Inferences about the coefficient of correlation in the standard bivariate normal distribution

The study of the association between two random variables that have a joint normal distribution is of interest in applied statistics; for example, in statistical genetics. This article, targeted to applied statisticians, addresses inferences about the coefficient of correlation (ρ) in the bivariate normal and standard bivariate normal distributions using likelihood, frequentist, and Baycsian perspectives. Some results are surprising. For instance, the maximum likelihood estimator and the posterior distribution of ρ in the standard bivariate normal distribution do not follow directly from results for a general bivariate normal distribution. An example employing bootstrap and rejection sampling procedures is used to illustrate some of the peculiarities.

Estimação Bayesiana dos parâmetros da distribuição Exponencial Generalizada Bivariada

Pós-graduação em Matematica Aplicada e Computacional - FCT

Univariate and bivariate distribution of growth traits in beef buffaloes from Brazil

The aim of this study was to analyze the weight at birth (BW) and adjusted at 205 (W205), 365 (W365) and 550 (W55O) days in beef buffaloes from Brazil, using two approaches: parametric, by normal distribution, and non-parametric, by kernel function, and thus estimating the genetic, environmental and phenotypic correlation among traits. Information of 5,169 animals at birth (BW), 3,792 at 205 days (W205), 3.883 at 365 days (W365) and 1,524 at 550 days of age (W550) were used. The birth weight distribution presented an evident discrepancy in relation to the normal distribution. However, W205, W365 and W550 presented normal distributions. The birth weight presented weak genetic, environmental, and phenotypic associations with the other weight measurements. on the other hand, the weight traits at 205, 365, 550 days of age showed a high genetic correlation.

Spontaneous Interblink Time Distributions in Patients with Graves' Orbitopathy and Normal Subjects

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Genetic associations of sexual precocity with growth traits and visual scores of conformation, finishing, and muscling in Nelore cattle

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Associação genética da prenhez aos 16 meses com o peso à desmama e o ganho de peso em animais da raça Nelore

Objetivou-se verificar a possibilidade de utilização da prenhez de novilhas aos 16 meses (Pr16) como critério de seleção e as possíveis associações genéticas entre prenhez em novilhas aos 16 meses e o peso à desmama (PD) e o ganho de peso médio da desmama ao sobreano (GP). Foram realizadas análises uni e bicaracterísticas para estimação dos componentes de co-variância, empregando-se um modelo animal linear para peso à desmama e ganho de peso da desmama ao sobreano e não-linear para Pr16. A estimação dos componentes de variância e da predição dos valores genéticos dos animais foi realizada por Inferência Bayesiana. Distribuições flat foram utilizadas para todos os componentes de co-variância. As estimativas de herdabilidade direta para Pr16, PD e GP foram 0,50; 0,24 e 0,15, respectivamente, e a estimativa de herdabilidade materna para o PD, de 0,07. As correlações genéticas foram -0,25 e 0,09 entre Pr16, PD e GP, respectivamente, e a correlação genética entre Pr16 e o efeito genético materno do PD, de 0,29. A herdabilidade da prenhez aos 16 meses indica que essa característica pode ser utilizada como critério de seleção. As correlações genéticas estimadas indicam que a seleção por animais mais pesados à desmama, a longo prazo, pode diminuir a ocorrência de prenhez aos 16 meses de idade. Além disso, a seleção para maior habilidade materna favorece a seleção de animais mais precoces. No entanto, a seleção para ganho de peso da desmama ao sobreano não leva a mudanças genéticas na precocidade sexual em fêmeas.

Genetic associations of conformation, finishing precocity and muscling visual scores with mature weight in Nelore cattle

Were estimate (co)variance and genetic associations between conformation, finishing precocity and muscling visual scores measured at weaning (SCW, SFW and SMW, respectively) and yearling (SCY. SFY and SMY, respectively) with mature weight (MW) in Nelore cows, in order to predict the possible changes that inclusion of visual scores in beef cattle selection indices would bring to female mature weight. The data set contained records of 36,757 females, born between 1993 and 2006, belonging to the Jacarezinho cattle raising farm. (Co)variance components were estimated by bivariate animal models using Bayesian inference method through Gibbs sampling, assuming a linear model for MW and a nonlinear (threshold) model for conformation, finishing precocity and muscling visual scores. The first 10,000 rounds were considered as the burn-in period and discarded. The posterior means of direct heritability distributions were: 0.16 +/- 0.02 (SCW); 0.20 +/- 0.02 (SFW); 0.19 +/- 0.02 (SMW); 0.24 +/- 0.02 (SCY); 0.31 +/- 0.02 (SFY); 0.32 +/- 0.02 (SMY) and 0.46 +/- 0.04 (MW). Estimates of genetic correlations between visual scores and MW were positive and moderate, ranging from 0.27 +/- 0.06 to 0.36 +/- 0.04. Visual scores and MW should respond favorably to direct selection. Mature weight can be used in Nelore breeding programs designed to monitor the cows' size. Selection of animals with higher conformation, finishing precocity and muscling scores, especially at yearling, should promote an increase in cows' mature weight. (c) 2010 Elsevier B.V. All rights reserved.

Spatial variations at different observational scales and the seasonal distributions of stream macroalgae in a Brazilian subtropical region

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A new chart for monitoring the covariance matrix of bivariate processes

In this article we consider a control chart based on the sample variances of two quality characteristics. The points plotted on the chart correspond to the maximum value of these two statistics. The main reason to consider the proposed chart instead of the generalized variance |S| chart is its better diagnostic feature, that is, with the new chart it is easier to relate an out-of-control signal to the variables whose parameters have moved away from their in-control values. We study the control chart efficiency considering different shifts in the covariance matrix. In this way, we obtain the average run length (ARL) that measures the effectiveness of a control chart in detecting process shifts. The proposed chart always detects process disturbances faster than the generalized variance |S| chart. The same is observed when the size of the samples is variable, except in a few cases in which the size of the samples switches between small size and very large size.

Control charts for monitoring the mean vector and the covariance matrix of bivariate processes

In this article, we propose new control charts for monitoring the mean vector and the covariance matrix of bivariate processes. The traditional tools used for this purpose are the T (2) and the |S| charts. However, these charts have two drawbacks: (1) the T (2) and the |S| statistics are not easy to compute, and (2) after a signal, they do not distinguish the variable affected by the assignable cause. As an alternative to (1), we propose the MVMAX chart, which only requires the computation of sample means and sample variances. As an alternative to (2), we propose the joint use of two charts based on the non-central chi-square statistic (NCS statistic), named as the NCS charts. Once the NCS charts signal, the user can immediately identify the out-of-control variable. In general, the synthetic MVMAX chart is faster than the NCS charts and the joint T (2) and |S| charts in signaling processes disturbances.

Bivariate control charts with double sampling

In this article, we consider the T(2) chart with double sampling to control bivariate processes (BDS chart). During the first stage of the sampling, n(1) items of the sample are inspected and two quality characteristics (x; y) are measured. If the Hotelling statistic T(1)(2) for the mean vector of (x; y) is less than w, the sampling is interrupted. If the Hotelling statistic T(1)(2) is greater than CL(1), where CL(1) > w, the control chart signals an out-of-control condition. If w < T(1)(2) <= CL(1), the sampling goes on to the second stage, where the remaining n(2) items of the sample are inspected and T(2)(2) for the mean vector of the whole sample is computed. During the second stage of the sampling, the control chart signals an out-of-control condition when the statistic T(2)(2) is larger than CL(2). A comparative study shows that the BDS chart detects process disturbances faster than the standard bivariate T(2) chart and the adaptive bivariate T(2) charts with variable sample size and/or variable sampling interval.

The double sampling and the EWMA charts based on the sample variances

We propose a new statistic to control the covariance matrix of bivariate processes. This new statistic is based on the sample variances of the two quality characteristics, in short VMAX statistic. The points plotted on the chart correspond to the maximum of the values of these two variances. The reasons to consider the VMAX statistic instead of the generalized variance vertical bar S vertical bar is its faster detection of process changes and its better diagnostic feature; that is, with the VMAX statistic it is easier to identify the out-of-control variable. We study the double sampling (DS) and the exponentially weighted moving average (EWMA) charts based on the VMAX statistic. (C) 2008 Elsevier B.V. All rights reserved.

Control charts for individual observations of a bivariate Poisson process

In this paper, three single-control charts are proposed to monitor individual observations of a bivariate Poisson process. The specified false-alarm risk, their control limits, and ARLs were determined to compare their performances for different types and sizes of shifts. In most of the cases, the single charts presented better performance rather than two separate control charts ( one for each quality characteristic). A numerical example illustrates the proposed control charts.

Parturition intervals and distributions of parturitions by months of buffalo in Southern and South-eastern Brazil

Reproductive rate is an important component of economic success in livestock production. Parturition interval (IEP) is a direct measure of the productivity of the animal. Long IEP reduce the number of calves produced per year. The objective this study was to determine the distribution of parturitions across month and to evaluate factors affecting IEP. The data included 7,588 parturitions of Murrah, Mediterranean and Carabobo buffalo from 10 herds in Southern and South-eastern Brazil. The analysis of distribution of parturitions evaluated the effects of month, year and their interaction on birth date of calves by using a Chi-Square test in SAS PROC FREQ (SAS Institute, Cary, NC, USA). Parturition intervals (n = 2,630) were evaluated using analysis of variance in SAS PROC GLM. The model for IEP included the fixed effects of season (December to May = 1, June to November = 2), year, season x year, sex of the preceding parturition, age of weaning of the previous calf, and herd. All sources of variation were significant (P<0.0001) except sex of the preceding parturition (P <0.85). The mean IEP was 446.7 +/- 10.4 days, for seasons 1 and 2 IEP were 419.8 +/- 11.3 and 473.6 +/- 40.7 days, respectively, a difference of 54 days. As weaning age increased there was a lengthening of IEP. Buffalo in Brazil showed seasonal parturition with calving concentrated from January to April, although the frequency by month differed across years (P<0.0001). These months also had the lowest calving interval.

Caracterização fenotípica e genética da produção de leite e do intervalo entre partos em bubalinos da raça Murrah

O objetivo deste trabalho foi estimar as correlações, herdabilidades, repetibilidades, tendências genéticas e fenotípicas, e avaliar as distribuições univariada e bivariada da produção de leite e do intervalo entre partos, em fêmeas bubalinas da raça Murrah, paridas no período de 1982 a 2003. As tendências genéticas e fenotípicas foram estimadas pelas regressões das variáveis dependentes sobre o ano de parto, pelos métodos: regressão linear e regressão não paramétrica, utilizando-se a função de alisamento Spline. As herdabilidades estimadas foram 0,21 e 0,02, e as repetibilidades, 0,32 e 0,06, para a produção de leite e intervalo entre partos, respectivamente. As correlações genética, fenotípica e ambiental foram -0,22, 0,01 e 0,03, respectivamente. As tendências genéticas (regressão linear) foram significativas e iguais a 1,57 kg por ano e 0,085 dia por ano, e as tendências fenotípicas foram 27,74 kg por ano e 0,647 dia por ano, para a produção de leite e intervalo entre partos, respectivamente, tendo sido significativa apenas para a produção de leite. A correlação negativa sugere a existência de antagonismo favorável entre produção de leite e intervalo entre partos; assim é possível selecionar animais com altos valores genéticos para a produção de leite e com menores valores para o intervalo entre partos.