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Teste_Normalidade_2024.R
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# Carregar pacotes necessários
library(DistributionTest)
library(irr)
library(moments)
library(nortest)
library(DescTools)
library(mvtnorm)
library(munsell)
library(fBasics)
library(dplyr)
library(tidyr)
library(magrittr)
library(ggplot2)
library(purrr)
library(knitr)
library(tinytex)
library(Publish)
library(furrr)
library(rlecuyer)
library(DT)
library(irr)
################################################################################
# Configurações
NN <- 100
tamanhos_amostra <- seq(25, 30, 5)
################################################################################
# Criar escopo de simulação
escopo <- expand.grid(
tamanho_amostra = tamanhos_amostra,
repeticao = seq(1, NN)
)
################################################################################
# Simulação e cálculo dos testes estatísticos
Resultados <- purrr::map2_dfr(escopo$tamanho_amostra, escopo$repeticao, function(tamanho_amostra, ii) {
print(paste0("Simulando: Tamanho Amostra = ", tamanho_amostra, ", Repetição = ", ii))
x <- rbeta(tamanho_amostra, 2,5)
# x <- rnorm(tamanho_amostra, 0, 1) # Gerar dados da distribuição normal
tibble(
Kolmogorov_Smirnov = ks.test(x, pnorm, mean(x), sd(x))$p.value,
Jarque_Bera = JarqueBeraTest(x)$p.value,
Anderson_Darling = AndersonDarlingTest(x, null = "pnorm", mean(x), sd(x))$p.value,
Lilliefors = LillieTest(x)$p.value,
Shapiro_Wilk = shapiro.test(x)$p.value,
Cramer_Von_Mises = cvm.test(x)$p.value,
D_Agostino = agostino.test(x)$p.value,
ZK = zk.test(x, 'norm')$p.value,
ZC = zc.test(x, 'norm')$p.value,
ZA = za.test(x, 'norm')$p.value,
amostra = tamanho_amostra,
tentativa = ii
)
})
################################################################################
# Calcular a taxa geral de acertos
taxa_acertos <- Resultados %>%
tidyr::pivot_longer(
cols = c(Kolmogorov_Smirnov,
Jarque_Bera,
Anderson_Darling,
Lilliefors,
Shapiro_Wilk,
Cramer_Von_Mises,
D_Agostino,
ZK,
ZC,
ZA
),
names_to = "modelo",
values_to = "estatistica") %>%
dplyr::summarise(
taxa_acertos = mean(estatistica > 0.05), # Proporção de p-valores > 0.05
.by = "modelo" # Agrupamento por "modelo"
) %>%
dplyr::arrange(desc(taxa_acertos)) %>%
dplyr::mutate(taxa_acertos = round(taxa_acertos, 3))
################################################################################
# Exibir a Tabela interativa para a Taxa Geral de Acertos
DT::datatable(
taxa_acertos,
options = list(pageLength = 10),
caption = "Taxa Geral de Acertos por Teste Estatístico"
)
################################################################################
# Calcular a variância para cada teste
variancia_resultados <- Resultados %>%
tidyr::pivot_longer(
cols = c(Kolmogorov_Smirnov,
Jarque_Bera,
Anderson_Darling,
Lilliefors,
Shapiro_Wilk,
Cramer_Von_Mises,
D_Agostino,
ZK,
ZC,
ZA
),
names_to = "modelo",
values_to = "estatistica"
) %>%
dplyr::group_by(modelo) %>%
dplyr::summarise(
variancia = var(estatistica), # Calculando a variância dos p-valores
.groups = "drop"
) %>%
dplyr::arrange(desc(variancia)) %>%
dplyr::mutate(variancia = round(variancia, 3))
# Exibir a tabela interativa com a variância
DT::datatable(
variancia_resultados,
options = list(pageLength = 10),
caption = "Variância dos P-valores por Teste Estatístico"
)
################################################################################
# Visualizar os Resultados em Gráficos
# Comparação do erro tipo I (P-valor médio, mínimo e máximo)
Resultados %>%
tidyr::pivot_longer(
cols = c(Kolmogorov_Smirnov,
Jarque_Bera,
Anderson_Darling,
Lilliefors,
Shapiro_Wilk,
Cramer_Von_Mises,
D_Agostino,
ZK,
ZC,
ZA
),
names_to = "modelo",
values_to = "estatistica"
) %>%
dplyr::group_by(amostra, modelo) %>%
dplyr::summarise(
minimo = min(estatistica),
mediana = mean(estatistica),
maximo = median(estatistica) + sd(estatistica),
.groups = "drop"
) %>%
ggplot2::ggplot(aes(x = amostra, y = mediana, ymin = minimo, ymax = maximo, color = modelo)) +
geom_line() +
geom_point() +
theme_bw() +
scale_y_continuous(labels = scales::percent, limits = c(0, 1)) +
labs(x = "Tamanho da Amostra (n)",
y = "Erro Tipo I",
color = "Testes")
################################################################################
# Visualizar o poder do teste
Resultados %>%
tidyr::pivot_longer(
cols = c(Kolmogorov_Smirnov, Jarque_Bera, Anderson_Darling, Lilliefors,
Shapiro_Wilk, Cramer_Von_Mises, D_Agostino, ZK, ZC, ZA),
names_to = "modelo",
values_to = "estatistica"
) %>%
dplyr::group_by(amostra, modelo) %>%
dplyr::summarise(
mediana = mean(estatistica < 0.05), # Proporção de p-valores < 0.05
minimo = min(estatistica),
maximo = median(estatistica) + sd(estatistica),
.groups = "drop"
) %>%
ggplot2::ggplot(aes(x = amostra, y = mediana, ymin = minimo, ymax = maximo, color = modelo)) +
geom_line() +
geom_point() +
theme_bw() +
scale_y_continuous(labels = scales::percent, limits = c(0, 1)) +
labs(x = "Tamanho da Amostra (n)",
y = "Poder do Teste",
color = "Testes")