AUC {DFA}

Area Under the Curve

Description

Applies the Area Under the Curve on the log-log curve.

Usage

AUC(x,data)

Arguments

x

Vector of the decimal logarithm of the boxes sizes.

data

A data frame of different decimal logarithm of the DFA calculated in each boxe.

Details

Compute the Area Under the Curve to a data frame. The method returns the curve with higher AUC.

Value

position

Position of the DFA curve with higher Area Under the Curve (AUC).

Area

Respective Area Under the Curve (AUC) computed by trapezoidal rule for the channel with higher AUC.

Note

All of log-log curve contained in the data frame must have the same sample size.

Author(s)

Victor Barreto Mesquita

References

https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-2/a/understanding-the-trapezoid-rule

https://en.wikipedia.org/wiki/Trapezoidal_rule

Examples

# Example with a data frame with different DFA exponents ranging from short 0.1 to long 0.9.
# The functions returns the channel with higher AUC and its respective area.

library(DFA)
#library(latex2exp) # it is necessary for legend of the plot function

data("lrcorrelation")

#plot(lrcorrelation$`log10(boxes)`,lrcorrelation$`log10(DFA(alpha = 0.9))`
#     ,xlab=TeX("$log_{10}(n)$"),ylab=TeX("$log_{10}F_{DFA}(n)$"),col="black"
#     ,pch=19, ylim= c(-0.8,1.2))
#lines(lrcorrelation$`log10(boxes)`,lrcorrelation$`log10(DFA(alpha = 0.8))`,type="p"
#      ,col="blue", pch=19)
#lines(lrcorrelation$`log10(boxes)`,lrcorrelation$`log10(DFA(alpha = 0.7))`,type="p"
#      ,col="red", pch=19)
#lines(lrcorrelation$`log10(boxes)`,lrcorrelation$`log10(DFA(alpha = 0.6))`,type="p"
#      ,col="green", pch=19)
#lines(lrcorrelation$`log10(boxes)`,lrcorrelation$`log10(DFA(alpha = 0.5))`,type="p"
#      ,col="brown", pch=19)
#lines(lrcorrelation$`log10(boxes)`,lrcorrelation$`log10(DFA(alpha = 0.4))`,type="p"
#      ,col="yellow", pch=19)
#lines(lrcorrelation$`log10(boxes)`,lrcorrelation$`log10(DFA(alpha = 0.3))`,type="p"
#      ,col="orange", pch=19)
#lines(lrcorrelation$`log10(boxes)`,lrcorrelation$`log10(DFA(alpha = 0.2))`,type="p"
#      ,col="pink", pch=19)
#lines(lrcorrelation$`log10(boxes)`,lrcorrelation$`log10(DFA(alpha = 0.1))`,type="p"
#      ,col="magenta", pch=19)

#legend("bottom", legend=c(TeX("$\alpha_{DFA} = 0.9$"),TeX("$\alpha_{DFA} = 0.8$")
#                          ,TeX("$\alpha_{DFA} = 0.7$"),TeX("$\alpha_{DFA} = 0.6$")
#                          ,TeX("$\alpha_{DFA} = 0.5$"),TeX("$\alpha_{DFA} = 0.4$")
#                          ,TeX("$\alpha_{DFA} = 0.3$"),TeX("$\alpha_{DFA} = 0.2$")
#                          ,TeX("$\alpha_{DFA} = 0.1$"))
#       , col=c("black","blue","red","green","brown","yellow","orange","pink","magenta")
#       , pch=c(19,19,19,19,19,19,19,19,19)
#       , cex = 0.55
#       , ncol = 5
#)

x = lrcorrelation$`log10(boxes)`

data = lrcorrelation

AUC(x,data)