SHE function

Sitthiyot-Holasut Equation

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. UTF-8

SHE(P, x)

Arguments

• P: the parameters of the Sitthiyot-Holasut equation.
• x: the given $x$ values ranging between 0 and 1.

Details

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.

Returns

The $y$ values predicted by the Sitthiyot-Holasut equation.

Note

The numerical range of $x$ should range between 0 and 1. When $x < \delta$, the $x$ value is assigned to be $\delta$.

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")

Author(s)

Peijian Shi pjshi@njfu.edu.cn , Johan Gielis johan.gielis@uantwerpen.be , Brady K. Quinn Brady.Quinn@dfo-mpo.gc.ca .

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()