共查询到20条相似文献,搜索用时 0 毫秒
1.
J. Pusz 《Australian & New Zealand Journal of Statistics》1995,37(1):83-87
The paper describes the Meixner hypergeometric distribution, characterised by properties of the regression of products of linear transformations of random variables with respect to residuals. 相似文献
2.
D. G. Kabe 《Australian & New Zealand Journal of Statistics》1968,10(1):21-23
In this paper we generalize a result of Kshirsagar's (1960, pp. 83–84) on the distribution of the regression coefficient matrix for a multivariate normal population. 相似文献
3.
P. J. Staff 《Australian & New Zealand Journal of Statistics》1964,6(1):12-20
Consideration of the number of events in a Poisson process in excess of a threshold value r , when it is assumed that at least r events do occur, leads to the Displaced Poisson Distribution. The recurrence relationship between successive probabilities is a simple generalization of that of the Poisson distribution. Accordingly the fitting of the distribution to data is straightforward, using either a desk machine or computer.
It is a highly flexible unimodal distribution catering for both under- and over-dispersed data and generally fits Poisson type data well. Its properties have been discussed, moment and maximum likelihood estimators for the cases, r known and unknown have been given, together with several numerical examples. 相似文献
It is a highly flexible unimodal distribution catering for both under- and over-dispersed data and generally fits Poisson type data well. Its properties have been discussed, moment and maximum likelihood estimators for the cases, r known and unknown have been given, together with several numerical examples. 相似文献
4.
ON THE DISTRIBUTION OF SPHERICITY TEST CRITERION IN THE MULTIVARIATE GAUSSIAN DISTRIBUTION 总被引:1,自引:0,他引:1
A. K. Gupta 《Australian & New Zealand Journal of Statistics》1977,19(3):202-205
In this paper, the exact distribution of the likelihood-ratio criterion for testing the hypothesis of sphericity in a multivariate normal distribution is derived as a mixture of incomplete beta functions. Some advantages of the present derivation are also indicated. 相似文献
5.
Chin-Yuan Hu Aleksander M. Iksanov Gwo Dong Lin Oleg K. Zakusylo 《Australian & New Zealand Journal of Statistics》2006,48(1):1-6
This paper shows that a normalization of the Hurwitz zeta function is a characteristic function. This generalizes the 1938 result of Khinchine about the Riemann zeta function. The paper investigates the infinite divisibility of the resulting distribution. 相似文献
6.
B. C. Arnold 《Australian & New Zealand Journal of Statistics》1979,21(2):166-169
If X and Y are independent standard Cauchy random variables then (i) Y and (X+Y)/(1-Xu) are independent, (ii) X and (X + Y)/(1 -XU) are identically distributed, and (iii) X and 2X/(1-X2 ) are identically distributed. Each of these three properties is shown to characterize the Cauchy distribution among absolutely continuous distributions. Some related uniform characterizations are discussed. 相似文献
7.
《统计学通讯:模拟与计算》2013,42(3):357-373
ABSTRACT This paper studies the asymptotic distribution of the largest eigenvalue of the sample covariance matrix. The multivariate distribution for the population is assumed to be elliptical with finite kurtosis 3κ. An expression as an expectation is obtained for the distribution function of the largest eigenvalue regardless of the multiplicity, m, of the population's largest eigenvalue. The asymptotic distribution function and density function are evaluated numerically for m = 2,3,4,5. The bootstrap of the average of the m largest eigenvalues is shown to be consistent for any underlying distribution with finite fourth-order cumulants. 相似文献
8.
An expression for the exact distribution of the Bell-Doksum test of independence based upon the use of order statistics from normally distributed random samples is derived and a table of critical values is provided. Two extensions of the theory are considered and possible applications to Poisson processes and queueing theory are noted. 相似文献
9.
Two procedures are considered for estimating the concentration parameters of the Fisher matrix distribution for rotations or orientations in three dimensions. The first is maximum likelihood. The use of a convenient 1-dimensional integral representation of the normalising constant, which greatly simplifies the computation, is suggested. The second approach exploits the equivalence of the Fisher distribution for rotations in three dimensions, and the Bingham distribution for axes in four dimensions. We describe a pseudo likelihood procedure which works for the Bingham distribution in any dimension. This alternative approach does not require numerical integration. Results on the asymptotic efficiency of the pseudo likelihood estimator relative to the maximum likelihood estimator are given, and the two estimators are compared in the analysis of a well-known vectorcardiography dataset. 相似文献
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Subhash C. Sharma 《Australian & New Zealand Journal of Statistics》1985,27(2):138-150
In this paper, we investigate the effects of correlation among observations on the accuracy of approximating the distribution of sample mean by its asymptotic distribution. The accuracy is investigated by the Berry-Esseen bound (BEB), which gives an upper bound on the error of approximation of the distribution function of the sample mean from its asymptotic distribution for independent observations. For a given sample size (n0) the BEB is obtained when the observations are independent. Let this be BEB. We then find the sample size (n*) required to have BEB below BEB0, when the observations are dependent. Comparison of n* with n0 reveals the effects of correlation among observations on the accuracy of the asymptotic distribution as an approximation. It is shown that the effects of correlation among observations are not appreciable if the correlation is moderate to small but it can be severe for extreme correlations. 相似文献
13.
SMOOTH TESTS FOR THE BIVARIATE POISSON DISTRIBUTION 总被引:1,自引:0,他引:1
A theorem of Rayner & Best (1989) is generalised to permit the construction of smooth tests of goodness of fit without requiring a set of orthonormal functions on the hypothesised distribution. This result is used to construct smooth tests for the bivariate Poisson distribution. The test due to Crockett (1979) is similar to a smooth test that assesses the variance structure under the bivariate Poisson model; the test due to Loukas & Kemp (1986) is related to a smooth test that seeks to detect a particular linear relationship between the variances and covariance under the bivariate Poisson model. Using focused smooth tests may be more informative than using previously suggested tests. The distribution of the Loukas & Kemp (1986) statistic is not well approximated by the x2distribution for larger correlations, and a revised statistic is suggested. 相似文献
14.
Timothy C. Brown Donald I. Cartwright G. K. Eagleson 《Australian & New Zealand Journal of Statistics》1986,28(1):89-96
Two characterizations of the uniform distribution on a suitable compact space are proved. These characterizations are applied to a number of particular examples of which the most interesting is the following: if X , Y and Z are independent n-vectors whose components are independent and identically distributed within a vector, then the pairwise independence of the product moment correlation coefficients between X , Y and Z implies that these vectors are normally distributed. 相似文献
15.
Goodness of fit testing for the binomial distribution can be carried out using Pearson's X2p statistic and its components. Applications of this technique are considered and compared with recently suggested empirical distribution function tests. Diagnostic use of components is discussed. 相似文献
16.
《统计学通讯:理论与方法》2013,42(7):1045-1054
ABSTRACT The paper considers the development of inferential techniques for the general half-normal distribution based on the maximum likelihood method. Point estimates and large-sample confidence sets are derived for the distribution's parameters, and the use of the confidence sets as a basis for hypothesis testing is discussed. Data on the percentage body fat of elite male athletes are used to illustrate the application of the new methods. 相似文献
17.
《统计学通讯:理论与方法》2013,42(11):1959-1975
ABSTRACT Bounds for the Fisher information metric associated with the Gamma statistical model are found in terms of Poincaré type metric. This results in the determination of bounds for the Rao distance, that is the Riemannian distance induced by the information metric, between Gamma distributions, and of bounds for the Gaussian curvature of the Gamma model. The bounds seem to be sharp, where the lower and upper Rao distance bounds are Poincaré distances with Gaussian curvatures ?1/4 and ?1/2, respectively. In addition, the sign of the Gaussian curvature of the Gamma model is shown to be negative which means, in particular, that the geometry of the model is hyperbolic. 相似文献
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P. G. Wong 《Australian & New Zealand Journal of Statistics》1978,20(3):262-269
In this paper, we propose a procedure for testing the location parameter of the exponential distribution for certain alternative hypotheses, which could result in the early rejection of the null hypothesis. This is a consequence of the monotone property of the test statistic which is based on the extremal quotient. The test being scale-free does not require the scale parameter to be known. 相似文献