k <- seq(0.2, 100, 0.05) # k o lam är parametrar i Weibull lam <- X/(-log(p))**(1/k) df <- data.frame(k, lam) yta <- pweibull(X, k, lam) my <- lam * gamma(1 + 1/k) df <- data.frame(k, lam, yta, my) df <- df[order(df$my), ] nummerLTmy <- length(df$my[df$my < mu]) myundre <- df$my[nummerLTmy] # Varje sida om mu myovre <- df$my[nummerLTmy+2] kundre <- df$k[nummerLTmy] # Varje sida om listat k kovre <- df$k[nummerLTmy+2] lamundre <- df$lam[nummerLTmy] # Varje sida om listat lam lamovre <- df$lam[nummerLTmy+2] kestimat <- (kundre + kovre)/2 # Medelvärden av parameter-est. lamestimat <- (lamundre + lamovre)/2 library(ggplot2) a <- kestimat b <- lamestimat upperlimit <- qweibull(0.9999, a, b) my <- b*gamma(1 + 1/a) ft <- function(xvar) {dweibull(xvar, a, b)} dweib_limit1 <- function(x) { y <- dweibull(x, a, b); y[x < 0 | x > upperlimit] <- NA; return(y)} dweib_limit2 <- function(x) { y <- dweibull(x, a, b); y[x < X | x > upperlimit] <- NA; return(y)} ggplot(data.frame(x = c(0, upperlimit)), aes(x = x)) + xlab("time (t)") + ylab("f(t)") + stat_function(fun = ft, colour="red") + stat_function(fun = dweib_limit1, geom="area", fill="red", alpha=0.08) + stat_function(fun = dweib_limit2, geom="area", fill="blue", alpha=0.08) + annotate("text", x = Inf, y = Inf, label = "Weibull distribution", vjust = 1.8, hjust = 1.5, fontface = "bold", color = "blue", size = 4) + annotate("text", x = Inf, y = Inf, label = "Probability distribution", vjust = 4.0, hjust = 1.4, fontface = "bold", color = "red", size = 3.5)

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52. Goal setting – a second thought

A model for a goal must be set carefully and unambiguously,

and at least two points on the F(x)-function are needed

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