Sequential Sampling for the Imported Cabbageworm, Pieris rapae (L.)

1966 ◽  
Vol 98 (7) ◽  
pp. 741-746 ◽  
Author(s):  
D. G. Harcourt
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Pieris Rapae ◽  
Sequential Sampling ◽  
Sampling Time ◽  
Field Conditions ◽  
Population Estimates ◽  
Population Means ◽  
Considerable Saving

AbstractSequential sampling, in which decisions depend upon the accumulated results of a series of observations, leads to considerable saving of time and money. A sequential plan, based on the negative binomial distribution and providing for population estimates in three infestation categories, was drawn up for use in control of the imported cabbageworm, Pieris rapae (L.), on cabbage. An appraisal of the plan under field conditions showed that it reduced the sampling time by 75% while rating the infestation correctly in 94 of 100 cases. With the six discrepancies, population means lay between the limits set for the infestation categories.

The Stability of Weed Seedling Population Models and Parameters in Eastern Nebraska Corn (Zea mays) and Soybean (Glycine max) Fields

Weed Science ◽  
1995 ◽  
Vol 43 (4) ◽  
pp. 604-611 ◽  
Author(s):  
Gregg A. Johnson ◽  
David A. Mortensen ◽  
Linda J. Young ◽  
Alex R. Martin
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Sequential Sampling ◽  
Mean Value ◽  
Distribution Model ◽  
Ratio Test ◽  
Weed Species ◽  
Sampling Procedures ◽  
Grass Weed

Intensive field surveys were conducted in eastern Nebraska to determine the frequency distribution model and associated parameters of broadleaf and grass weed seedling populations. The negative binomial distribution consistently fit the data over time (1992 to 1993) and space (fields) for both the inter and intrarow broadleaf and grass weed seedling populations. The other distributions tested (Poisson with zeros, Neyman type A, logarithmic with zeros, and Poisson-binomial) did not fit the data as consistently as the negative binomial distribution. Associated with the negative binomial distribution is akparameter.kis a nonspatial aggregation parameter related to the variance at a given mean value. Thekparameter of the negative binomial distribution was consistent across weed density for individual weed species in a given field except for foxtail spp. populations. Stability of thekparameter across field sites was assessed using the likelihood ratio test There was no stable or commonkvalue across field sites and years for all weed species populations. The lack of stability inkacross field sites is of concern, because this parameter is used extensively in the development of parametric sequential sampling procedures. Becausekis not stable across field sites,kmust be estimated at the time of sampling. Understanding the variability in it is critical to the development of parametric sequential sampling strategies and understanding the dynamics of weed species in the field.

scholarly journals SPATIAL DISTRIBUTION AND SEQUENTIAL SAMPLING OF Brevipalpus phoenicis IN CITRUS

2016 ◽  
Vol 38 (4) ◽  
Author(s):  
WALTER MALDONADO JR ◽  
JOSÉ CARLOS BARBOSA ◽  
MARÍLIA GREGOLIN COSTA ◽  
PAULO CÉSAR TIBURCIO GONÇALVES ◽  
TIAGO ROBERTO DOS SANTOS
Keyword(s):  
Spatial Distribution ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Sequential Sampling ◽  
Sampling Plan ◽  
Goodness Of Fit Test ◽  
Control Plan ◽  
Sequential Sampling Plan ◽  
Brevipalpus Phoenicis

ABSTRACT Among the pests of citrus, one of the most important is the red and black flat mite Brevipalpus phoenicis (Geijskes), which transmits the Citrus leprosis virus C (CiLV-C).When a rational pest control plan is adopted, it is important to determine the correct timing for carrying out the control plan. Making this decision demands constant follow-up of the culture through periodic sampling where knowledge about the spatial distribution of the pest is a fundamental part to improve sampling and control decisions. The objective of this work was to study the spatial distribution pattern and build a sequential sampling plan for the pest. The data used were gathered from two blocks of Valencia sweet orange on a farm in São Paulo State, Brazil, by 40 inspectors trained for the data collection. The following aggregation indices were calculated: variance/ mean ratio, Morisita index, Green’s coefficient, and k parameter of the negative binomial distribution. The data were tested for fit with Poisson and negative binomial distributions using the chi-square goodness of fit test. The sequential sampling was developed using Wald’s Sequential Probability Ratio Test and validated through simulations. We concluded that the spatial distribution of B. phoenicis is aggregated, its behavior best fitted to the negative binomial distribution and we built and validated a sequential sampling plan for control decision-making.

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.

Niche Sharing in Intertidal Mollusks and Decapods in Rocky Shore of Easter Island

2019 ◽  
Vol 53 (5) ◽  
pp. 417-422
Author(s):  
P. De los Ríos ◽  
E. Ibáñez Arancibia
Keyword(s):  
Spatial Distribution ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Rocky Shore ◽  
Negative Binomial ◽  
Null Model ◽  
Easter Island ◽  
Published Data ◽  
Distribution Analysis ◽  
Field Works

Abstract The coastal marine ecosystems in Easter Island have been poorly studied, and the main studies were isolated species records based on scientific expeditions. The aim of the present study is to apply a spatial distribution analysis and niche sharing null model in published data on intertidal marine gastropods and decapods in rocky shore in Easter Island based in field works in 2010, and published information from CIMAR cruiser in 2004. The field data revealed the presence of decapods Planes minutus (Linnaeus, 1758) and Leptograpsus variegatus (Fabricius, 1793), whereas it was observed the gastropods Nodilittorina pyramidalis pascua Rosewater, 1970 and Nerita morio (G. B. Sowerby I., 1833). The available information revealed the presence of more species in data collected in 2004 in comparison to data collected in 2010, with one species markedly dominant in comparison to the other species. The spatial distribution of species reported in field works revealed that P. minutus and N. morio have aggregated pattern and negative binomial distribution, L. variegatus had uniform pattern with binomial distribution, and finally N. pyramidalis pascua, in spite of aggregated distribution pattern, had not negative binomial distribution. Finally, the results of null model revealed that the species reported did not share ecological niche due to competition absence. The results would agree with other similar information about littoral and sub-littoral fauna for Easter Island.

ANALISIS RISIKO OPERASIONAL MENGGUNAKAN PENDEKATAN DISTRIBUSI KERUGIAN DENGAN METODE AGREGAT

2011 ◽  
Vol 10 (2) ◽  
pp. 1
Author(s):  
Y. ARBI ◽  
R. BUDIARTI ◽  
I G. P. PURNABA
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Financial Institution ◽  
Expected Value ◽  
Insurance Companies ◽  
Limited Data ◽  
Loss Distribution Approach ◽  
Potential Loss ◽  
The Impact

Operational risk is defined as the risk of loss resulting from inadequate or failed internal processes or external problems. Insurance companies as financial institution that also faced at risk. Recording of operating losses in insurance companies, were not properly conducted so that the impact on the limited data for operational losses. In this work, the data of operational loss observed from the payment of the claim. In general, the number of insurance claims can be modelled using the Poisson distribution, where the expected value of the claims is similar with variance, while the negative binomial distribution, the expected value was bound to be less than the variance.Analysis tools are used in the measurement of the potential loss is the loss distribution approach with the aggregate method. In the aggregate method, loss data grouped in a frequency distribution and severity distribution. After doing 10.000 times simulation are resulted total loss of claim value, which is total from individual claim every simulation. Then from the result was set the value of potential loss (OpVar) at a certain level confidence.

scholarly journals On the Accuracy of the Generalized Gamma Approximation to Generalized Negative Binomial Random Sums

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1571
Author(s):  
Irina Shevtsova ◽  
Mikhail Tselishchev
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Law Of Large Numbers ◽  
Negative Binomial ◽  
Infinite Divisibility ◽  
Random Sums ◽  
Generalized Gamma ◽  
Second Moments ◽  
Large Numbers ◽  
Generalized Negative Binomial Distribution

We investigate the proximity in terms of zeta-structured metrics of generalized negative binomial random sums to generalized gamma distribution with the corresponding parameters, extending thus the zeta-structured estimates of the rate of convergence in the Rényi theorem. In particular, we derive upper bounds for the Kantorovich and the Kolmogorov metrics in the law of large numbers for negative binomial random sums of i.i.d. random variables with nonzero first moments and finite second moments. Our method is based on the representation of the generalized negative binomial distribution with the shape and exponent power parameters no greater than one as a mixed geometric law and the infinite divisibility of the negative binomial distribution.

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