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251.
In this paper we consider the behavior of the roots of random algebraic polynomials. A code was developed which generates a sample of random algebraic polynomials, calculates the roots of each sample polynomial, and then calculates the averages of the roots. Finally, the roots of the deterministic algebraic polynomial whose coefficients are the averages of the sample coefficients are calculated. These data are then tabulated and graphically displayed. The relationship between the averages of the roots of the sample polynomials and the roots of the average polynomial is discussed. 相似文献
252.
Three tables provide coefficients for polynomial approximations of Student's t and chi-square percentage points at 10 probability levels, with relative error less than .00005 相似文献
253.
The least-squares cross-validation is a completely automatic method for choosing the smoothing parameter in probability density estimation but this method consume large amounts of computer time. This article concerns an efficient computational algorithm for this method when the kernel is symmetric and polynomial functions. 相似文献
254.
Priyanka Aggarwal 《统计学通讯:理论与方法》2013,42(8):1397-1408
We obtain a Bayes predictor and a Bayes prediction risk of the mean of a finite population relative to the balanced loss function. The predictive expected losses associated with classical and standard Bayes predictors are derived and compared with that of a Bayes predictor under a balanced loss function. Specific expressions for a regular exponential family distributed superpopulation are presented and illustrated for some well-known superpopulations. 相似文献
255.
For normally distributed populations, we obtain confidence bounds on a ratio of two coefficients of variation, provide a test for the equality of k coefficients of variation, and provide confidence bounds on a coefficient of variation shared by k populations. 相似文献
256.
The local polynomial methods and martingale estimating equations are used to develop closed form estimators of the intensity function and its derivatives for multiplicative counting process models. The consistency and asymptotic normality of the estimators are established. The estimator generalizes that proposed by Ramlau-Hansen (1983) with a smaller bias than the Ramlau-Hansen intensity estimator. The derivative estimators give smoother estimates than the Ramlau-Hansen derivative estimators. The proposed estimators are applied to analyze the infection rate and its derivatives of the 2003 Severe Acute Respiratory Syndrome (SARS) epidemic in Beijing, China. 相似文献
257.
c-optimal designs for estimating the model parameters of the quadratic logistic regression model are considered. The designs are constructed via the canonical design space. It is shown that the number of design points varies between 1 and 4 depending on the parameter being estimated. Furthermore, formulae for finding the design points along with the corresponding design weights are derived. 相似文献
258.
This note mainly aims to illustrate that some quadratic problems are robust in a sense with respect to the probabilistic distributions involved. The secondary moments of the quadratic forms of a multivariate t distribution are calculated. Then, the resulting formulae are applied to the quadratic problems of quadratic sufficiency and quadratic prediction. It is shown by revisiting the two problems that the same conclusions hold when the multivariate normal distribution is replaced with a multivariate t distribution. 相似文献
259.
A characterization of the distribution of the multivariate quadratic form given by X A X′, where X is a p × n normally distributed matrix and A is an n × n symmetric real matrix, is presented. We show that the distribution of the quadratic form is the same as the distribution of a weighted sum of non central Wishart distributed matrices. This is applied to derive the distribution of the sample covariance between the rows of X when the expectation is the same for every column and is estimated with the regular mean. 相似文献
260.
Nripes Kumar Mandal 《统计学通讯:理论与方法》2013,42(11):1989-1999
This article studies a mixture-amount model, which is quadratic both in the proportions of mixing components and the amount of mixture. Using the pseudo-Bayesian approach of Pal and Mandal (2006), it attempts to find the A-optimal design for the estimation of the optimum mixing proportions and the optimum amount. 相似文献