Mercurial > octave
diff scripts/statistics/base/skewness.m @ 24511:4f0e6ee6c9b8 stable
Make documentation Sec 26.1 more consistent and Sec 25.4 clearer (bug #52685)
* corr.m: Add space in LaTeX formula. For the example, place variables in a
@var qualifier.
* cov.m: Use @var in LaTeX for x and y when referring to function input vector.
Correct Octave-help formula by placing parentheses around N-1 so that -1 is
in the denominator. Define N after the formula in which it is used.
* gls.m: Define what GLS stands for. Use @var instead of @math for function
input and output variables. Move the description of matrix O and scalar s
to a third paragraph, ensuring s is lower case. Give a little more context
to the description of X and Y in the second paragraph. Add an expansive
paragraph three for details about the error variables E including the
description of O and s along with their dimensions. Add "matrix" before
B and "scalar" before s for clarity. Place @var around variables r, y, x
and beta to make those upper case in Octave-help.
* histc.m: Use LaTeX math rather than @code for the @tex scenario.
* kendall.m: Treat tau differently for LaTeX and Octave-help scenarios. Add
space in LaTeX formulas. Treat tau as @var in Octave-help case. Use lower
case 'i' for index variable and upper case 'N' for vector length.
* kurtosis.m: For mean value of x, use script rather than non-script. Define
N after the formula in which it is used for Octave-help case.
* mean.m: Indicate N is number of elements. Use @var on input vector x for
Octave-help case.
* meansq.m: Indicate N is number of elements, but drop the reference to mean
value because there is none. Use @var on input vector x for Octave-help
case. Use "If x is a matrix" consistent with all others.
* median.m: Indicate N is number of elements for LaTeX case. For Octave-help
place some vertical lines to represent case curly-bracket. Place @math
around N. Define an intermediate vector S representing sorted X and use
that in the math formula.
* moment.m: Define x-bar as mean and N as number of elements. Use @var on
x and p in the Octave-help formulas.
* ols.m: Define meaning of OLS. Add @var to LaTeX variables to make them
non-script vectors. Use @var instead of @math for function input and output
variables. Use hyphens for matrix dimensions in Octave-help formula. Move
the description of matrix S to a third paragraph. Give a little more context
to the description of X and Y in the second paragraph. Add an expansive
paragraph three for details about the error variables E including the
description of matrix S along with its dimensions, ensuring S is upper case.
Add "matrix" before B for clarity. Make the definition of SIGMA one line for
appearance in Octave-help.
* prctile.m: Change a mistaken 'y' to 'q' to work in LaTeX as well.
* quantile.m: Use @var{method} rather than METHOD. Break up all the method
formulas for p(k) into LaTeX and Octave-help versions for better control.
Use upper case N for the length of P.
* skewness.m: Remove @var from x when referring to vector elements in LaTeX.
Indicate N is number of elements.
* spearman.m: Break into separate LaTeX and Octave-help cases rather than
use @code for LaTeX. Use Greek symbol rho in LaTeX.
* std.m: Add @var to x variable to indicate LaTeX or Octave-help vector. Add
clarification about N being number elements of x to both LaTeX and
Octave-help formulas.
* var.m: Indicate N is number of elements. Apply @var to x to show it is a
vector. Change == to "is equal to" for normal text.
author | Daniel J Sebald <daniel.sebald@ieee.org> |
---|---|
date | Wed, 27 Dec 2017 23:38:25 -0600 |
parents | 3ac9f9ecfae5 |
children | 3fc1c8ebe5c3 |
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--- a/scripts/statistics/base/skewness.m Wed Jan 03 21:49:38 2018 -0800 +++ b/scripts/statistics/base/skewness.m Wed Dec 27 23:38:25 2017 -0600 @@ -27,9 +27,9 @@ ## @tex ## $$ ## {\rm skewness} (@var{x}) = {{{1\over N}\, -## \sum_{i=1}^N (@var{x}_i - \bar{@var{x}})^3} \over \sigma^3}, +## \sum_{i=1}^N (x_i - \bar{x})^3} \over \sigma^3}, ## $$ -## where $N$ is the length of @var{x}, $\bar{@var{x}}$ its mean and $\sigma$ +## where $N$ is the length of @var{x}, $\bar{x}$ its mean and $\sigma$ ## its (uncorrected) standard deviation. ## @end tex ## @ifnottex @@ -52,7 +52,7 @@ ## @tex ## $$ ## {\rm skewness} (@var{x}) = {\sqrt{N (N - 1)} \over N - 2} \times \, -## {{{1 \over N} \sum_{i=1}^N (@var{x}_i - \bar{@var{x}})^3} \over \sigma^3} +## {{{1 \over N} \sum_{i=1}^N (x_i - \bar{x})^3} \over \sigma^3} ## $$ ## @end tex ## @ifnottex @@ -65,6 +65,8 @@ ## @end group ## @end example ## +## where @math{N} is the length of the @var{x} vector. +## ## @end ifnottex ## The adjusted skewness coefficient is obtained by replacing the sample second ## and third central moments by their bias-corrected versions.