SarabiaE function

Sarabia Equation

SarabiaE is used to calculate $y$ values at given $x$ values using the Sarabia equation. The equation describes the $y$ coordinates of the Lorenz curve. UTF-8

SarabiaE(P, x)

Arguments

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

Details

Here, $x$ and $y$ represent the independent and dependent variables, respectively; and $\lambda$, $\eta$, $a_1$ and $a_2$ are constants to be estimated, where $a_1 \ge 0$, $a_2 + 1 \ge 0$, $\eta\,a_2 + \lambda \le 1$, $\lambda \ge 0$, and $\eta\,a_2 \ge 0$. There are four elements in P, representing the values of $\lambda$, $\eta$, $a_1$ and $a_2$, respectively.

Returns

The $y$ values predicted by the Sarabia equation.

Note

The numerical range of $x$ should range between 0 and 1.

References

Sarabia, J.-M. (1997) A hierarchy of Lorenz curves based on the generalized Tukey's lambda distribution. Econometric Reviews 16, 305$-$320. tools:::Rd_expr_doi("10.1080/07474939708800389")

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, SCSE, SHE

Examples

X1  <- seq(0, 1, len=2000)
Pa1 <- c(0.295, 101.485, 0.705, 0.003762)
Y1  <- SarabiaE(P=Pa1, x=X1)

dev.new()
plot( X1, Y1, 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()