Zero Class Research Articles

Robust estimation in truncated discrete distributions with application to capture-recapture experiments

Abstract A family of estimators is proposed for the relative frequency of the unobservable zero class in a truncated Poisson distribution. Large sample behavior is described by asymptotic expansion and robust properties are discussed in the presence of compound distributions. Two applications are presented involving the estimation of the number of unobserved individuals in complex capture-recapture experiments.

On the admissibility of estimators of the zero class in poisson populations

Let T = x1+ x2 + … + xn where x1,…, xn are independent and identically distributed randon variables each having a poission distribution with mean θ. It is proved that each of the estimators ((n+k−1)/(n+k))T, k = 0,1,2,… is admissible for estimating exp(−θ) when the loss function is squared error.

Design and manufacture of gear cutting tools and gears with an arbitrary profile.

The authors introduced a new method (element removal method) for calculating the profiles of the tools (hob, form grinding wheel, etc.) used for finishing gears with an arbitrary tooth profile. Because this method simulates exactly the metal removing process in the gear tooth profile generation, it is possible to calculate the generated tooth profile when interference occurs between the cutting edge and the finished tooth profile. Using this method, the authors calculated the exact wheel profile which can produce and involute tooth profile with a tip relief at a transverse section of the involute helical gears. The wheel profile was generated by a single point diamond dresser using a universal NC milling machine with an attachment made by the authors. The tooth flank and root of test gears were ground at the same time to prevent a step (notch), which is apt to be produced at the boundary of ground and unground surfaces. The accuracy of the form ground test gears was in the zero class of JIS and the surface roughness was in the range of 0.5 to 1.0 μm Rmax.

Comments on "On blocking zeros in linear multivariable systems"

Reference is made to a recently published correspondence by P.G. Ferreira in which concern was expressed about the name 'blocking zeros' given in a paper by R.V. Patel (see ibid., vol.AC-31, p.239-41, Mar. 1986) to a newly defined class of zeros for multivariable linear systems. The commenter refers to a few remarks about some 'well-known' results by Ferreira, and objects to the lack of precision in the wording of two of these remarks. Counterexamples to these 'well-known' results are presented. In replying, the original author claims that Example 1 is not a counterexample to his statement, and objects to some lack of precision in Martin's words. >

Nontrivial zeros of the Racah quadrupole invariant

It is shown that a class of nontrivial zeros of the Racah quadrupole invariant operator is given by two orbits of the group action of an infinite discrete subgroup of the proper two-dimensional Lorentz group SO(1,1) on the hyperbola 4x2−3y2= (11)/(4) .

Minimum variance unbiased estimation for the zero class truncated bivariate poisson and logarithmic series distributions

The minimum variance unbiased estimation for the zero class truncated bivariate Poisson and logarithmic series distributions is discussed. The distribution of a suitable complete and sufficient statistic is obtained in each case. These distributions, as well as the corresponding minimum variance unbiased estimators have been expressed in terms of certain polynomials with coefficients Stirling numbers.

A class of supersymmetric radiation zeros

We present a proof of a radiation interference theorem for processes involving the emission of a massless gauge fermion (photino) from interactions between members of chiral superfields, and derive the conditions for radiation zeros to exist.

Classical radiation zeros in gauge-theory amplitudes

The electromagnetic radiation from classical convection currents in relativistic $n$-particle collisions is shown to vanish in certain kinematical zones, due to complete destructive interference of the classical radiation patterns of the incoming and outgoing charged lines. We prove that quantum tree photon amplitudes vanish in the same zones, at arbitrary photon momenta including spin, seagull, and internal-line currents, provided only that the electromagnetic couplings and any other derivative couplings are as prescribed by renormalizable local gauge theory (spins \ensuremath{\le}1). In particular, the existence of this new class of amplitude zeros requires the familiar gyromagnetic-ratio value $g=2$ for all particles. The location of the zeros is spin independent, depending only on the charges and momenta of the external particles. Such null zones are the relativistic generalization of the well-known absence of electric and magnetic dipole radiation for nonrelativistic collisions involving particles with the same charge-to-mass ratio and $g$ factor. The origin of zeros in reactions such as $u\overline{d}\ensuremath{\rightarrow}{W}^{+}\ensuremath{\gamma}$ is thus explained and examples with more particles are discussed. Conditions for the null zones to lie in physical regions are established. A new radiation representation, with the zeros manifest and of practical utility independently of whether the null zones are in physical regions is derived for the complete single-photon amplitude in tree approximation, using a gauge-invariant vertex expansion stemming from new internal-radiation decomposition identities. The question of whether amplitudes with closed loops can vanish in null zones is addressed. A low-energy theorem for general quantum amplitudes (including closed loops) is found. Important relations between the photon couplings and Poincar\'e transformations are discovered. The null zone and these relations are discussed in terms of the Bargmann-Michel-Telegdi equation. The extension from photons to general massless gauge bosons is carried out.

Equations for the angles of arrival and departure for multivariable root loci using frequency-domain methods

Frequency-domain methods are used to study the angles of arrival and departure for multivariable root loci. Explicit equations are obtained. For a special class of poles and zeros, some simpler equations that are generalizations of the single-input-single-output equations are presented.

Bayesian estimation of the complete sample size from an incomplete poisson sample

For the Poisson a posterior distribution for the complete sample size, N, is derived from an incomplete sample when any specified subset of the classes are missing.Means as well as other posterior characteristics of N are obtained for two examples with various classes removed. For the special case of a truncated ‘missing zero class’ Poisson sample a simulation experiment is performed for the small ‘N=25’ sample situation applying both Bayesian and maximum likelihood methods of estimation.

Predicting Future Random Events Based on Past Performance

There are many situations where one is interested in predicting the expected number of events in period 2 given that x events occurred in period 1. For example, insurance companies must decide whether or not to cancel the insurance of drivers who had 3 or more accidents during the previous year. In analyzing marketing research data an analyst may wish to predict the number of future purchases to be made by those customers who made x purchases in the previous 3 months. The owner of a baseball team may wish to estimate the number of home runs a batter will hit this year given he hit (say) 40 home runs last year. When the events (e.g., accidents, purchase occasions, home runs) can be assumed to occur randomly over time a very general result due to Robbins (Robbins, H. 1977. Prediction and estimation for the compound Poisson distribution. Proc. National Acad Sci. USA 74 2670–2671.) is available. This approach has certain advantages and disadvantages with respect to the negative binomial model that is commonly used to analyze purchasing and accident data. The Robbins result is particularly appropriate for predicting what the zero class in period 1 will do in period 2. The main purpose of this paper is to present the Robbins result in a form that can be readily understood by applied researchers in a variety of disciplines. Data on consumer purchases, motor vehicle violations and accidents are analyzed and applications to other areas are discussed.

The estimation of the number of mutationally silent loci in saturation-mapping experiments.

SUMMARYWhen the technique of saturation mapping is employed to estimate the number of loci in a distinct chromosomal region, there is always the possibility that some loci will not be detected. If the number of mutants per locus follows a Poisson distribution, the number of mutationally silent loci can be estimated. This paper describes a method for fitting such data to a Poisson distribution truncated at the zero class and a method for estimating the number of mutationally silent loci. The use of these methods is demonstrated by their application to some published data.

The cohomology groups of a special Einstein manifold

We consider a compact orientable Einstein manifold of even dimension n=2m, which is k-pinched. If k>[m(m−1) 2 (2m−1) 2 (2m−1)+3], then there exists no element, different from zero of the H 2 (M,R) such that its exterior m-power belongs to a zero class. This result has some applications to the topological product of manifold.

Modified borel distributions†

Modified forms of the Borel distribution are fitted to the distribution of organisms in the following cases:(1) Empty colonies, i.e. zero class, are included in the samples;(2) some of the colonies with one organism have been included in the zero class; and(3) empty colonies and some colonies with one organism have been left out.

Estimating the Complete Sample Size from an Incomplete Poisson Sample

Abstract Maximum likelihood estimators and a modified maximum likelihood estimator are developed for estimating the zero class from a truncated Poisson sample when the available sample size itself is a random variable. All the estimators considered here are asymptotically equivalent in the usual sense; hence their asymptotic properties are investigated in some detail theoretically as well as by making use of Monte Carlo experiments. One modified estimator appears to be best with respect to the chosen criteria. An example is given to illustrate the results obtained.

Estimating the Complete Sample Size from an Incomplete Poisson Sample

Abstract Maximum likelihood estimators and a modified maximum likelihood estimator are developed for estimating the zero class from a truncated Poisson sample when the available sample size itself is a random variable. All the estimators considered here are asymptotically equivalent in the usual sense; hence their asymptotic properties are investigated in some detail theoretically as well as by making use of Monte Carlo experiments. One modified estimator appears to be best with respect to the chosen criteria. An example is given to illustrate the results obtained.

Estimating the Zero Class from a Truncated Poisson Sample

Abstract A procedure for estimating the zero class from a truncated Poisson sample is developed. Asymptotic normality of the estimator is proved so that a confidence interval for the missing zero class can be obtained. An example is given to illustrate the results obtained.

Estimating the Zero Class from a Truncated Poisson Sample

Abstract A procedure for estimating the zero class from a truncated Poisson sample is developed. Asymptotic normality of the estimator is proved so that a confidence interval for the missing zero class can be obtained. An example is given to illustrate the results obtained.

Zeros of generalized hypergeometric functions

In this paper we derive the conditions which have to be satisfied in order to obtain some classes of zeros of the generalized hypergeometric series of the typeThese conditions read:

Relative Estimates of Small-Mammal Populations in Relation to the Spatial Pattern of Trappability

The principles of evaluating relative estimates is described on the basis of a study of Clethrionomys glareolus (Schreber) and Apodemusflavicollis (Melchior). The frequency distribution of the trappability of the two species conforms to a Poisson distribution with added zeros. These surplus zeros are considered to be inversely proportional to the habitat penetration. If unrestricted trapping capacity (or a good approximation of it) is applied at each trap site, the mean of the catches at the trap sites constitutes a rectified population density index. Rectified means that a doubled index value always implies a doubled population density. The properties of the Poisson distribution makes it possible, however, to sketch a theoretical model of relative estimates in which only one single-catching trap is set at each trap site. The known relation between the mean and the zero class of the Poisson distribution (a non-linear asymptotic regression) may be used to calculate a rectified population density index from such presence/absence data. In this case the surplus zeros must be formulated as a population parameter.