SCSE function

Sarabia-Castillo-Slottje Equation (SCSE)

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

SCSE(P, x)

Arguments

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

Details

Here, $x$ and $y$ represent the independent and dependent variables, respectively; and $\gamma$, $\alpha$ and $\beta$ are constants to be estimated, where $\gamma \ge 0$, $0 < \alpha \le 1$, and $\beta \ge 1$. There are three elements in P, representing the values of $\gamma$, $\alpha$ and $\beta$, respectively.

Returns

The $y$ values predicted by the Sarabia-Castillo-Slottje equation.

Note

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

References

Sarabia, J.-M., Castillo, E., Slottje, D.J. (1999) An ordered family of Lorenz curves. Journal of Econometrics. 91, 43$-$60. tools:::Rd_expr_doi("10.1016/S0304-4076(98)00048-7")

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, SHE

Examples

X1  <- seq(0, 1, len=2000)
Pa2 <- c(0, 0.790, 1.343)
Y2  <- SCSE(P=Pa2, x=X1)

dev.new()
plot( X1, Y2, 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()