datana (version 1.1.4)

simmeind: Computes the simmetry index

Description

Computes the simmetry index of a random variable.

Usage

simmeind(y = y, lt = lt)

Value

The function returns the simmetry index, a numeric scalar.

Arguments

y

is a numeric vector.

lt

is the lower treshold used to collect the sample data represented by the vector y.

Author

Christian Salas-Eljatib.

Details

A more sensitive indicator of skewness is the the symmetry index, defined as the ratio between the mode and the 95th percentileof the observed distribution, as follows. $${SimmI} = \frac{y_{Mode}-y_{LT}}{y_{.95} -y_{LT}}$$ where \(y_{Mode}\), \(y_{LT}\) and \(y_{.95}\) are the mode of the distribution, the lower treshold of the variable, and the 95th percentile of the distribution.

According to Lorimer and Krug (1983) helps to distinguish between descending monotonic, skewed unimodal and symmetric unimodal curves. Negative exponential distributions have \({SimmI}\) close to 0, Gaussian distribution have \({SimmI}\) close to 0.5, and positively skewed unimodal curves have values intermediate between the two. Negatively skewed distributions have values \(>0.5\), with a theoretical maximum of 1.0.

References

• Lorimer CG. and Krug AG. 1983. Diameter Distributions in Even-aged Stands of Shade-tolerant and Midtolerant Tree Species. American Midland Naturalist 109 (2):331--345.

Examples

library(datana)
data(casen)
head(casen)
df<-casen
#Compare 
summary(df$edad)
mean(df$edad)
median(df$edad)
moda(df$edad)
simmeind(y=df$edad,lt = 0)