product ◽  
Boundary Effect ◽  
Kernel Estimation ◽  
Regression Function ◽  
Random Variable ◽  
Boundary Region ◽  
Kernel Estimators ◽  
Functional Characteristics ◽  
Estimator Bias

For a random variable with bounded support, the kernel estimation of functional characteristics may lead to the occurrence of the so-called boundary effect. In the case of the kernel density estimation it can mean an increase of the estimator bias in the areas near the ends of the support, and can lead to a situation where the estimator is not a density function in the support of a random variable. In the paper the procedures for reducing boundary effect for kernel estimators of density function, distribution function and regression function are analyzed. Modifications of the classical kernel estimators and examples of applications of these procedures in the analysis of the functional characteristics relating to gross national product per capita are presented. The advantages of procedures are indicated taking into account the reduction of the bias in the boundary region of the support of the random variable considered.

The Convergence Rate with Bootstrap for Multidimensional Density Functional Kernel Estimation

2012 ◽  
Vol 591-593 ◽  
pp. 2559-2563
Author(s):  
De Wang Li
Keyword(s):  
Distribution Function ◽  
Convergence Rate ◽  
Density Function ◽  
Density Functional ◽  
Bootstrap Method ◽  
Kernel Estimation ◽  
Random Variable ◽  
University Professor ◽  
The Common ◽  
Independent Identically Distributed

Bootstrap method is a statistical method proposed by the American Stanford University professor of Statistics Efron, which belongs to the parameters of statistical methods. According to a given sub-sample, we do not need its distributional assumptions or increase the sample information which can be described the overall distribution characteristics of statistical inference. The basic idea of the Bootstrap statistics is unknown and can not repeat the sampling distribution function instead of using a repeat sampling of the distribution function estimates. The independent identically distributed random variable series ,have the common probability density function, with .In the paper, combining with multidimensional density function, we discuss the convergence rate with Bootstrap method for the kernel estimation of the density functional .

On application of a certain formula

1971 ◽  
Vol 70 (1) ◽  
pp. 57-59
Author(s):  
J. K. Wani
Keyword(s):  
Density Function ◽  
Divided Difference ◽  
Random Variable ◽  
Multiple Integral

In this paper we first demonstrate how a certain formula, which expresses (n − 1 )th divided difference in the form of a multiple integral, may be used to obtain the density function of a suitable random variable and then apply this to obtain the density of a useful variate.

A renewal density theorem in the multi-dimensional case

1967 ◽  
Vol 4 (1) ◽  
pp. 62-76 ◽  
Author(s):  
Charles J. Mode
Keyword(s):  
Density Function ◽  
Covariance Matrix ◽  
Branching Processes ◽  
Random Variable ◽  
Density Theorem ◽  
Positive Definite ◽  
Dimensional Case ◽  
Age Dependent ◽  
Image Position ◽  
Mean Vector

SummaryIn this note a renewal density theorem in the multi-dimensional case is formulated and proved. Let f(x) be the density function of a p-dimensional random variable with positive mean vector μ and positive-definite covariance matrix Σ, let hn(x) be the n-fold convolution of f(x) with itself, and set Then for arbitrary choice of integers k1, …, kp–1 distinct or not in the set (1, 2, …, p), it is shown that under certain conditions as all elements in the vector x = (x1, …, xp) become large. In the above expression μ‵ is interpreted as a row vector and μ a column vector. An application to the theory of a class of age-dependent branching processes is also presented.

On the linear exponential family

1968 ◽  
Vol 64 (2) ◽  
pp. 481-483 ◽  
Author(s):  
J. K. Wani
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Scalar Product ◽  
Exponential Family ◽  
Characterization Theorem ◽  
Random Variable ◽  
Moment Generating Function ◽  
The Moment ◽  
Image Position

In this paper we give a characterization theorem for a subclass of the exponential family whose probability density function is given bywhere a(x) ≥ 0, f(ω) = ∫a(x) exp (ωx) dx and ωx is to be interpreted as a scalar product. The random variable X may be an s-vector. In that case ω will also be an s-vector. For obvious reasons we will call (1) as the linear exponential family. It is easy to verify that the moment generating function (m.g.f.) of (1) is given by

A generalized Ostrowski type inequality for a random variable whose probability density function belongs to L∞[a, b]

2008 ◽  
Vol 41 (3) ◽  
Author(s):  
Arif Rafiq ◽  
Nazir Ahmad Mir ◽  
Fiza Zafar
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Type Inequality ◽  
Random Variable ◽  
Ostrowski Type Inequality

AbstractWe establish here an inequality of Ostrowski type for a random variable whose probability density function belongs to L

scholarly journals Determining the First Probability Density Function of Linear Random Initial Value Problems by the Random Variable Transformation (RVT) Technique: A Comprehensive Study

2014 ◽  
Vol 2014 ◽  
pp. 1-25 ◽  
Author(s):  
M.-C. Casabán ◽  
J.-C. Cortés ◽  
J.-V. Romero ◽  
M.-D. Roselló
Keyword(s):  
Stochastic Process ◽  
Probability Density Function ◽  
Differential Equations ◽  
Probability Density ◽  
Density Function ◽  
Initial Value Problems ◽  
Random Variable ◽  
Initial Value ◽  
Variable Transformation ◽  
Comprehensive Study

Deterministic differential equations are useful tools for mathematical modelling. The consideration of uncertainty into their formulation leads to random differential equations. Solving a random differential equation means computing not only its solution stochastic process but also its main statistical functions such as the expectation and standard deviation. The determination of its first probability density function provides a more complete probabilistic description of the solution stochastic process in each time instant. In this paper, one presents a comprehensive study to determinate the first probability density function to the solution of linear random initial value problems taking advantage of the so-called random variable transformation method. For the sake of clarity, the study has been split into thirteen cases depending on the way that randomness enters into the linear model. In most cases, the analysis includes the specification of the domain of the first probability density function of the solution stochastic process whose determination is a delicate issue. A strong point of the study is the presentation of a wide range of examples, at least one of each of the thirteen casuistries, where both standard and nonstandard probabilistic distributions are considered.

scholarly journals Kernel estimators of density function of directional data

1988 ◽  
Vol 27 (1) ◽  
pp. 24-39 ◽  
Author(s):  
Z.D. Bai ◽  
C.Radhakrishna Rao ◽  
L.C. Zhao
Keyword(s):  
Density Function ◽  
Directional Data ◽  
Kernel Estimators
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