compute the coefficient of skewness

はじめる前に
新機能一覧
Maple ワークシートの作成
Mapleワークシートを共有
Maple ウィンドウのカスタマイズ
Maple システムのカスタマイズ
コネクティビティ
Mathematics
数学
- テンソル解析
- パッケージ
- ファンクションアドバイザ
- ベキ級数
- ベクトル解析
- 不活性関数
- 代数
- 因数分解と方程式解法
- 基本数学
- 基本的な注意事項
- 変分法
- 変換
- 幾何
- 微分代数方程式
- 微分幾何学
- 微分方程式
- 微積分
- 数
- 数値計算
- 数学関数
- 数論
- 最適化
- 特殊関数
- 統計
  - ProcessControl パッケージ
  - Statistics パッケージ
    - 例題
    - シミュレーション
    - データ処理
    - データ平滑化
    - 可視化
    - 回帰
    - 検定
    - 確率分布
    - 確率変数
    - 統計推量
    - 統計量
    - 要約と一覧
    - 記述統計
    - 概要
    - コマンド
    - 対話的データ解析
    - 効率的な計算
    - 行列データセット
    - 確率分布の作成
- 線形代数
- 群論
- 評価
- 論理
- 過去のパッケージ
- 金融
- 離散数学
- piecewise examples
- グラフ電卓
- 区分関数
物理
プログラミング
グラフィックス
Student パッケージ
Science and Engineering
科学・エンジニアリング
アプリケーションと例題
リファレンス
システム
MapleSim
MapleSim ツールボックス
MapleSim ヘルプ
Tasks
Toolboxes
エラーメッセージガイド
マニュアル
数学アプリ

Statistics[Skewness] - compute the coefficient of skewness

	Calling Sequence
	Skewness(A, ds_options) Skewness(X, rv_options)

Parameters

A	-	Array or Matrix data set; data sample
X	-	algebraic; random variable or distribution
ds_options	-	(optional) equation(s) of the form option=value where option is one of ignore, or weights; specify options for computing the coefficient of skewness of a data set
rv_options	-	(optional) equation of the form numeric=value; specifies options for computing the coefficient of skewness of a random variable

Description

•	The Skewness function computes the coefficient of skewness of the specified random variable or data set. In the data set case the following formula for computing the coefficient of skewness is used:

where N is the number of elements in A.

•	The first parameter can be a data set (represented as an Array or a Matrix data set), a distribution (see Statistics[Distribution]), a random variable, or an algebraic expression involving random variables (see Statistics[RandomVariable]).

Computation

•	By default, all computations involving random variables are performed symbolically (see option numeric below).

•	All computations involving data are performed in floating-point; therefore, all data provided must have type realcons and all returned solutions are floating-point, even if the problem is specified with exact values.

•	For more information about computation in the Statistics package, see the Statistics[Computation] help page.

Data Set Options

The ds_options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[DescriptiveStatistics] help page.

•

ignore=truefalse -- This option controls how missing data is handled by the Skewness command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the Skewness command will return undefined. If ignore=true all missing items in A will be ignored. The default value is false.

•	weights=Vector -- Data weights. The number of elements in the weights array must be equal to the number of elements in the original data sample. By default all elements in A are assigned weight .

Random Variable Options

The rv_options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[RandomVariables] help page.

•	numeric=truefalse -- By default, the coefficient of skewness is computed using exact arithmetic. To compute the coefficient of skewness numerically, specify the numeric or numeric = true option.

Compatibility

•	The A parameter was updated in Maple 16.

Examples

Compute the coefficient of skewness of the log normal distribution with parameters and .

(exp(3*mu+(9/2)*sigma^2)-3*exp(3*mu+(5/2)*sigma^2)+2*exp((3/2)*sigma^2+3*mu))/(exp(2*mu+sigma^2)*(exp(sigma^2)-1))^(3/2)

(1)

Use numeric parameters.

(2)

(3)

Generate a random sample of size 100000 drawn from the above distribution and compute the sample skewness.

(4)

Compute the standard error of the sample skewness for the normal distribution with parameters 5 and 2.

(5)

(6)

Compute the coefficient of skewness of a weighted data set.

(7)

(8)

Consider the following Matrix data set.

M := Matrix([[3, 1130, 114694], [4, 1527, 127368], [3, 907, 88464], [2, 878, 96484], [4, 995, 128007]])

(9)

We compute the skewness of each of the columns.

(10)

	See Also
	Statistics, Statistics[Computation], Statistics[DescriptiveStatistics], Statistics[Distributions], Statistics[ExpectedValue], Statistics[RandomVariables], Statistics[StandardError]