On the generalization and estimation for the double poisson distribution

Summary The Double Poisson Distribution introduced by Joshi is a bivariate analogue of the univariate counterpart. In this paper we define a generalized double Poisson distribution based on four parameters. We prove it is a probability function and derive a recurrence relation among the moments. The maximum likelihood, minimum variance unbiased, and Bayes estimators are considered. Finally, we give a numerical example for the goodness of fit of the distribution.

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Resumen La distribución doble de Poisson introducida por Joshi es una generalización bivariada de la correspondiente distribución univariada. En el presente trabajo se define una distribución de Poisson doble generalizada con cuatro parámetros. Se demuestra que es una función de probabilidad y se establece una relación de recurrencia entre los momentos. Se consideran los estimadores de máxima verosimilitud, los estimadores insesgados de variancia mínima, y los estimadores de Bayes. Finalmente se da un ejemplo numérico de la bondad de ajuste de la distribución.

     

On the generalization of equicofactor matrices

Eguicofactor properties of the entities occurring in electric networks and discrete elastic systems extend beyond the present definition of such entities. For instance, the zero-sum property of these matrices is, in fact, a particular version of a broader definition. The generalization is accomplished in using higher order submatrices as opposed to scalars (submatrices of order 1) in the present literature.     

Molecular-kinetic generalization of the heat-transfer equation

Starting from microscopic theory, the authors generalize the heat-conduction equation to the case where the gradients in molecular transport velocities vary appreciably over a mean free path.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 2, pp. 330–335, February, 1977.     

One generalization of the hypothesis of local determinability

The article deals with the problem of constructing determining relations of the theory of plasticity for arbitrary complex processes of deformation. The point of departure are relations based on V. S. Lenskii's hypothesis of local determinability. It is suggested to generalize the equations of the hypothesis of local determinability to the scalar characteristics of the functional of plasticity. It is shown that analogous relations can be obtained in the endochronic theory of plasticity. The results of calculation are compared with the experiment entailing complex loading, and it is established that not only vector characteristics but also scalar characteristics of the functional of plasticity are perfectly satisfactorily described within the generalized variant of the hypothesis of local determinability suggested in the present work.Institute of Mechanics, Academy of Sciences of the USSR, Moscow. Translated from Problemy Prochnosti, No. 9, pp. 10–14, September, 1989.     

A generalization of the method of incompatible modes

A generalization of the classical method of incompatible modes is presented, containing the original formulation as a special case. The method constitutes a class of finite elements which is equivalent to the class of enhanced assumed strain elements, yet based on a pure displacement formulation. Copyright © 2006 John Wiley & Sons, Ltd.     

Quasilinear generalization of onsager thermodynamics

The law of linearity is substituted by a more complicated relation in which, apart from fluxes and forces, also their derivatives with respect to time occur. The properties of phenomenological and relaxation coefficients are studied. An analogy of Kramers-Kroning relations are derived. The theory of relaxation phenomena is formulated as part of the quasilinear axiomatics.     

A generalization of justesen codes

Abstract

By using alternant codes as outer codes in the concatenated structure for Justesen codes, a generalization of Justesen codes which completely meets the Zyablov bound is constructed. For this class of codes, the inner codes are explicitly defined while the outer codes are not.     

Another look at the Grubbs estimators

We consider estimation of the precision of a measuring instrument without the benefit of replicate observations on heterogeneous sampling units. Grubbs (1948) proposed an estimator which involves the use of a second measuring instrument, resulting in a pair of observations on each sampling unit. Since the precisions of the two measuring instruments are generally different, these observations cannot be treated as replicates. Very large sample sizes are often required if the standard error of the estimate is to be within reasonable bounds and if negative precision estimates are to be avoided. We show that the two instrument Grubbs estimator can be improved considerably if fairly reliable preliminary information regarding the ratio of sampling unit variance to instrument variance is available.Our results are presented in the context of the evaluation of on-line analyzers. A data set from an analyzer evaluation is used to illustrate the methodology.     

Another look at the disjoint blocks bootstrap

We revisit the Disjoint Blocks Bootstrap and establish Empirical Central Limit Theorem under minimal conditions. This result is much more general than similar results for the Moving Blocks Bootstrap and nicely complements the results for independent variables. We perform a comprehensive numerical study comparing these two methods.     

Another Look at the Process Capability Index

Process capability indices (PCIs) have been widely used in manufacturing industries. In this paper, we take a very specific view that a proper value of the process capacity index (PCI) represents the true yield of the process. Following this logic, a universal PCI, C_y, is proposed and derived. The superiority of the new PCI is presented in theory and demonstrated through examples. Copyright © 2005 John Wiley & Sons, Ltd.     

On the generalization of constitutive laws from their arotational forms

Summary Most of the practical materials may be regarded as Noll's simple materials and their constitutive laws are, in general, determined through some arotational constitutive experiments. The perfixa — in the term arotational from Greek denotes without. In this paper we give an equivalence theorem between the objectivity axiom and the formulation of the generalized constitutive laws from their arotational forms for simple materials. Finally, an example of simple shearing is given.     

Determining the geometric parameters of diffuse scattering objects

A spectral-correlation diagnostic method has been used for determining the linear dimensions of inhomogeneities with diffuse scattering surfaces in optical media. Experimental data are in good agreement with the results of numerical simulations and are consistent with theoretical notions. It is shown that the proposed method can be implemented on a simple technical basis and used is practice.     

Contributions to the generalization of advancing front particle packing algorithms

The generation of a set of particles with high initial volume fraction is a major problem in the context of discrete element simulations. Advancing front algorithms provide an effective means to generate dense packings when spherical particles are assumed. The objective of this paper is to extend an advancing front algorithm to a wider class of particles with generic size and shape. In order to get a dense packing, each new particle is placed in contact with other two (or three in 3D) particles of the advancing front. The contact problem is solved analytically using wrapping intersection technique. The results presented herein will be useful in the application of these algorithms to a wide variety of practical problems. Examples of geometric models for applications to biomechanics and cutting tools are presented. Copyright © 2015 John Wiley & Sons, Ltd.