biogeom (version 1.4.3)

SCSE: Sarabia-Castillo-Slottje Equation (SCSE)

Description

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.

Usage

SCSE(P, x)

Value

The \(y\) values predicted by the Sarabia-Castillo-Slottje equation.

Arguments

P

the parameters of the Sarabia-Castillo-Slottje equation.

x

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

Author

Peijian Shi , Johan Gielis , Brady K. Quinn .

Details

$$y = x^{\gamma}\left[1-\left(1-x\right)^{\alpha}\right]^{\beta}.$$

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.

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")

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()