biogeom (version 1.4.3)

SHE: Sitthiyot-Holasut Equation

Description

SHE is used to calculate \(y\) values at given \(x\) values using the Sitthiyot-Holasut equation. The equation describes the \(y\) coordinates of the Lorenz curve.

Usage

SHE(P, x)

Value

The \(y\) values predicted by the Sitthiyot-Holasut equation.

Arguments

P

the parameters of the Sitthiyot-Holasut equation.

x

the given \(x\) values ranging between 0 and 1.

Author

Peijian Shi , Johan Gielis , Brady K. Quinn .

Details

$$\mbox{if } x > \delta,$$ $$y = \left(1-\rho\right)\,\left[\left(\frac{2}{P+1}\right)\left(\frac{x-\delta}{1-\delta}\right)\right] + \rho\,\left[\left(1-\omega\right)\left(\frac{x-\delta}{1-\delta}\right)^{P}+\omega\,\left\{1-\left[1-\left(\frac{x-\delta}{1-\delta}\right)\right]^{\frac{1}{P}}\right\}\right];$$ $$\mbox{if } x \le \delta,$$ $$y = 0.$$ Here, \(x\) and \(y\) represent the independent and dependent variables, respectively; and \(\delta\), \(\rho\), \(\omega\) and \(P\) are constants to be estimated, where \(0 \le \delta < 1\), \(0 \le \rho \le 1\), \(0 \le \omega \le 1\), and \(P \ge 1\). There are four elements in P, representing the values of \(\delta\), \(\rho\), \(\omega\) and \(P\), respectively.

References

Sitthiyot, T., Holasut, K. (2023) A universal model for the Lorenz curve with novel applications for datasets containing zeros and/or exhibiting extreme inequality. Scientific Reports 13, 4729. tools:::Rd_expr_doi("10.1038/s41598-023-31827-x")

See Also

fitLorenz, MPerformanceE, SarabiaE, SCSE

Examples

X1  <- seq(0, 1, len=2000)
Pa3 <- c(0, 1, 0.446, 1.739)
Y3  <- SHE(P=Pa3, x=X1)

dev.new()
plot( X1, Y3, cex.lab=1.5, cex.axis=1.5, type="l", asp=1, xaxs="i", 
      yaxs="i", xlim=c(0, 1), ylim=c(0, 1), 
      xlab="Cumulative proportion of the number of infructescences", 
      ylab="Cumulative proportion of the infructescence length" )

graphics.off()