SHE | R Documentation |
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.
SHE(P, x)
P |
the parameters of the Sitthiyot-Holasut equation. |
x |
the given |
\mbox{if } x > \delta,
y = \left(1-\rho\right)\,\left[\left(\frac{2}{P+1}\right)\left(\frac{x-\delta}{1-\delta}\right)\right] +
\rho\,\left[\left(1-\omega\right)\left(\frac{x-\delta}{1-\delta}\right)^{P}+\omega\,\left\{1-\left[1-\left(\frac{x-\delta}{1-\delta}\right)\right]^{\frac{1}{P}}\right\}\right];
\mbox{if } x \le \delta,
y = 0.
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.
The y
values predicted by the Sitthiyot-Holasut equation.
The numerical range of x
should range between 0 and 1.
When x < \delta
, the x
value is assigned to be \delta
.
Peijian Shi pjshi@njfu.edu.cn, Johan Gielis johan.gielis@uantwerpen.be, Brady K. Quinn Brady.Quinn@dfo-mpo.gc.ca.
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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1038/s41598-023-31827-x")}
fitLorenz
, MPerformanceE
, SarabiaE
, SCSE
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()
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