DFA (version 1.0.0)

AUC: Area Under the Curve

Description

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

Usage

AUC(x,data)

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.

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.

Author

Victor Barreto Mesquita

Details

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

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)