SPATIAL PATTERN OF THE IMMATURE STAGES AND TENERAL ADULTS OF PHYLLOPHAGA SPP. (COLEOPTERA: SCARABAEIDAE) IN A PERMANENT MEADOW

1970 ◽  
Vol 102 (11) ◽  
pp. 1354-1359 ◽  
Author(s):  
J. C. Guppy ◽  
D. G. Harcourt
Keyword(s):  
Spatial Pattern ◽  
Poisson Distribution ◽  
Negative Binomial ◽  
Fractional Power ◽  
Immature Stages ◽  
Expected Number ◽  
White Grubs ◽  
Chi Square ◽  
First Instar ◽  
The Mean

Abstract Random counts of the white grubs, Phyllophaga fusca Froelich and P. anxia LeConte, in a permanent meadow did not conform to the Poisson distribution, there being an excess of uninfested and highly infested sample units over the expected number. But when the negative binomial series was fitted to the observed distribution, the discrepancies were not significant when tested by chi-square. Using a common k, the distribution of the various stages may be described by expansion of (q-p)−k, when values of k are as follows: egg 0.15, first instar 0.41, second instar 1.30, third instar 2.00, pupa 1.62, teneral adult 1.30. Aggregation resulted from the clumping of eggs at oviposition, and randomness increased with dispersal of the larvae. For all stages, the variance was proportional to a fractional power of the mean. Three transformations are offered for stabilizing the variance of field counts.

SPATIAL PATTERN OF THE IMMATURE STAGES OF HYLEMYA BRASSICAE ON CABBAGE

1970 ◽  
Vol 102 (10) ◽  
pp. 1216-1222 ◽  
Author(s):  
M. K. Mukerji ◽  
D. G. Harcourt
Keyword(s):  
Spatial Pattern ◽  
Poisson Distribution ◽  
Negative Binomial ◽  
Immature Stages ◽  
Expected Number ◽  
Chi Square ◽  
Binomial Series ◽  
Binomial Parameter ◽  
Hylemya Brassicae ◽  
Cabbage Maggot

AbstractCounts of the cabbage maggot, Hylemya brassicae (Bouché), on cabbage did not conform to the Poisson distribution, there being an excess of uninfested and highly infested plants over the expected number. But when the negative binomial series was fitted to the observed distribution, the discrepancies were not significant when tested by chi-square. The negative binomial parameter k tended to increase with density. Using a common k, the distribution of the various stages may be described by expansion of (q − p)−k, when values of k are as follows: egg 0.78, larva 0.71, pupa 0.84. Three different transformations are offered for stabilizing the variance of field counts.

Population Dynamics ofLeptinotarsa decemlineata(Say) in Eastern Ontario: I. Spatial Pattern and Transformation of Field Counts

1963 ◽  
Vol 95 (8) ◽  
pp. 813-820 ◽  
Author(s):  
D. G. Harcourt
Keyword(s):  
Negative Binomial ◽  
Fractional Power ◽  
Fourth Instar ◽  
Egg Mass ◽  
Chi Square ◽  
First Instar ◽  
Potato Beetle ◽  
Binomial Parameter ◽  
The Mean ◽  
The Individual

AbstractCounts of the Colorado potato beetle on potato did not conform to the Poisson distribution, there being an excess of uninfested and highly infested hills over the expected numbers. However, when observed distributions were fitted to the negative binomial series, the discrepancies were not significant when tested by chi-square. The negative binomial parameterktended to increase with density. Using a commonk, the distribution of the various stages may be described by expansion of (q−px)−k, when values ofkare as follows: adult, 1.95; egg mass, 4.10; first instar, 0.68; second instar, 0.78; third instar, 1.04; fourth instar, 1.07.For all stages, the variance was proportional to a fractional power of the mean. Use of the individual potato stalk as a sample unit had little effect on the skewness of the distribution. Four transformations are offered for stabilizing the variance of field counts.

NOTES ON THE SPATIAL PATTERN OF HYPERA POSTICA (COLEOPTERA: CURCULIONIDAE) ON ALFALFA

1972 ◽  
Vol 104 (12) ◽  
pp. 1995-1999 ◽  
Author(s):  
C. D. F. Miller ◽  
M. K. Mukerji ◽  
J. C. Guppy
Keyword(s):  
Spatial Pattern ◽  
Power Law ◽  
Negative Binomial ◽  
Immature Stages ◽  
Hypera Postica ◽  
Taylor’S Power Law ◽  
Binomial Series ◽  
Taylor's Power Law

AbstractThe Poisson and the negative binomial series, Taylor’s power law, and Morisita’s Iδ-index were used to interpret the dispersion of field counts of the immature stages of Hypera postica (Gyll.) on alfalfa. The data conformed consistently to an overdispersed distribution. Transformations are offered for stabilizing the variance of field counts.

The statistical distribution of involved axillary lymph nodes in breast cancer: A SEER population-based study

2007 ◽  
Vol 25 (18_suppl) ◽  
pp. 11031-11031
Author(s):  
V. Vinh-Hung ◽  
A. Guern ◽  
G. Storme
Keyword(s):  
Breast Cancer ◽  
Lymph Nodes ◽  
Poisson Distribution ◽  
Negative Binomial ◽  
Likelihood Method ◽  
Axillary Lymph ◽  
Cascade Process ◽  
Nodal Involvement ◽  
Lack Of Fit ◽  
The Mean

11031 Background: The number of involved lymph nodes in patients with breast cancer is highly variable. It might be important to examine the frequency distribution (FD) of these numbers in order to characterize their variability. This study examines the FD’s statistical properties and determines what they imply in terms of statistical analyses. Methods: The data was based on the National Cancer Institute’s Surveillance, Epidemiology and Ends Results (SEER). It covered 109618 patients, in whom axillary dissection had been performed between 1973 and 2002, in 9 states or towns of the USA. The involved lymph nodes were fitted to different statistical distributions adapted to count data using the maximum likelihood method (ML). The fittings were evaluated with the Kolmogorov-Smirnov (KS) statistic (KS close to 1 indicates lack of fit and KS close to 0 indicates good fit) and with the chi2 statistic (large chi2 indicates lack of fit). Results: The FD showed a logarithmically decreasing frequency, i.e. log-concave type. The mean number of involved nodes was 1.1465 and the variance was 9.54. The fit with a Poisson distribution gave a chi2=7.18*106 and the KS was 0.389. The fit with a negative binomial distribution using the ML gave a chi2=291.7, and the KS was 0.0086, i.e. 45-fold improved fit. Discussion: The FD’s variance 9-fold larger than the mean number of involved nodes indicates important overdispersion, i.e. the variability increases when the number of involved nodes increase. The Poisson distribution is inappropriate as was shown by the chi2 and KS. Overdispersion implies that nodal metastases are not independent random events. Overdispersion might be explained by 1) subsets of patients had a higher than expected propensity of nodal involvement, and/or 2) nodal involvement is a cascade process in which the likelihood of involvement increases when more nodes are involved. The implication for further analyses is that building predictive models of nodal involvement should take into account overdispersion and use appropriate modeling distributions such as the negative binomial. Conclusion: The FD characterization indicated a log-concave type with overdispersion. This might be important to gain an insight into the mechanisms of nodal involvement and to improve their analyses. No significant financial relationships to disclose.

Population studies on the infective stage of some nematode parasites of sheep

Parasitology ◽  
1968 ◽  
Vol 58 (4) ◽  
pp. 951-960 ◽  
Author(s):  
A. D. Donald
Keyword(s):  
Poisson Distribution ◽  
Negative Binomial ◽  
Single Species ◽  
Nematode Parasites ◽  
Random Samples ◽  
Alternative Hypotheses ◽  
Nematode Eggs ◽  
The Mean ◽  
Constructive Criticism ◽  
Strongyloid Nematode

Studies have been undertaken to examine the alternative hypotheses of a Poisson or a negative binomial distribution of the numbers of strongyloid nematode eggs in deposits of faeces produced by flocks of grazing sheep, which were proposed in certain mathematical models for the distribution of strongyloid infective larvae on pastures.Observations were made on the distribution of the weights of faecal deposits produced by flocks of ewes and lambs. In all cases the distribution was found to be significantly positively skewed. A possible fundamental basis for this skewness has been suggested.The distribution of strongyloid egg concentration in random samples of faecal deposits collected from pasture, and the distribution of egg concentration for the single species N. battus and N. filicollis in rectal samples of faeces collected from a lamb flock, have both shown highly significant departures from a Poisson distribution. This, coupled with the fact that the weights of individual deposits vary widely, provide strong empirical grounds for rejecting the Poisson distribution as a model for the distribution of egg numbers per deposit.An examination of the distribution of egg counts for N. battus and N. filicollis in samples of faeces collected from a lamb flock at weekly intervals through the spring and summer has suggested that the distribution tends to become more overdispersed with the passage of time and as the mean egg count is falling.Fundamental grounds for preferring a more general model, such as the negative binomial, to describe the distribution of strongyloid egg output in flocks of sheep have been discussed.These studies were carried out under the supervision of Dr H. D. Crofton, to whom I am deeply grateful for his stimulating encouragement and constructive criticism. My thanks go also to Professor J. E. Harris, C.B.E., F.R.S., for the provision of facilities in the Department of Zoology, and to Professor T. K. Ewer and Mr M. R. McCrea for the provision and handling of pastures and sheep at the School of Veterinary Science, Langford. This work was undertaken during tenure of a C.S.I.R.O. Overseas Research Studentship.

SPATIAL ARRANGEMENT OF THE EGGS OF HYLEMYA BRASSICAE (BOUCHÉ), AND A SEQUENTIAL SAMPLING PLAN FOR USE IN CONTROL OF THE SPECIES

1967 ◽  
Vol 47 (5) ◽  
pp. 461-467 ◽  
Author(s):  
D. G. Harcourt
Keyword(s):  
Spatial Pattern ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Sequential Sampling ◽  
Spatial Arrangement ◽  
Sampling Plan ◽  
Chi Square ◽  
Sequential Sampling Plan ◽  
Hylemya Brassicae

Counts of eggs of Hylemya brassicae (Bouché) in cabbage did not conform to the Poisson distribution owing to a preponderance of uninfested and highly infested plants. But when the negative binomial series was fitted to the observed distribution, the discrepancies were not significant when tested by chi-square. The spatial pattern may be described by expansion of (q—px)−k with a common k of 0.95.Three methods of transformation stabilized the variance of field counts. A sequential sampling plan based on the negative binomial distribution and providing for two infestation classes was drawn up for use in control of the insect in the stem brassicas.

Polygenic Inheritance of Bracts Number in Sunflower

Helia ◽  
2019 ◽  
Vol 42 (71) ◽  
pp. 221-228
Author(s):  
A. I. Soroka ◽  
V. A. Lyakh
Keyword(s):  
Degrees Of Freedom ◽  
Mean Value ◽  
Actual Number ◽  
Expected Number ◽  
Chi Square ◽  
Polygenic Inheritance ◽  
Significance Level ◽  
Average Value ◽  
The Mean ◽  
4 Degrees Of Freedom

Abstract Two inbreds of mutant origin, differing in the number of bracts, were crossed to obtain the F1 hybrid. One mutant line had 24.5 ± 1.01 bracts, while the other, 78.6 ± 1.69 bracts. The F1 hybrid had an average value between parents, which practically did not differ from the mean value in the F2 population. The variability of the trait under study in the F2 population was continuous, varying from 20 to 84 bracts. This indicated the probable participation of several genes with an additive effect in the control of the number of bracts. Assuming that the differences between the parental lines are due to two pairs of genes, the F2 plant population, grown in 2016, was divided into 5 classes. In that population the observed classes ratio turned out to be close to the theoretically expected ratio of 1 : 4 : 6 : 4 : 1. Over the next two years F2 populations were tested in a similar way. In all the cases, the calculated chi-square value did not exceed the critical value for 4 degrees of freedom and 5 % significance level. This gave reason to talk about the two-loci control of a such quantitative trait as the number of bracts. The participation of two non-allelic genes in the control of this trait is also proved by matching the actual number of plants in the parental classes to the theoretically expected number of plants. Thus, the number of bracts depends on the number of dominant alleles of two different genes in the genotype.

SPATIAL DISTRIBUTION OF INSECT SPECIES IN GRANARY RESIDUES IN THE PRAIRIE PROVINCES

1987 ◽  
Vol 119 (12) ◽  
pp. 1123-1130 ◽  
Author(s):  
P.S. Barker ◽  
L.B. Smith
Keyword(s):  
Spatial Distribution ◽  
Poisson Distribution ◽  
Negative Binomial Distribution ◽  
Negative Binomial ◽  
Insect Species ◽  
Pest Species ◽  
Logarithmic Series ◽  
The Mean ◽  
Number Of Individuals ◽  
Prairie Provinces

AbstractThe distribution of selected insect species among samples from empty farm granaries in the Prairie Provinces was determined as a guide to determining the number of samples that would have to be collected to obtain reliable estimates of the average number of these species. The number of pest and fungivorous species (adults) per sample followed a negative bionomial distribution for Manitoba data but the number of pest species adults from Sasktachewan followed a Poisson distribution. In Alberta, 39 granary samples contained only one pest species and 507 had none. The number of pests per sample from Manitoba and Saskatchewan and the number of fungivorous species from Manitoba also fitted logarithmic series.The mean number of individuals of each species found in samples (adults or larvae) was always smaller than the variance and the distribution of insect counts followed the negative binomial distribution. Tribolium audax Halstead adults from Alberta also followed a Poisson distribution.The numbers of samples required to provide a predetermined measure of precision for the numbers of species per sample (Manitoba data) and for the numbers of individuals per sample of 15 species (adults or larvae) for each of the three Prairie Provinces were calculated.

scholarly journals Parameterization of the COM-Poisson Distribution through the Mean Using Spectral Algorithms for Solving Nonlinear Equations

2019 ◽  
pp. 701-712
Author(s):  
Isaac Adeola Adeniyi ◽  
Dolapo Abidemi Shobanke ◽  
Helen Olaronke Edogbanya
Keyword(s):  
Poisson Distribution ◽  
Nonlinear Equations ◽  
Negative Binomial ◽  
Likelihood Function ◽  
Real Life ◽  
Location Parameter ◽  
Real Data ◽  
Probability Models ◽  
Spectral Algorithm ◽  
The Mean

The Poisson regression is popularly used to model count data. However, real data often do not satisfy the assumption of equality of the mean and variance which is an important property of the Poisson distribution. The Poisson – Gamma (Negative binomial) distribution and the recent Conway-Maxwell-Poisson (COM-Poisson) distributions are some of the proposed models for over- and under-dispersion respectively. Nevertheless, the parameterization of the COM-Poisson distribution still remains a major challenge in practice as the location parameter of the original COM-Poisson distribution rarely represents the mean of the distribution. As a result, this paper proposes a new parameterization of the COM-Poisson distribution via the central location (mean) so that more easily-interpretable models and results can be obtained.  The parameterization involves solving nonlinear equations which do not have analytical solutions. The nonlinear equations are solved using the efficient and fast derivative free spectral algorithm. Implementation of the parameterization in R (R Core Team, 2018) is used to present useful numerical results concerning the relationship between the mean of the COM-Poisson distribution and the location parameter in the original COM-Poisson parameterization. The proposed technique is further used to fit COM-Poisson probability models to real life datasets. It was found that obtaining estimates via this parameterization makes the estimation easier and faster compared to directly maximizing the likelihood function of the standard COM-Poisson distribution.

Poisson convergence and random graphs

1982 ◽  
Vol 92 (2) ◽  
pp. 349-359 ◽  
Author(s):  
A. D. Barbour
Keyword(s):  
Graph Theory ◽  
Poisson Distribution ◽  
Random Graphs ◽  
Factorial Moment ◽  
Expected Number ◽  
Factorial Moments ◽  
Random Graph Theory ◽  
The Mean ◽  
Fundamental Paper ◽  
Combinatorial Methods

Approximation by the Poisson distribution arises naturally in the theory of random graphs, as in many other fields, when counting the number of occurrences of individually rare and unrelated events within a large ensemble. For example, one may be concerned with the number of times that a particular small configuration is repeated in a large graph, such questions being considered, amongst others, in the fundamental paper of Erdös and Rényi (4). The technique normally used to obtain such approximations in random graph theory is based on showing that the factorial moments of the quantity concerned converge to those of a Poisson distribution as the size of the graph tends to infinity. Since the rth factorial moment is just the expected number of ordered r-tuples of events occurring, it is particularly well suited to evaluation by combinatorial methods. Unfortunately, such a technique becomes very difficult to manage if the mean of the approximating Poisson distribution is itself increasing with the size of the graph, and this limits the scope of the results obtainable.

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