SCSE {biogeom}

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)

Arguments

P

the parameters of the Sarabia-Castillo-Slottje equation.

x

the given x values ranging between 0 and 1.

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.

Value

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

Note

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

Author(s)

Peijian Shi [e-mail], Johan Gielis [e-mail], Brady K. Quinn [e-mail].

References

Sarabia, J.-M., Castillo, E., Slottje, D.J. (1999) An ordered family of Lorenz curves. Journal of Econometrics. 91, 43-60. 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. 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()