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31.
In this article, we introduce new asymptotic expansions for probability functions of sums of independent and identically distributed random variables. Results are obtained by efficiently employing information provided by lower-order convolutions. In comparison with Edgeworth-type theorems, advantages include improved asymptotic results in the case of symmetric random variables and ease of computation of main error terms and asymptotic crossing points. The first-order estimate can perform quite well against the corresponding renormalized saddlepoint approximation and, pointwise, requires evaluation of only a single convolution integral. While the new expansions are fairly straightforward, the implications are fortuitous and may spur further related work. 相似文献
32.
A discrete distribution in which the probabilities are expressible as Laguerre polynomials is formulated in terms of a probability generating function involving three parameters. The skewness and kurtosis is given for members of the family corresponding to various parameter values. Several estimators of the parameters are proposed, including some based on minimum chi-square. All the estimators are compared on the basis of asymptotic relative efficiency. 相似文献
33.
We consider the Lindeberg-Feller model for independent random variables and focus our attention on the behaviour of the probability densities q_{n} of sums S_{n}, n\geq 1 . We obtain a theorem on the convergence of q_{n} to the standard normal density \varphi which resembles the well known limit theorem for distribution functions--provided that the q_{n} are positive definite. A special case is the following: if q_{n}(0)\rightarrow\varphi(0) as n\rightarrow\infty then the Lindeberg condition guarantees that the convergence of q_{n} to \varphi continues to the real line. 相似文献
34.
In this article, we introduce a framework for analyzing the risk of systems failure based on estimating the failure probability. The latter is defined as the probability that a certain risk process, characterizing the operations of a system, reaches a possibly time‐dependent critical risk level within a finite‐time interval. Under general assumptions, we define two dually connected models for the risk process and derive explicit expressions for the failure probability and also the joint probability of the time of the occurrence of failure and the excess of the risk process over the risk level. We illustrate how these probabilistic models and results can be successfully applied in several important areas of risk analysis, among which are systems reliability, inventory management, flood control via dam management, infectious disease spread, and financial insolvency. Numerical illustrations are also presented. 相似文献
35.
ABSTRACT. The problem of boundary bias is associated with kernel estimation for regression curves with compact support. This paper proposes a simple and uni(r)ed approach for remedying boundary bias in non-parametric regression, without dividing the compact support into interior and boundary areas and without applying explicitly different smoothing treatments separately. The approach uses the beta family of density functions as kernels. The shapes of the kernels vary according to the position where the curve estimate is made. Theyare symmetric at the middle of the support interval, and become more and more asymmetric nearer the boundary points. The kernels never put any weight outside the data support interval, and thus avoid boundary bias. The method is a generalization of classical Bernstein polynomials, one of the earliest methods of statistical smoothing. The proposed estimator has optimal mean integrated squared error at an order of magnitude n −4/5 , equivalent to that of standard kernel estimators when the curve has an unbounded support. 相似文献
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EXACT AND APPROXIMATED RELATIONS BETWEEN NEGATIVE HYPERGEOMETRIC AND NEGATIVE BINOMIAL PROBABILITIES
《统计学通讯:理论与方法》2013,42(5):957-967
We derive orthogonal expansions in terms of the Meixner polynomials of the first kind for hypergeometric probabilities. We show how these expansions can be used to obtain negative binomial approximations to negative hypergeometric probabilities. Some limit properties of these approximations are studied and also the extension of these results to cumulative probabilities. 相似文献
40.
Jianhua Ding 《统计学通讯:模拟与计算》2017,46(1):779-794
We develope an M-estimator for partially linear models in which the nonparametric component is subject to various shape constraints. Bernstein polynomials are used to approximate the unknown nonparametric function, and shape constraints are imposed on the coefficients. Asymptotic normality of regression parameters and the optimal rate of convergence of the shape-restricted nonparametric function estimator are established under very mild conditions. Some simulation studies and a real data analysis are conducted to evaluate the finite sample performance of the proposed method. 相似文献