Sample skewness functions

Calculates sample measures of skewness (the sample quartile skewness or standardized sample skewness) of a vector of data, or of each column of a matrix of data, based on the estimators described in the the STAT002 notes.

Usage

q_skew(x, type = 6, na.rm = FALSE)

skew(x, na.rm = FALSE)

Arguments

x

A numeric vector or matrix.

type

Relevant to q_skew only. Argument type used in the call to quantile to estimate the 25%, 50% and 75% quantiles.

na.rm

A logical scalar. If true, any NA and NaNs are removed from x before the constituent parts of the sample skewness are computed.

Value

A numeric scalar (if the input was a vector) or vector (if the input was a matrix).

Details

See Chapter 2 of the STAT002 notes.

Sample quartile skewness. Let \(q_L\), \(m\) and \(q_U\) be the sample lower quartile, mean and upper quartile respectively. A measure of skewness often called the quartile skewness is given by $$[ (q_U - m) - (m - qL) ] / (q_U - q_L).$$

Standardized sample skewness. Denote a vector of data by \((x_1, ..., x_n)\) and let \(\bar{x}\) and \(s\) be the sample mean and sample standard deviation respectively. The standardized sample skewness is given by $$(1 / n) \sum_{i=1}^n (x_i - \bar{x}) ^ 3 / s ^ 3.$$

See also

quantile for calculating sample quantiles.

mean for the sample mean.

sd for the sample standard deviation.

Examples

birth_times <- ox_births[, "time"]
skew(birth_times)
#> [1] 0.6254774
q_skew(birth_times)
#> [1] -0.07216495