摘要:

A simple form for the fixed point probability row vector of regular or ergodic transition matrices is developed using some of the theory of generalized matrix inversion, together with the well known existence and uniqueness of a fixed point probability row vector. The forms for both the regular and ergodic case are identical and afford the easy calculation of the fixed point without calculating powers of the transition matrix or considering the usual convergence methods.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482932

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482933

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

It is claimed that the reasons for using matrices of derivatives, in appropriate situations, are as compelling as those for using matrices. This paper provides basic material for such use. Different types of matrix derivatives are defined and illustrated. Simple and easy techniques are then derived and are shown to be applicable to a considerable collection of matrix functions. Applications are made to such problems as establishing matrix integrals from scalar ones, determining maximum likelihood estimates for complex likelihood functions, optimizing matrix functions when there are matrices of side conditions, and evaluating the Jacobians of certain classes of transformations. The emphasis is on simplicity of derivation and on breadth of application.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482934

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

For rectangular confidence regions for the mean values of multivariate normal distributions the following conjecture of 0. J. Dunn [3], [4] is proved: Such a confidence region constructed for the case of independent coordinates is, at the same time, a conservative confidence region for any case of dependent coordinates. This result is based on an inequality for the probabilities of rectangles in normal distributions, which permits one to factor out the probability for any single coordinate.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482935

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

By using the information provided by the first κ, 2 ≤ κ< N, members of a random sample of sizeNfrom a univariate normal distribution, Hickman [3] obtains prediction intervals for the sample mean, and the sample variance of the complete sample of sizeN.He gives similar results for a univariate normal regression model. Here we present straightforward generalizations of Hickman's results to the multivariate case.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482936

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

Many confounded factorial arrangements have the property of obtaining the same precision for any component of a particular main effect or interaction. A procedure for recovery of inter-block information developed by the author (Ann. Math. Statist 1964) is applied to such designs to obtain combined estimators having smaller variance than the corresponding intra-block estimators for all values of the inter and intrablock variances. The procedure has been illustrated for a confounded factorial arrangement of the above type.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482937

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

The two-parameter (λ,r) probability function which arises from a generalization,px=λpx-1/(x+r), of the recurrence relationship between successive probabilities of a Poisson process, has been termed the ‘Displaced Poisson Distribution’ and is considered here over the parameter space λ > 0,r≤ 0.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482938

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

A growing interest has been witnessed in recent years in multivariate discrete probability models. The multivariate logarithmic series distribution (LSD) is a multivariate analogue of the univariate LSD. This paper investigates the marginal and the conditional distributions of the multivariate LSD. It records its moment properties and also provides some regression and correlation analysis. An interesting modal property of the distribution is discovered. The paper also discusses the estimation of the parameters by the methods of maximum likelihood and unbiased minimum variance. At the end is discussed in detail an application of the multivariate LSD to the field of population and community ecology.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482939

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482940

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482941

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor