diff --git a/vignettes/v06_gamma_count.Rmd b/vignettes/v06_gamma_count.Rmd index efbec4922c7de9c98df2dacd44a77ea3993a0368..bcd2f3b1b60dd6ec52588d16fdc482d254248f82 100644 --- a/vignettes/v06_gamma_count.Rmd +++ b/vignettes/v06_gamma_count.Rmd @@ -98,7 +98,7 @@ $$ Como $$ F_n(T) = G(n\alpha, \beta T) = - \int_{0}^{T} \frac{\beta^{n\alpha}}{\Gamma(n\alpha)} + \int_{0}^{T} \frac{\beta^{n\alpha}}{\Gamma(n\alpha)} t^{n\alpha-1}\cdot\exp\{-\beta t\}\, \text{d}t, $$ podemos escrever $\Pr(N = n)$ como sendo a diferença de acumuladas da @@ -350,6 +350,53 @@ c(mean(y), exp(coef(n1)[2]), fitted.gcnt(lambda = exp(coef(n1)[2]), alpha = exp(coef(n1)[1]), ymax = 100)) + +#----------------------------------------------------------------------- +# A E(y) por sum(y * p(py)) e por lambda como função de alpha. + +grid <- expand.grid(lambda = exp(seq(-3, 3, length.out = 30)), + alpha = exp(seq(-2, 2, length.out = 11)), + KEEP.OUT.ATTRS = FALSE) +summary(grid) + +y <- 0:500 +py <- mapply(FUN = dgcnt, + lambda = grid$lambda, + alpha = grid$alpha, + MoreArgs = list(y = y), SIMPLIFY = FALSE) +grid$m <- sapply(py, FUN = function(py) sum(y * py)) +grid$alpha <- round(grid$alpha, 3) +str(grid) + +cl <- brewer.pal(n = 10, name = "Spectral") + +xyplot(m ~ lambda, groups = alpha, data = grid, type = "l", + aspect = "iso", grid = TRUE, lwd = 2, + xlab = expression(lambda), + ylab = expression(sum(y %.% f(y))), + auto.key = list(space = "right", + title = expression(alpha), + points = FALSE, lines = TRUE), + par.settings = list(superpose.line = list(col = cl))) + + layer(panel.abline(a = 0, b = 1, lty = 2)) + + layer(panel.rect(xleft = 0, ybottom = 0, + xright = 5, ytop = 5, lty = 2)) + + layer(panel.arrows(7, 13, 13, 7, length = 0.1)) + + layer(panel.text(x = 13, y = 7, + labels = expression(alpha), pos = 4)) + +xyplot(m ~ lambda, groups = alpha, type = "l", + data = subset(grid, findInterval(lambda, vec = c(0, 5)) == 1), + xlab = expression(lambda), + ylab = expression(sum(y %.% f(y))), + aspect = "iso", grid = TRUE, lwd = 2, + auto.key = list(space = "right", + title = expression(alpha), + points = FALSE, lines = TRUE), + par.settings = list(superpose.line = list(col = cl))) + + layer(panel.abline(a = 0, b = 1, lty = 2)) + + layer(panel.abline(a = -0.5, b = 1, lty = 2)) + + layer(panel.abline(a = 1, b = 1, lty = 2)) ``` ## Número de Vagens Produzidas em Soja ##