Resumen Los métodos para obtener análogos discretos de distribuciones continuas han sido ampliamente considerados en los últimos años. En general, el pro ceso de discretización proporciona funciones de probabilidad en masa que pueden ser competitivas con el modelo tradicional utilizado en el análisis de datos de conteo, la distribución de Poisson. El procedimiento de discretización también evita el uso de la distribución continua en el análisis de datos estrictamente discretos. En este artículo, intentamos introducir dos análogos discretos para la distribución de Shanker utilizando el método de la serie infinita y el método basado en la función de supervivencia como al ternativas para modelar conjuntos de datos sobre dispersados. A pesar de la diferencia entre los métodos de discretización, las distribuciones resultantes son intercambiables. Sin embargo, la distribución generada por el método de series infinitas tiene expresiones matemáticas más simples para la forma, las funciones de generación y los momentos centrales. La teoría de máxi ma verosimilitud se considera para la estimación y las preocupaciones de inferencia asintótica. Se lleva a cabo un estudio de simulación para evaluar algunas propiedades frecuentistas de la metodología desarrollada. La utili dad de los modelos propuestos se evalúa utilizando conjuntos de datos reales proporcionados por la literatura.

Abstract The methods to obtain discrete analogs of continuous distributions have been widely considered in recent years. In general, the discretization process provides probability mass functions that can be competitive with the tra ditional model used in the analysis of count data, the Poisson distribution. The discretization procedure also avoids the use of continuous distribution in the analysis of strictly discrete data. In this paper, we seek to introduce two discrete analogs for the Shanker distribution using the method of the in finite series and the method based on the survival function as alternatives to model overdispersed datasets. Despite the difference between discretization methods, the resulting distributions are interchangeable. However, the dis tribution generated by the method of the infinite series method has simpler mathematical expressions for the shape, the generating functions, and the central moments. The maximum likelihood theory is considered for estima tion and asymptotic inference concerns. A simulation study is carried out in order to evaluate some frequentist properties of the developed methodology. The usefulness of the proposed models is evaluated using real datasets pro vided by the literature.

ABSTRACT The Half-Normal distribution has been intensively extended in the recent years. A review of the literature showed that at least 10 extensions of the Half-Normal distribution were introduced between 2008 and 2016. These extensions generalized the behavior of the density and hazard functions, which are restricted to monotonous decreasing and monotonically increasing, respectively. In this paper we propose a new extension called the transmuted Half-Normal distribution using the quadratic rank transmutation map, introduced by Shaw & Buckley (2009). A comprehensive account of mathematical properties of the new distribution is presented. We provide explicit expressions for the moments, moment-generating function, Shannon’s entropy, mean deviations, Bonferroni and Lorenz curves, order statistics, and reliability. The estimation of the parameters is implemented by the maximum likelihood method. The bias and accuracy of the estimators are assayed by the Monte Carlo simulations. This proposed distribution allows us to incorporate covariates directly in the mean and consequently to quantify their influences on the average of the response variable. Experiment with two real data sets show usefulness and its value as a good alternative to several extensions of the Half-Normal distribution in data modeling with and without covariates.

Resumo Este trabalho teve como objetivo avaliar o desempenho da distribuição Nakagami na análise de séries de precipitação mensal, ao longo de vários anos, visando à seleção de uma distribuição útil para o planejamento e gestão de atividades dependentes dos índices de precipitação na Região Sul do Brasil. Para tanto, compara-se a mesma com cinco distribuições alternativas: Weibull, Gama, Log-Normal, Log-Logística e Inversa-Gaussiana. Foram utilizadas séries históricas de 33 estações meteorológicas observadas entre janeiro de 1970 a dezembro de 2014, totalizando 396 séries (33 estações × 12 meses). Para a escolha da distribuição, que forneceu o melhor ajuste, foram utilizados os valores dos critérios de informação de Akaike, de Kolmogorov-Smirnov, de Anderson-Darling e de Cramér-von Mises. Segundo estes critérios se encontrou que as distribuições Nakagami e Weibull foram selecionadas o maior número de vezes (Nakagami: 146 vezes e Weibull: 100 vezes). Embora a distribuição Nakagami não seja muito utilizada, na descrição de dados de precipitação, recomenda-se sua utilização na descrição do comportamento da pluviosidade mensal como alternativa para distribuições tradicionalmente utilizadas.

Abstract This research had as its objective evaluating if Nakagami distribution achieves in precipitation data analysis, by considering monthly data series over several years, in an attempt to select a useful distribution that helps in the management and administration of those activities that depends on Southern Brazil precipitation index. For this purpose Nakagami distribution was compared with five alternatives: Weibull, Gamma, Log-Normal, Log-Logistic e Inverse-Gaussian. In the analysis, data series belonging to 33 weather stations between January 1970 and December 2014 were used, amounting 396 data series (33 weather × stations 12 months). In order to choose the best distribution were used the Akaike Information, the Kolmogorov-Smirnov, then Anderson-Darling and the Cramér-von Mises criterions. According to these criterions, it can be found that Nakagami and Weibull distributions were selected the greatest number of times (Nakagami: 146 times and Weibull: 100 times). Even though Nakagami distribution is not too used in rain precipitation data description, we recommend its application in the description of monthly precipitation behavior as an alternative of distributions that have been traditionally applied.

The aim of this study was to evaluate if the methods of weighing Nellore cattle by digital scale (gold standard) and indirect by thoracic measurement are concordant applying the Lin’s Concordance Correlation Coefficient (CCC), the Bland-Altman Graph and the Survival Curve of the difference of the mean. The data of 46 steers reported in Watanabe et al. (2017) was analyzed applying these alternative methods. A greater average weight was observed in the measurements obtained with the digital scale, while the range obtained with the thoracic tape was greater, with an average difference between weights of 13.8 kg. In addition, the weight obtained with the digital balance has a minimum and median greater than that obtained by the thoracic tape. It was verified with the three methods that the measurements with the digital balance and the thoracic tape are not concordant for the weight data of Nelore steers. The measures present differences that make it impossible for these methods to be interchangeable, therefore, the calculation of the weight of Nelore cattle through the thoracic tape provides measures that can lead to erroneous conclusions.

El objetivo del presente estudio fue evaluar si los métodos de pesaje mediante balanza digital (gold standard) e indirecto por medición torácica son concordantes aplicando el Coeficiente de Concordancia Lin (CCC), el Gráfico de Bland-Altman y la Curva de Supervivencia de la diferencia de las medias en bovinos Nelore. Se analizaron los datos de 46 novillos reportados en Watanabe et al. (2017) aplicando métodos alternativos. Se observó un peso medio mayor en las medidas obtenidas con balanza digital, mientras que el rango obtenido con la cinta torácica fue mayor, con una diferencia media entre los pesos de 13.8 kg. Además, el peso obtenido con la balanza digital presenta un mínimo y mediana mayor que el obtenido mediante la cinta torácica. Se comprobó con los tres métodos que las mediciones con la balanza digital y la cinta torácica no son concordantes para los datos del peso de novillos Nelore. Las medidas presentan diferencias que imposibilitan que estos métodos sean intercambiables; por lo tanto, el cálculo del peso de bovinos Nelore mediante la cinta torácica proporciona medidas que pueden llevar a conclusiones erróneas.

ABSTRACT. The aim of this study was to model the individual height and volume of eucalyptus wood in two integrated crop-livestock-forest systems (ICLF1 and ICLF2) in Campo Grande, a city in the state of Mato Grosso do Sul, Brazil. Classic nonlinear growth models were adjusted for height (Logistic, Gompertz, Richards, Weibull, Van Bertalanffy, Brody, Mitscherlich, and Chapman and Richards) and volume (Shumacher-hall nonlinear, Takata, Honner, Logistic, Gompertz, and Weibull) in two structural arrangements: ICLF1, with a spacing of 14 x 2 m and density of 357 trees ha-1, and ICLF2, with a spacing of 22 x 2 m and density of 227 trees ha-1. Diameter at Breast Height (DBH) measurements were performed in 100% of trees, with measurements of the total height of some individuals and a rigorous scaling procedure in diameter classes. According to the calculated value of Student's t-test, there was no significant evidence that DBH and the average height of the trees were different between ICLF1 and ICLF2. Based on the Akaike information criterion (AIC), the corrected Akaike information criterion (AICC) and the Bayesian information criterion (BIC), the Richards model was selected to estimate heights and the Takata model was selected to estimate the volume.

ABSTRACT This paper addresses the different methods of estimation of the unknown parameters of a two-parameter unit-logistic distribution from the frequentist point of view. We briefly describe different approaches, namely, maximum likelihood estimators, percentile based estimators, least squares estimators, maximum product of spacings estimators, methods of minimum distances: Cramér-von Mises, AndersonDarling and four variants of Anderson-Darling. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. The performances of the estimators have been compared in terms of their relative bias, root mean squared error, average absolute difference between the theoretical and empirical estimate of the distribution functions and the maximum absolute difference between the theoretical and empirical distribution functions using simulated samples. Also, for each method of estimation, we consider the interval estimation using the Bootstrap confidence interval and calculate the coverage probability and the average width of the Bootstrap confidence intervals. Finally, two real data sets have been analyzed for illustrative purposes.

ABSTRACT In this paper, a new compounding distribution, named zero truncated Lindley-Poisson distribution is introduced. The probability density function, cumulative distribution function, survival function, failure rate function and quantiles expressions of it are provided. The parameters estimatives were obtained by six methods: maximum likelihood (MLE), ordinary least-squares (OLS), weighted least-squares (WLS), maximum product of spacings (MPS), Crame´r-von-Mises (CM) and Anderson-Darling (AD), and intensive simulation studies are conducted to evaluate the performance of parameter estimation. Some generalizations are also proposed. Application in a real data set is given and shows that the composed zero truncated Lindley-Poisson distribution provides better fit than the Lindley distribution and three of its generalizations. The paper is motivated by application in real data set and we hope this model may be able to attract wider applicability in survival and reliability.

ABSTRACT Recently,12 introduced a generalization of a one parameter Lindley distribution and named it as a weighted Lindley distribution. Considering this new introduced weighted Lindley distribution, we propose a reparametrization on the shape parameter leading it to be orthogonal to the other shape parameter. In this alternative parametrization, we get a direct interpretation for this transformed parameter which is the mean survival time. For illustrative purposes, the weighted Lindley distribution on the new parametrization is applied on two real data sets. The one parameter Lindley distribution and its generalized form are fitted for the considered data sets.

ABSTRACT This study was conducted to evaluate the effects of long-chain fatty acid soaps (LCFAS) of soybean oil on the production and quality of aspirated cumulus-oocyte complexes (COC) of lactating Nellore (Bos taurus indicus) cows. The effects of LCFAS on the plasma concentration of lipoproteins, total cholesterol, triacylglycerol, urea N, and insulin were also addressed. Thirty lactating Nellore cows were randomly assigned to one of two dietary groups. Cows were grazed on a Tifton 85 pasture throughout the experiment (100 days). Treatments consisted of a supplement with no fat included (CONT); and a supplement containing 47.2 g/kg of LCFAS on a dry matter basis. After 14 days of treatment, animals were subjected to 4.93±1.55 rounds of consecutive ovum pickup (OPU) at intervals of 21.71±11.76 days. Blood samples were collected from all cows throughout the experiment at 25-day intervals (four samples per cow). Cows that were fed LCFAS supplements and cows that were fed CONT supplements had similar numbers of total aspirated oocytes (viable and not viable) by OPU and grades of viable oocytes. Plasma concentrations of high-density lipoprotein (HDL) were increased in cows supplemented with LCFAS. Plasma concentrations of LDL and total cholesterol were increased by LCFAS supplementation after 50 days on dietary treatment and insulin concentration was increased from 75 days on treatment. Long-chain fatty acid soaps from soybean oil added at 47.2 g/kg have no effect on the number of aspirated COC or their quality in Nellore lactating cows even with changes in plasma concentration of HDL, LDL, total cholesterol, and insulin. Thus, this supplementation has no benefits when the main objective is to improve oocyte production and quality.

Foram estimados os componentes de variância para produção de leite e avaliado o impacto do aumento do número de animais na matriz de parentesco sobre os componentes de variância usando os métodos de Máxima Verossimilhança Restrita (REML) e Bayesiano via amostragem de Gibbs (GS). Utilizaram-se registros de produção de leite de vacas da raça Holandesa dos estados de Minas Gerais, São Paulo, Paraná, Santa Catarina e Rio Grande do Sul. Para cada estado, foram analisados dois conjuntos de dados: no primeiro, pedigree restrito, a matriz de parentesco foi constituída dos animais do respectivo estado; e, no segundo, pedigree completo, foram incluídos na matriz de parentesco os animais de todos os estados. Utilizou-se um modelo animal que incluiu os efeitos da estação de parto, rebanho-ano, grupo genético, ordem de parto e os efeitos genéticos aditivos e de ambiente permanente. As estimativas REML dos componentes de variância e de herdabilidade em todos os estados, obtidas com o pedigree restrito e com pedigree completo, foram similares. As estimativas REML de herdabilidade em Minas Gerais, São Paulo, Paraná, Santa Catarina e Rio Grande do Sul foram 0,19; 0,18; 0,26; 0,43 e 0,48, respectivamente. Houve fortes evidências de que as estimativas Bayesianas da variância genética com o PEDA foram superiores àquelas obtidas utilizando o PEDR. As herdabilidades e os desvios-padrão obtidos pelo método Bayesiano em Minas Gerais, São Paulo, Paraná, Santa Catarina e Rio Grande do Sul utilizando os pedigrees restrito e completo foram 0,21 ± 0,032 e 0,40 ± 0,025; 0,20 ± 0,017 e 0,27 ± 0,017; 0,28 ± 0,014 e 0,31 ± 0,014; 0,42 ± 0,041 e 0,56 ± 0,021; e 0,43 ± 0,039 e 0,55 ± 0,019, respectivamente. A variância genética aumentou significativamente em cada estado quando os animais dos outros estados foram incorporados na matriz de parentesco. Os menores desvios-padrão e intervalos de credibilidade dos componentes de variância foram estimados nos estados com maior número de lactações e sugerem que a precisão dos componentes de variância foi maior para esses estados.

Variance components (VC) for milk yield of Holstein cows were estimated and the effects of increasing of the number of animals in the numerator relationship matrix (NRM) were evaluated on VC estimates obtained by REML and Bayesian inference via Gibbs sampling (GS). Data were obtained from herds in the states of Minas Gerais, São Paulo, Paraná, Santa Catarina, and Rio Grande do Sul. Two data sets were created for each state. In the first set, the NRM included only the pedigree of the animals of the state under consideration (PEDR). In the second, the NRM included animals from the five states (PEDA). An animal model including the effects of herd-year, parity, season, genetic group, effects of additive genetic and permanent environment was used. The REML estimates of VC and heritability in each state obtained from PEDR and PEDA were similar. The heritability in Minas Gerais, São Paulo, Paraná, Santa Catarina, and Rio Grande do Sul was 0.19, 0.18, 0.26, 0.43, and 0.48, respectively. There was evidence that the posterior means of the genetic variance of PEDA analyses were significantly greater than PEDR. Heritability and standard deviations estimated by GS in Minas Gerais, São Paulo, Paraná, Santa Catarina, and Rio Grande do Sul, using PEDR (PEDA), were 0.21 ± 0.032 (0.40 ± 0.025), 0.20 ± 0.017 (0.27 ± 0.017), 0.28 ± 0.014 (0.31 ± 0.014), 0.42 ± 0.041 (0.56 ± 0.021) and 0.43 ± 0.039 (0.55 ± 0.019), respectively. The genetic variance of each state increased significantly when animals from the other states were incorporated in its NRM. The smallest standard deviations and VC credibility intervals were estimated in the states with more records, which suggested that the precision of the VC estimates was higher in those states.

Registros de produção de leite ajustados para 305 dias de lactação (PL305) em vacas da raça Holandesa que pariram entre 1980 e 1993 foram utilizados para investigar a existência de heterogeneidade de variância e a interação genótipo × ambiente. Supondo-se variâncias heterogêneas, as PL305 nos estados de Minas Gerais, São Paulo, Paraná, Santa Catarina e Rio Grande do Sul foram tratadas como características diferentes. Admitindo-se homogeneidade de variância, a PL305 foi analisada segundo um modelo unicaracter. Os componentes de (co)variância e os parâmetros genéticos foram estimados utilizando-se métodos Bayesianos, via amostrador de Gibbs (GS), sob um modelo animal que incluiu os efeitos fixos de estação de parto, grupo genético, ordem de parição e classes rebanho-ano de parto e os efeitos genéticos aditivos e de ambiente permanente. A monitoração de convergência das distribuições das cadeias foi realizada pelo método de Heidelberg & Welch (1983). As estimativas dos componentes de variância e de herdabilidade foram obtidas com grande precisão na análise unicaracter. A média e o desvio-padrão (DP) a posteriori da herdabilidade foram 0,278±0,012. Na análise multicaracter, as estimativas mais precisas da (co)variância genética foram as obtidas em São Paulo e Paraná. As médias e os desvios-padrão a posteriori de herdabilidade para Minas Gerais, São Paulo, Paraná, Santa Catarina e Rio Grande do Sul, foram 0,280±0,021, 0,233±0,015, 0,280±0,012, 0,393±0,026 e 0,382±0,022, respectivamente. A baixa magnitude das correlações genéticas entre os estados (0,070 a 0,364) sugere a existência da interação genótipo × ambiente, logo, as PL305 em cada estado devem ser tratadas como características diferentes. O maior valor de correlação genética foi encontrado em São Paulo e Paraná. As variâncias genética e residual para PL305 foram significativamente diferentes entre a maioria dos estados.

Adjusted for 305 days milk yield records of Holstein cows calving from 1980 to 1993 in the states of MG, SP, PR, SC, and RS were used to investigate heterogeneity of variance and to evaluate the genotype by environment interaction. Milk production from each State was considered as a different trait and variances were assumed heterogeneous. Milk production was also analyzed using a single-trait model assuming homogeneity of variance. (Co)variance components and genetic parameters were estimated by Bayesian inference, via Gibbs sampler (GS), using a model which included season of calving, genetic group, herd-year of calving and parity as fixed effects and animal additive genetic, permanent environmental and residual as random effects. Convergence of the GS chain to the stationary distribution was diagnosed using the method described by Heidelberg & Welch (1983). The posterior precision of the variance components and the heritability were high in the single-trait analysis. Posterior mean and standard deviation (SD) of heritability of milk yield were 0,278±0,012. For the multiple-trait analysis, posterior precisions of the (co)variance components were larger for SP and PR states. Posterior means and standard errors of heritability for MG, SP, PR, SC, and RS were 0.280±0.021, 0.233±0.015, 0.280±0.012, 0.393±0.026, and 0.382±0.022, respectively. Genetic correlations for milk yield between the five states were very low and ranged from 0.070 to 0.364, suggesting the presence of genotype by environment interaction. Differences in genetic and residual variances of milk yield among the states indicate it would be necessary to account for heterogeneous variances in genetic evaluations.