共查询到20条相似文献,搜索用时 31 毫秒
1.
A. N. Philippou 《Biometrical journal. Biometrische Zeitschrift》1989,31(1):67-74
The Poisson-binomial, the Poisson-negative binomial (or Pascal) and Neyman's Type A distribution, which are Poisson mixtures of the binomial, the negative binomial and the Poisson distribution, respectively, have received a lot of attention in statistical literature [see e.g. Katti and Gurland (1961, 1962), Anscombe (1950), and Neyman (1939)]. In the present paper, their respective generalizations are introduced and briefly studied, when the Poisson distribution of order k [see Philippou (1983), Philippou, Georghiou and Philippou (1983), and Charalambides (1986)] replaces the Poisson distribution in its mixing role. 相似文献
2.
Generalized Poisson distribution: the property of mixture of Poisson and comparison with negative binomial distribution 总被引:2,自引:0,他引:2
We prove that the generalized Poisson distribution GP(theta, eta) (eta > or = 0) is a mixture of Poisson distributions; this is a new property for a distribution which is the topic of the book by Consul (1989). Because we find that the fits to count data of the generalized Poisson and negative binomial distributions are often similar, to understand their differences, we compare the probability mass functions and skewnesses of the generalized Poisson and negative binomial distributions with the first two moments fixed. They have slight differences in many situations, but their zero-inflated distributions, with masses at zero, means and variances fixed, can differ more. These probabilistic comparisons are helpful in selecting a better fitting distribution for modelling count data with long right tails. Through a real example of count data with large zero fraction, we illustrate how the generalized Poisson and negative binomial distributions as well as their zero-inflated distributions can be discriminated. 相似文献
3.
M. J. Faddy 《Biometrical journal. Biometrische Zeitschrift》1997,39(4):431-440
It is shown that any discrete distribution with non-negative support has a representation in terms of an extended Poisson process (or pure birth process). A particular extension of the simple Poisson process is proposed: one that admits a variety of distributions; the equations for such processes may be readily solved numerically. An analytical approximation for the solution is given, leading to approximate mean-variance relationships. The resulting distributions are then applied to analyses of some biological data-sets. 相似文献
4.
S. G. CANDY 《Austral ecology》1997,22(2):233-235
Abstract Mac Nally (1996), in describing the application of ‘hierarchical partitioning’ in regression modelling of species richness of breeding passerine birds with response variable the species count, rejects the use of Poisson regression in favour of normal-errors regression on an incorrect basis. Mac Nally uses a function of the residual sum of squares, the root-mean square prediction error (RMSPE), calculated from predictions from each regression and rejects the Poisson regression because its RMSPE was 20% larger. This note points out that the RMSPE will always be larger for the Poisson regression, given the same link function and linear predictor is used, even if the response is truly Poisson. References to appropriate methods of determining the most suitable response distribution and link function in the context of generalized linear models are given. 相似文献
5.
Frank Krummenauer 《Biometrical journal. Biometrische Zeitschrift》1998,40(7):823-832
Power investigations, for example, in statistical procedures for the assessment of agreement among multiple raters often require the simultaneous simulation of several dependent binomial or Poisson distributions to appropriately model the stochastical dependencies between the raters' results. Regarding the rather large dimensions of the random vectors to be generated and the even larger number of interactions to be introduced into the simulation scenarios to determine all necessary information on their distributions' dependence stucture, one needs efficient and fast algorithms for the simulation of multivariate Poisson and binomial distributions. Therefore two equivalent models for the multivariate Poisson distribution are combined to obtain an algorithm for the quick implementation of its multivariate dependence structure. Simulation of the multivariate Poisson distribution then becomes feasible by first generating and then convoluting independent univariate Poisson variates with appropriate expectations. The latter can be computed via linear recursion formulae. Similar means for simulation are also considered for the binomial setting. In this scenario it turns out, however, that exact computation of the probability function is even easier to perform; therefore corresponding linear recursion formulae for the point probabilities of multivariate binomial distributions are presented, which only require information about the index parameter and the (simultaneous) success probabilities, that is the multivariate dependence structure among the binomial marginals. 相似文献
6.
Optimal foraging theory is being used increasingly as a means of understanding human foraging behavior. One of the central assumptions of optimal foraging theory is that prey items or patches are encountered sequentially and as a Poisson process. Using empirical data gathered on the Barí hunters of Venezuela, we assess the validity of this central assumption. We compare our observed distribution of encounter frequencies with an expected Poisson distribution, utilizing chisquare tests and graphic representations. The results are strikingly consonant with the expected Poisson distribution and lend support to the applicability of optimal foraging models to human hunting behavior. 相似文献
7.
M. S. H. Khan 《Biometrical journal. Biometrische Zeitschrift》1985,27(2):217-223
This paper considers some approximations for the Borel-Tanner (Generalized Poisson) sums by using (i) Gram-Charlier Poisson expansion, (ii) Mixture of two Poisson distributions, (iii) Variance stabilizing technique, and (iv) negative binomial distribution. It has been found that the approximation obtained by using the negative binomial distribution seems to be more efficient than the other approximation. 相似文献
8.
Devendra Gupta 《Biometrical journal. Biometrische Zeitschrift》1984,26(1):89-94
CONSUL and JAIN (1973a) introduced a generalized Poisson distribution, which has applications in reliability theory and many biometric studies, and described some of its properties. Here we obtain two new distributions treating two of the parameters of the above distribution as random variables having gamma and absolute value distributions. One of the new distributions is related to the negative binomial distribution. Their moments also have been obtained. 相似文献
9.
P. Dhanavanthan 《Biometrical journal. Biometrische Zeitschrift》1998,40(5):641-646
The nature and characteristics of Intervened Poisson Distribution (IPD) has been well discussed by Shanmugam (1985). In this paper, Compound Intervened Poisson Distribution (CIPD) is introduced and its properties are studied. 相似文献
10.
A score test for testing a zero-inflated Poisson regression model against zero-inflated negative binomial alternatives 总被引:3,自引:0,他引:3
Count data often show a higher incidence of zero counts than would be expected if the data were Poisson distributed. Zero-inflated Poisson regression models are a useful class of models for such data, but parameter estimates may be seriously biased if the nonzero counts are overdispersed in relation to the Poisson distribution. We therefore provide a score test for testing zero-inflated Poisson regression models against zero-inflated negative binomial alternatives. 相似文献
11.
Hugo Naya Jorge I Urioste Yu-Mei Chang Mariana Rodrigues-Motta Roberto Kremer Daniel Gianola 《遗传、选种与进化》2008,40(4):379-394
Dark spots in the fleece area are often associated with dark fibres in wool, which limits its competitiveness with other textile fibres. Field data from a sheep experiment in Uruguay revealed an excess number of zeros for dark spots. We compared the performance of four Poisson and zero-inflated Poisson (ZIP) models under four simulation scenarios. All models performed reasonably well under the same scenario for which the data were simulated. The deviance information criterion favoured a Poisson model with residual, while the ZIP model with a residual gave estimates closer to their true values under all simulation scenarios. Both Poisson and ZIP models with an error term at the regression level performed better than their counterparts without such an error. Field data from Corriedale sheep were analysed with Poisson and ZIP models with residuals. Parameter estimates were similar for both models. Although the posterior distribution of the sire variance was skewed due to a small number of rams in the dataset, the median of this variance suggested a scope for genetic selection. The main environmental factor was the age of the sheep at shearing. In summary, age related processes seem to drive the number of dark spots in this breed of sheep. 相似文献
12.
Testing approaches for overdispersion in poisson regression versus the generalized poisson model 总被引:1,自引:0,他引:1
Overdispersion is a common phenomenon in Poisson modeling, and the negative binomial (NB) model is frequently used to account for overdispersion. Testing approaches (Wald test, likelihood ratio test (LRT), and score test) for overdispersion in the Poisson regression versus the NB model are available. Because the generalized Poisson (GP) model is similar to the NB model, we consider the former as an alternate model for overdispersed count data. The score test has an advantage over the LRT and the Wald test in that the score test only requires that the parameter of interest be estimated under the null hypothesis. This paper proposes a score test for overdispersion based on the GP model and compares the power of the test with the LRT and Wald tests. A simulation study indicates the score test based on asymptotic standard Normal distribution is more appropriate in practical application for higher empirical power, however, it underestimates the nominal significance level, especially in small sample situations, and examples illustrate the results of comparing the candidate tests between the Poisson and GP models. A bootstrap test is also proposed to adjust the underestimation of nominal level in the score statistic when the sample size is small. The simulation study indicates the bootstrap test has significance level closer to nominal size and has uniformly greater power than the score test based on asymptotic standard Normal distribution. From a practical perspective, we suggest that, if the score test gives even a weak indication that the Poisson model is inappropriate, say at the 0.10 significance level, we advise the more accurate bootstrap procedure as a better test for comparing whether the GP model is more appropriate than Poisson model. Finally, the Vuong test is illustrated to choose between GP and NB2 models for the same dataset. 相似文献
13.
Computer simulation of error rates of Poisson-based interval estimates of plankton abundance 总被引:1,自引:1,他引:0
The routine assignment of error rates (confidence intervals) to Poisson distribution estimates of plankton abundance should be rejected. In addition to the interval estimation procedure being pseudoreplicative, it is not robust to common violations of its assumptions. Because the spatial dispersion of organisms in sampling units from the counting chamber to the field is rarely random and because counting protocols are usually terminated by a count threshold having been equalled or exceeded, Poisson based estimates are usually derived from sampling non-Poisson distributions. Computer simulation was used to investigate the quantitative consequences of such estimates. The expected mean error rate of 95% confidence intervals is inflated from 5% to 15% as contagion increases, as the parametric variance-mean ratio increases from 1 to 2. Also, count threshold termination of the counting protocol effects both a biased estimate of the parametric mean (or total) and alters expected mean error rates, especially if the total count is low (< 100 organisms) and the mean density in the sampling unit is low. 相似文献
14.
ZhangFaqin 《生物数学学报》1996,(2)
Thispaperdiscussesthelimitdistributionofnumberofraremutantsinamutationprocess.Theresultofthepapergeneralizedthatof[1].Meanwhile,theauthoralsodiscusscompoundPoissonapproximationtheoremforakindofrandomsum. 相似文献
15.
Yongmin Zhong Bijan Shirinzadeh Gursel Alici Julian Smith 《Computer methods in biomechanics and biomedical engineering》2013,16(5):289-304
In this paper, we present a new methodology for the deformation of soft objects by drawing an analogy between the Poisson equation and elastic deformation from the viewpoint of energy propagation. The potential energy stored due to a deformation caused by an external force is calculated and treated as the source injected into the Poisson system, as described by the law of conservation of energy. An improved Poisson model is developed for propagating the energy generated by the external force in a natural manner. An autonomous cellular neural network (CNN) model is established by using the analogy between the Poisson equation and CNN to solve the Poisson model for the real-time requirement of soft object deformation. A method is presented to derive the internal forces from the potential energy distribution. The proposed methodology models non-linear materials with the non-linear Poisson equation and thus non-linear CNN, rather than geometric non-linearity. It not only deals with large-range deformations, but also accommodates isotropic, anisotropic and inhomogeneous materials by simply modifying constitutive coefficients. A haptic virtual reality system has been developed for deformation simulation with force feedback. Examples are presented to demonstrate the efficiency of the proposed methodology. 相似文献
16.
H. Papageorgiou S. Loukas S. Loukas 《Biometrical journal. Biometrische Zeitschrift》1995,37(1):105-117
A bivariate distribution is introduced with marginals convolutions of a binomial and a Poisson random variables. Various properties of the distribution are examined. Estimation is discussed and illustrated by fitting the distribution to two sets of data. An application to ornithology is also indicated. 相似文献
17.
Population models concern collections of discrete entities such as atoms, cells, humans, animals, etc., where the focus is on the number of entities in a population. Because of the complexity of such models, simulation is usually needed to reproduce their complete dynamic and stochastic behaviour. Two main types of simulation models are used for different purposes, namely micro-simulation models, where each individual is described with its particular attributes and behaviour, and macro-simulation models based on stochastic differential equations, where the population is described in aggregated terms by the number of individuals in different states. Consistency between micro- and macro-models is a crucial but often neglected aspect. This paper demonstrates how the Poisson Simulation technique can be used to produce a population macro-model consistent with the corresponding micro-model. This is accomplished by defining Poisson Simulation in strictly mathematical terms as a series of Poisson processes that generate sequences of Poisson distributions with dynamically varying parameters. The method can be applied to any population model. It provides the unique stochastic and dynamic macro-model consistent with a correct micro-model. The paper also presents a general macro form for stochastic and dynamic population models. In an appendix Poisson Simulation is compared with Markov Simulation showing a number of advantages. Especially aggregation into state variables and aggregation of many events per time-step makes Poisson Simulation orders of magnitude faster than Markov Simulation. Furthermore, you can build and execute much larger and more complicated models with Poisson Simulation than is possible with the Markov approach. 相似文献
18.
Jerrold H. Zar 《Biometrical journal. Biometrische Zeitschrift》1984,26(1):83-88
The Poisson distribution may be employed to test whether mutation frequencies differ from control frequencies. This paper describes how this testing procedure may be used for either one-tailed or two-tailed hypotheses. It is also shown how the power of the statistical test can be calculated, the power being the probability of correctly concluding the null hypothesis to be false. 相似文献
19.
Molecular dynamics simulations have been carried out for simple electrolyte systems to study the electrokinetically driven osmotic flow in parallel-plate channels of widths ~10–120?nm. The results are compared with the classical theory predictions based on the solution to the Poisson–Boltzmann equation. We find that despite some of the limitations in the Poisson–Boltzmann equation, such as assumption of the Boltzmann distribution for the ions, the classical theory captures the general trend of the variations of the osmotic flow with channel width, as characterized by the mobility of the fluid in channels between ~10 and 120?nm at moderate to low ion concentration. At moderate concentration (corresponding to relatively low surface potential), the classical theory is almost quantitative. The theory and simulation show more disagreement at low concentration, primarily caused by the high surface potential where the assumption of Boltzmann distribution becomes inaccurate. We discuss the limitations of the Poisson–Boltzmann equation as applied to the nanoscale channels. 相似文献
20.
J. Campione-Piccardo 《Biometrical journal. Biometrische Zeitschrift》1983,25(8):807-815
The use of an approximation to the median of the Poisson distribution to represent each occurrence of mutations in a growing clone permits the prediction of the number of mutants per clone without the limitations imposed by more heuristic expressions. Its application to the evaluation of mutation rates yields results comparable to those obtained by fluctuation analysis. 相似文献