Brazilian Journal of Biometrics

An interesting measure of variability in multivariate populations is the determinant of the covariance matrix Σp×p, denoted as |Σ|, commonly referred to as generalized variance. This measure succinctly captures the dispersion of a multivariate population into a single value, while accounting for inter-variable dependencies. Consequently, it finds applications across various domains concerned with assessing dispersion within multivariate populations of interest. In this study, we introduce a likelihood ratio test for the generalized variance of multivariate normal distributions, accompanied by a theoretical exposition on the distribution theory of sample generalized variances. We propose both the Likelihood Ratio Test (LRT) and the Bartlett-Corrected Likelihood Ratio Test (BCLRT) for assessing the hypothesis that the generalized variance equals a parameter η, where η ∈ R. The development of these tests is purely theoretical. Our recommendation is to employ the BCLRT test primarily in scenarios where p = 2, particularly when n &gt; 30. As for the LRT test, we suggest its application in cases where p = 2 or p = 3, provided that n &gt; 30, and for p = 5 when n &gt; 50.

Roger Almeida Pereira Melo

Marcel Irving Pereira Melo

Daniel Furtado Ferreira

Likelihood Ratio Test For The Multivariate Normal Generalized Variance

多元正态广义方差的似然比检验

The crime of intentional homicide in Brazil is worrying. In the northern region, this type of crime has been growing since 2020. In this sense, we decided to apply Kuldorff's prospective space-time scan statistics in order to identify emerging counties. We conclude that there are two emerging clusters of high relative risk (Amazonas and Pará) that require rapid intervention and two clusters of low relative risk (Acre, Roraima, Amazonas, Amapá and Pará) that do not require urgent intervention. Some characteristics of these two clusters are presented: radius, population, relative risk, likelihood ratio.

Henrique José de Paula Alves

Ben Dêivide de Oliveira Batista

Application of spatiotemporal scan statistics in cases of intentional homicides in northern Brazil

巴西北部故意杀人案件中的时空扫描统计应用

The aim of this study is to evaluate the efficiency of images analyzer applications in determining substrate quality for vegetable seedling development. Two leaf coverage determiner apps using digital images, Canopeo and GreenTest, were tested and their values were compared with results obtained from NDVI, fresh mass, dry mass, and humidity in a substrate testing experiment for lettuce seedling development. The experiment, employing a completely redomized design with 4 treatments (control, witness, humus and organic compost) and 4 repetitions, took place in a greenhouse in Londrina, Paraná, Brazil, in April 2022. Results indicated that the Canopeo app demonstrated greater sensitivity in distinguishing between treatments and exhibited a very strong correlation with other scientifically employed analyses. In contrast, GreenTest showed moderate correlation and lower sensitivity in the analyses. In conclusion, Canopeo proves to be a reliable application for determining leaf coverage and analyzing the performance of vegetable seedlings.

Roger Nabeyama Michels

Tatiane Cristina Dal Bosco

Murilo Chennecdge Vieira

Assessment of the efficiency of image analyzer applications in determining substrate quality for vegetable seedling development

评估图像分析仪在确定蔬菜幼苗发育基质质量中的应用效率

Adequate planning of experiments is extremely important and for this to occur, the appropriate choice ofplot size is essential. Thus, determining the plot size seeks to increase experimental precision, since precision decreases when a plot size smaller than the ideal is chosen; on the other hand, when opting for plot sizes larger than the ideal, the researcher may use more resources than necessary, as well as increasing the time to set up the experiment. Therefore, this work aimed to propose two new methods for determining the optimal size of experimental plots, which were applied in experiments with yellow passion fruit in the field, and compare them to the modified maximum curvature method. The maximum curvature method of the modified Vx function uses the equation proposed by Smith and the maximum curvature method of the modified CVx function uses the equation proposed by Thomas. The modified maximum curvature method of the CV(x) function proved to be suitable for estimating the optimal size of plots in experiments with yellow passion fruit. It is recommended to use the optimal plot size of 4 plants per plot for variables related to the fruit, 5 plants per plot for variables related to the pulp and for the production variables of 9 plants per plot.

Beatriz Garcia Lopes

Taciana Villela Savian

Glaucia Amorim Faria

Joel Augusto Muniz

Proposal of methods for determining the optimal size of experimental plots

实验小区最优大小确定方法的建议

This article introduces a novel class of estimators and several new novel member estimators, combining the ratio and product forms, within the framework of Adaptive Cluster Sampling (ACS) design for estimating finite population mean. Specifically designed for rare or hidden clustered populations, the new novel estimators developed from the proposed class offer enhanced efficiency in estimation. To study the proposed class comprehensively, we derive expressions for the bias and Mean Squared Error (MSE) up to the first order of approximation. Through comprehensive simulation studies, we demonstrate the superior efficiency of the new developed estimators over several existing alternatives considered in this study.

Rohan Mishra

Rajesh Singh

Yashpal Singh Raghav

On Combining Ratio and Product Type Estimators For Estimation of Finite Population Mean In Adaptive Cluster Sampling Design

关于在自适应群抽样设计中结合比率和乘积型估计量估计有限总体均值的研究

Publication Information	Publisher: Universidade Federal de Lavras -Departamento de Estatistica，Publishing cycle: ，Journal Type: journal，Open Access Journals: Yes
Basic data	Year of publication: 2022，Proportion of original research papers: ，Self Citation Rate:， Gold OA Rate:
Average review cycle	30 weeks

Brazilian Journal of Biometrics

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Likelihood Ratio Test For The Multivariate Normal Generalized Variance

Application of spatiotemporal scan statistics in cases of intentional homicides in northern Brazil

Assessment of the efficiency of image analyzer applications in determining substrate quality for vegetable seedling development

Proposal of methods for determining the optimal size of experimental plots

On Combining Ratio and Product Type Estimators For Estimation of Finite Population Mean In Adaptive Cluster Sampling Design

Likelihood Ratio Test For The Multivariate Normal Generalized Variance

Application of spatiotemporal scan statistics in cases of intentional homicides in northern Brazil

Assessment of the efficiency of image analyzer applications in determining substrate quality for vegetable seedling development

Proposal of methods for determining the optimal size of experimental plots

On Combining Ratio and Product Type Estimators For Estimation of Finite Population Mean In Adaptive Cluster Sampling Design