CpFromDensities {RVCompare} | R Documentation |
Returns a real number in the interval [0,1] that represents the probability that a sample observed from X_A is lower than a sample observed from X_B.
CpFromDensities(densityX_A, densityX_B, xlims)
densityX_A |
The probability density function of the random variable X_A. |
densityX_B |
The probability density function of the random variable X_B. |
xlims |
an interval that represents the domain of definition the density functions. |
Returns the probability that X_A < X_B.
### Example 1 ### # If two symmetric distributions are centered in the same point (x = 0 in # this case), then their Cp will be 0.5. densityX_A <- normalDensity(0,1) densityX_B <- uniformDensity(c(-2,2)) Cp = CpFromDensities(densityX_A, densityX_B, c(-5,5)) plot(densityX_A, from=-5, to=5, type="l", col="red", xlab="x", ylab="probability density") curve(densityX_B, add=TRUE, col="blue", type="l", lty=2) mtext(paste("Cp(X_A, X_B) =", format(round(Cp, 3), nsmall = 3)), side=3) # add Cp to plot as text legend(x = c(-4.5, -2), y = c(0.325, 0.4),legend=c("X_A", "X_B"), col=c("red", "blue"), lty=1:2, cex=0.8) # add legend ### Example 2 ### # If two distributions are equal, Cp will be 0.5. Cp(X_A,X_A) = 0.5 CpFromDensities(densityX_A, densityX_A, c(-10,10)) ### Example 3 ### densityX_A <- normalDensity(-2,1) densityX_B <- uniformDensity(c(-2,2)) # Cp(X_A,X_B) = 1 - Cp(X_B, X_A) CpFromDensities(densityX_A, densityX_B, c(-8,4)) 1 - CpFromDensities(densityX_B, densityX_A, c(-8,4))