## File: skewness.Rd

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r-cran-e1071 1.7-3-1
 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960 \name{skewness} \alias{skewness} \title{Skewness} \description{ Computes the skewness. } \usage{ skewness(x, na.rm = FALSE, type = 3) } \arguments{ \item{x}{a numeric vector containing the values whose skewness is to be computed.} \item{na.rm}{a logical value indicating whether \code{NA} values should be stripped before the computation proceeds.} \item{type}{an integer between 1 and 3 selecting one of the algorithms for computing skewness detailed below.} } \details{ If \code{x} contains missings and these are not removed, the skewness is \code{NA}. Otherwise, write \eqn{x_i} for the non-missing elements of \code{x}, \eqn{n} for their number, \eqn{\mu}{mu} for their mean, \eqn{s} for their standard deviation, and \eqn{m_r = \sum_i (x_i - \mu)^r / n}{m_r = \sum_i (x_i - mu)^r / n} for the sample moments of order \eqn{r}. Joanes and Gill (1998) discuss three methods for estimating skewness: \describe{ \item{Type 1:}{ \eqn{g_1 = m_3 / m_2^{3/2}}{g_1 = m_3 / m_2^(3/2)}. This is the typical definition used in many older textbooks.} \item{Type 2:}{ \eqn{G_1 = g_1 \sqrt{n(n-1)} / (n-2)}{ G_1 = g_1 * sqrt(n(n-1)) / (n-2)}. Used in SAS and SPSS. } \item{Type 3:}{ \eqn{b_1 = m_3 / s^3 = g_1 ((n-1)/n)^{3/2}}{ b_1 = m_3 / s^3 = g_1 ((n-1)/n)^(3/2)}. Used in MINITAB and BMDP.} } All three skewness measures are unbiased under normality. } \value{ The estimated skewness of \code{x}. } \references{ D. N. Joanes and C. A. Gill (1998), Comparing measures of sample skewness and kurtosis. \emph{The Statistician}, \bold{47}, 183--189. } \examples{ x <- rnorm(100) skewness(x) } \keyword{univar}