Showing papers on "Poisson distribution published in 1980"
TL;DR: Techniques are presented for calculating the drain current of small-geometry MOSFET's in the linear, subthreshold, and punch-through regions of device operation and the solution method demonstrates good convergence characteristics and minimizes computer storage requirements.
Abstract: Techniques are presented for calculating the drain current of small-geometry MOSFET's in the linear, subthreshold, and punch-through regions of device operation. The current calculation depends only on the electrostatic solution of the two-dimensional Poisson equation in the device. The accuracy of the techniques is established by comparisons with full two-dimensional simulations based on the simultaneous solution of the Poisson and minority-carrier current-continuity equations. The results of simulation also agree well with measurements on MOSFET's having submicrometer effective channel lengths. The application of the simulations to nonplanar technologies is illustrated by the analysis of a taper-isolated dynamic-gain RAM cell. A description is given of simple numerical techniques for solving Poisson's equation in the presence of nonplanar boundaries. The solution method demonstrates good convergence characteristics and minimizes computer storage requirements. Consequently, the simulation capabilities have been successfully implemented on a desktop calculator (Hewlett-Packard 9845) and on minicomputers (Hewlett-Packard 2100 and 1000-F).
141 citations
01 Apr 1980
TL;DR: Discrete (binomial and Poisson) software reliability models, previously developed by IBM, are presented and it is indicated that the models provide reasonable fits to the historical error data.
Abstract: : Discrete (binomial and Poisson) software reliability models, previously developed by IBM, are presented. They were examined for their validity using historical data provided by RADC from seven development projects. Simulated error data that closely agreed with the model assumptions were also used for validation. The results indicated that the models provide reasonable fits to the historical error data.
115 citations
TL;DR: In this article, the distance from the root to the nearest endertex other than itself is estimated for a random rooted labeled tree on n vertices, where each generation of a branching process with Poisson family sizes, parameter one, is supplemented by a single additional member added at random to one of the families in that generation.
Abstract: A random rooted labelled tree on n vertices has asymptotically the same shape as a branching-type process, in which each generation of a branching process with Poisson family sizes, parameter one, is supplemented by a single additional member added at random to one of the families in that generation. In this note we use this probabilistic representation to deduce the asymptotic distribution of the distance from the root to the nearest endertex other than itself.
81 citations
TL;DR: In this paper, the authors applied Poisson and negative binomial models to the number of multiple victimizations reported in the National Crime Surveys (NCS) and found that the negative model was more accurate than the Poisson model.
Abstract: Poisson and negative binomial models are applied to the number of multiple victimizations reported in the National Crime Surveys. The negative binomial but not the Poisson models is shown to be com...
81 citations
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TL;DR: In this article, a graphical technique, similar in spirit to probability plotting, is used to judge whether a Poisson model is appropriate for an observed frequency distribution, which can be applied to truncated Poisson situations.
Abstract: A graphical technique, similar in spirit to probability plotting, can be used to judge whether a Poisson model is appropriate for an observed frequency distribution. This “Poissonness plot” can equally be applied to truncated Poisson situations. It provides a type of robustness for detecting isolated discrepancies in otherwise well-behaved frequency distributions.
71 citations
68 citations
TL;DR: An accurate acceptance-rejection algorithm is devised and tested, which requires an average of less than 3 uniform deviates whenever the standard deviation σ of the distribution is at least 4, and this number decreases monotonically to 2.63 as σ→∞.
Abstract: An accurate acceptance-rejection algorithm is devised and tested. The procedure requires an average of less than 3 uniform deviates whenever the standard deviation σ of the distribution is at least 4, and this number decreases monotonically to 2.63 as σ→∞. Variable parameters are permitted, and no subroutines for sampling from other statistical distributions are needed.
56 citations
TL;DR: In this article, a multigrade population with semi-Markov transitions between grades, Poisson arrivals to each grade, and departures from each grade is considered and the joint distribution of the numbers in each grade at any time is found, and the limiting distributions shown to be independently Poisson.
Abstract: We consider a multigrade population with semi-Markov transitions between grades, Poisson arrivals to each grade, and departures from each grade. For this model the joint distribution of the numbers in each grade at any time is found, and the limiting distributions shown to be independently Poisson; this extends a previous result for a multigrade population with Markov transitions and Poisson recruitment. This model is particularly applicable to manpower planning. The inclusion of semi-Markov transitions allows us to take into account existing knowledge of the distribution of length of service until an individual leaves his firm.
51 citations
TL;DR: In this article, the authors consider the problem of characterizing functions on a bounded symmetric domain of tube type with Shilov boundary S to be the Poisson integrals of functionals on S.
Abstract: Let Q c C" be a bounded symmetric domain of tube type with Shilov boundary S. On S? there is a Cauchy integral mapping function on 3 to holomorphic functions on Q. By a classical device and also by Hua [51 one can thus define a Poisson kernel on 3 x Q and a Poisson integral which maps functions on ? to functions on Q. Now any holomorphic or antiholomorphic function on Q is the Poisson integral ?P(f) of a hyperfunction on 3_; however, it is not true in general that every harmonic function on Q can be realized as the Poisson integral of some functional on S. How can one characterize the functions on Q which are the Poisson integrals of functionals on _? We now consider the following problem.
41 citations
TL;DR: By studying these equations separately in between jumps and at the jumps, series expansions are obtained for these generating functions and densities in a number of examples that arise in applications to optical modulation and communications networks.
Abstract: A conditional Poisson process is observed, whose rate is a diffusion process of known structure. The problem is to estimate the rate from the observed point process. Recursive equations are given for the conditional moment generating function and for an unnormalized conditional probability density of the rate. By studying these equations separately in between jumps and at the jumps, series expansions are obtained for these generating functions and densities in a number of examples that arise in applications to optical modulation and communications networks.
36 citations
TL;DR: It is shown that the dilemma of estimating the tax parameter E(thetax = a) for some given a = 0,1,....
Abstract: Let x be a random variable such that, given θ, x is Poisson with mean θ, while θ has an unknown prior distribution G. In many statistical problems one wants to estimate as accurately as possible the parameter E(θǀx = a) for some given a = 0,1,.... If one assumes that G is a Gamma prior with unknown parameters α and β, then the problem is straightforward, but the estimate may not be consistent if G is not Gamma. On the other hand, a more general empirical Bayes estimator will always be consistent but will be inefficient if in fact G is Gamma. It is shown that this dilemma can be more or less resolved for large samples by combining the two methods of estimation.
TL;DR: The customer waiting time distribution is derived for an S − 1, S continuous review inventory system experiencing Poisson demands and general independent identically distributed lead times and uses results from the infinite server Poisson queue.
Abstract: The customer waiting time distribution is derived for an S − 1, S continuous review inventory system experiencing Poisson demands and general independent identically distributed lead times. The analysis uses results from the infinite server Poisson queue. Some comparisons are made with an approximation to the waiting time distribution due to Higa et al.
TL;DR: In this paper, the perturbed evolution of a free evolution by gentle, possibly velocity dependent, potential, in terms of the expectation with respect to a Poisson process on a group, is studied.
Abstract: We give an expression for the perturbed evolution of a free evolution by gentle, possibly velocity dependent, potential, in terms of the expectation with respect to a Poisson process on a group. Various applications are given in particular to usual quantum mechanics but also to Fermi and spin systems.
TL;DR: The queueing model developed is quite general in a sense that it covers pure Poisson and burst Poisson arrival processes and the mixture of the two as well and may be used as guidelines in buffer design problems in digital voice-data systems.
Abstract: A queueing model with finite buffer size, mixed input traffic (Poisson and burst Poisson arrivals), synchronous transmission and server interruptions through a Bernoulli sequence of independent random variables is studied. Using average burst length, traffic intensity and input traffic mixture ratio as parameters, the relationships among buffer size, overflow probability and expected message queueing delay are obtained. An integrated digital voice-data system with synchronous time division multiplexing (STDM) for a large number of voice sources and mixed arrival process for data messages is considered as an application for this model. The results of this study are portrayed on graphs and may be used as guidelines in buffer design problems in digital voice-data systems. The queueing model developed is quite general in a sense that it covers pure Poisson and burst Poisson arrival processes and the mixture of the two as well.
TL;DR: In this paper, the problem of finding the minimum variance unbiased (MVU) estimators of the functions of the para-meters of the modified power series distributions (MPSD) was studied.
Abstract: In this paper we study the problem of finding the minimum variance unbiased (MVU) estimators of the functions of the para-meters of the modified power series distributions (MPSD). A theorem giving the necessary and sufficient conditions for the existence of the MVU estimators has been proved. Also, the estimators for a number of estimable functions of a parameter are obtained. Two other theorems dealing with the MVU estimation of the left truncated MPSD with unknown truncation point are also given. The particular case of the Lagrangian Poisson, the Lagrangian binomial and the Borel-Tanner distributions are considered and tables are also provided for the MVU estimators for some functions of the parameters. The variances of the estimators are also given for some cases.
TL;DR: Techniques are presented for calculating the drain current of small-geometry MOSFET's in the linear, subthreshold, and punch-through regions of device operation and the solution method demonstrates good convergence characteristics and minimizes computer storage requirements.
Abstract: Techniques are presented for calculating the drain current of small-geometry MOSFET's in the linear, subthreshold, and punch-through regions of device operation. The current calculation depends only on the electrostatic solution of the two-dimensional Poisson equation in the device. The accuracy of the techniques is established by comparisons with full two-dimensional simulations based on the simultaneous solution of the Poisson and minority-carrier current-continuity equations. The results of simulation also agree well with measurements on MOSFET's having submicrometer effective channel lengths. The application of the simulations to nonplanar technologies is illustrated by the analysis of a taper-isolated dynamic-gain RAM cell. A description is given of simple numerical techniques for solving Poisson's equation in the presence of nonplanar boundaries. The solution method demonstrates good convergence characteristics and minimizes computer storage requirements. Consequently, the simulation capabilities have been successfully implemented on a desktop calculator (Hewlett-Packard 9845) and on minicomputers (Hewlett-Packard 2100 and 1000-F).
TL;DR: In this paper, the authors measure the center of a set of observations and measure the variability of the centre of the observations using simple linear regression and multiple regression with the normal distribution.
Abstract: Populations and variates. Measures of the centre of a set of observations. Samples and populations. The measurement of variability. Looking at data. Probability. Probabilities of compound events. Discrete random variable. Expectation of a random variable. Joint distributions. Estimation. Collecting data. Significance testing. Continuous random variables. The normal distribution. Sampling distributions of means and related quantities. Significance tests using the normal distribution. Estimation of intervals and parameters. Hypothesis tests using the chi-squared distribution. Poisson distribution. Correlation. The analysis of variance. Simple linear regression. Multiple regression.
TL;DR: In this paper, an alternative model, the Poisson-binomial, P-B, model, is proposed to express the relationship between the number of accidents and number of fatalities.
Abstract: Suppose X denotes the number of injury accidents on a given stretch of highway in a given period, Y denotes the number of these accidents which resulted in one or more fatalities and Z denotes the number of fatalities recorded among the X accidents. In this Review, Leiter amd Hamdan (1973) suggested that the joint distribution of the number of accidents and the number of fatal accidents can be expressed by a Poisson-Bernoulli model (Poisson-Binomial in their terminology) and the joint distribution of the number of accidents and the number of fatalities by a Poisson-Poisson, P-P, distribution. In the present paper an alternative model, the Poisson-Binomial, P-B, model, is proposed to express the relationship between the number of accidents and the number of fatalities. Various properties of this model were investigated including the derivation of the conditional probability generating function (p.g.f.) using the basic relation between the Bell polynomials and the derivatives of a composite function (see for example Riordan, 1958, p. 34). For comparison purposes the P-B model is fitted to the same set of accident data used by Leiter and Hamdan. The present representation of Z, the number of fatalities, as a sum of X binomial variables, each with parameters n and p, means that the n passengers in a motor vehicle involved in an injury accident play the role of n independent Bernoulli trials; this assumption of independence is, of course, rather unrealistic since the fate (fatality or not) of a passenger is correlated with that of his co-passengers. Nevertheless the Poisson-Binomial model is almost as good as the Poisson-Poisson model, even for small n = 2, 3. As n gets larger (n = 4 or 5) the P-B model approaches the P-P model, as reflected in the values of the X2-criterion. This is expected since the values ofp, the probability of a passenger being killed in an injury accident, are small and so the binomial distribution can be approximated by the Poisson distribution, even for moderate values of n. The P-P model was further studied and expressions for the bivariate p.g.f. and the conditional p.g.f.'s were obtained. Finally, it is pointed out that the Poisson-Bernoulli model is a special case of the well known bivariate Poisson distribution (see for example Johnson and Kotz, 1968, p. 297 and the references therein).
TL;DR: In this article, a method of including the effect of unknown initial conditions in the general algorithms for transfer function synthesis via Poisson moment functionals was presented, and tested with process data containing zero mean noise and is found to be remarkably immune to such noise.
Abstract: This paper presents a method of including the effect, of unknown initial conditions in the general algorithms for transfer function synthesis recently developed by the authors (Saha and Prasada Rao 1979) via Poisson moment functionals. The proposed technique is of considerable practical importance in problems of parameter identification in which input-output data is available on an arbitrary but active interval of time. The technique is tested with process data containing zero mean noise and is found to be remarkably immune to such noise.
TL;DR: In this article, a mathematical model of the observed pattern of spots is given and a method for its statistical analysis is proposed, in which disc centres are distributed in a Poisson field of constant intensity A and the disc radii r are independent, identically distributed according to a probability density f(r)
Abstract: SUMMARY In the plane, a Poisson field of discs with random radii is considered. A method of estimating the Poisson intensity and the expectation and variance of the radii is proposed, and then investigated in detail for normally distributed radii. Foils consisting of a fission material and an isolation material are exposed to neutron radiation. Tracks caused by fission products in the isolation material are enlarged by a chemical etching process and made observable under an optical microscope as dark spots on the surface of the foil. Up to a clumping effect, the number of spots is proportional to the measured neutron flux, the shape and size of the spots depending mainly on the process of etching. In what follows, a mathematical model of the observed pattern of spots is given and a method for its statistical analysis proposed. Discs of random size are placed at random on the plane. More precisely, we suppose that the disc centres are distributed in a Poisson field of a constant intensity A and that the disc radii r are independent, identically distributed according to a probability density f(r)
TL;DR: In this paper, for three types of exploration of a rectangle D, vertical, horizontal and diagonal, the reference probability method is used to derive filtering equations according to a partial ordering of.
Abstract: Observed point data on a rectangle D of are represented by a doubly stochastic Poisson measure Y. Its intensity is supposed to be a known function of a two-parameter process X, a semi-martingale of a Brownian sheet. As in the one-parameter case, the identification of the model goes through a recursive estimation of X. For three types of exploration of D— vertical, horizontal and diagonal—, we wish to derive filtering equations according to a partial ordering of . These are obtained by the reference probability method
TL;DR: In this article, Bayes estimates of failure intensity, MTBF, and reliability are compared for five classes of loss functions and numerical comparisons are made to show the widely different decisions that may be reached if different loss functions are used and to aid researchers in selecting a loss function to meet experimental objectives.
TL;DR: In this article, the Ruark-Devol statistical density function was proposed to describe the process of radioactive disintegration where the only fundamental property is independence and stationarity are the fundamental properties that must be possessed by a physical process to obey Poisson statistics.
DOI•
01 Dec 1980TL;DR: It is shown that the expression for the buffer-content state probability of the finite buffer of any length can be directly deduced from that of the infinite buffer, and hence various performance parameters can be evaluated.
Abstract: A closed-form solution to the buffer design problem is presented by studying a queueing model with a hybrid input traffic arrival process (mixture of Poisson and burst Poisson processes), synchronous output and single server with random interruptions. The queueing model developed is of unified nature as it includes Poisson and burst Poisson arrival processes and the mixture of the two as well. It is shown that, at a modified offered load, the empty buffer probability in an infinite buffer equals that of a finite buffer with actual offered load as its input. The modified offered load is shown to be equal to the carried load of the finite buffer. Thus, it is shown that the expression for the buffer-content state probability of the finite buffer of any length can be directly deduced from that of the infinite buffer, and hence various performance parameters can be evaluated. An integrated digital voice-data system is taken as an example for the model developed. The relationships among buffer size, overflow probability and average message queueing delay due to buffering are portrayed on graphs with the average burst length, the traffic intensity and the input traffic mixture ratio taken as parameters. It is concluded that the burst nature of the input traffic is a very important factor in the buffer design problem.
TL;DR: In this paper, the authors provide explicit solutions to the problem of estimating the arrival rate of a Poisson process using a Bayes sequential approach, where the cost of observation includes both a time cost and an event cost.
Abstract: This paper provides explicit solutions to the problem of estimating the arrival rate $\lambda$ of a Poisson process using a Bayes sequential approach. The loss associated with estimating $\lambda$ by $d$ is assumed to be of the form $(\lambda - d)^2\lambda^{-p}$ and the cost of observation includes both a time cost and an event cost. A discrete time approach is taken in which decisions are made at the end of time intervals having length $t$. Limits of the procedures as $t$ approaches zero are discussed and related to the continuous time Bayes sequential procedure.
TL;DR: A generalized increment threshold law is obtained that describes the relationship between the just detectable average signal increment and the noise when the threshold is stabilized, for the usual yes-no (nonorthogonal) signal format.
TL;DR: In this article, it is suggested that estimation of arbitrary linear combin can be used to make simultaneous confidence interval statements concerning the parameters and linear functions of the combinatorial functions.
Abstract: Given independent observations from k Poisson populations it is frequently of interest to make simultaneous confidence interval statements concerning the parameters and linear functions of them. It is suggested that estimation of arbitrary linear combin..
TL;DR: In this article, the effect of unknown initial conditions of the process is included in the related operational matrices thereby making the algorithm useful in the important practical situation wherein process data is available over an arbitrary but active length of time.
Abstract: Poisson Moment Functionals (PMF) of input and ouput of a Single-Input-Single-Output (SISO) system characterized by a linear differential equation with time varying coefficients, are used in a general algorithm of parameter identification. The method is a generalized version of certain recent algorithms proposed by Saba and Prasada Rao (1979) for fixed parameter systems. The effect of unknown initial conditions of the process is included in the related operational matrices thereby making the algorithm useful in the important practical situation wherein process data is available over an arbitrary but active length of time.