Use este identificador para citar ou linkar para este item: http://repositorio.ufla.br/jspui/handle/1/29962
Título: Externally studentized normal midrange distribution
Título(s) alternativo(s): Distribuição da midrange estudentizada externamente
Palavras-chave: Distribution function
Density function
Gauss-Legendre quadrature
Newton-Raphson method
Software R
Função de distribuição
Função densidade
Quadratura Gauss-Legendre
Método Newton-Raphson
Algoritmo
Data do documento: 2017
Editor: Universidade Federal de Lavras
Citação: BATISTA, B. D. de O.; FERREIRA, D. F.; CHAVES L. M. Externally studentized normal midrange distribution. Ciência e Agrotecnologia, Lavras, v. 41, n. 4, p. 378-389, July/Aug. 2017.
Resumo: The distribution of externally studentized midrange was created based on the original studentization procedures of Student and was inspired in the distribution of the externally studentized range. The large use of the externally studentized range in multiple comparisons was also a motivation for developing this new distribution. This work aimed to derive analytic equations to distribution of the externally studentized midrange, obtaining the cumulative distribution, probability density and quantile functions and generating random values. This is a new distribution that the authors could not find any report in the literature. A second objective was to build an R package for obtaining numerically the probability density, cumulative distribution and quantile functions and make it available to the scientific community. The algorithms were proposed and implemented using Gauss-Legendre quadrature and the Newton-Raphson method in R software, resulting in the SMR package, available for download in the CRAN site. The implemented routines showed high accuracy proved by using Monte Carlo simulations and by comparing results with different number of quadrature points. Regarding to the precision to obtain the quantiles for cases where the degrees of freedom are close to 1 and the percentiles are close to 100%, it is recommended to use more than 64 quadrature points.
URI: http://repositorio.ufla.br/jspui/handle/1/29962
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