Probability Distributions

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

This help page describes the probability distributions provided in the Statistics package, how to construct random variables using these distributions and the functions that are typically used in conjunction with these distributions.

Constructors

•	The constructors are used to create objects that wrap distributions. However, most functions generally allow access to the distributions directly through their inert form.

DiscreteValueMap	create a
Distribution	create new distribution
RandomVariable	create new random variable

Discrete Distributions

•	Discrete distributions have nonzero probability only at discrete points. Discrete distributions are defined by their probability function rather than by their probability density function in order to avoid singularities.

Bernoulli	Bernoulli distribution
Binomial	binomial distribution
DiscreteUniform	discrete uniform distribution
EmpiricalDistribution	empirical distribution
Geometric	geometric distribution
Hypergeometric	hypergeometric distribution
NegativeBinomial	negative binomial (Pascal) distribution
Poisson	poisson distribution
ProbabilityTable	probability table

Continuous Distributions

•	Continuous distributions are defined along the real line by their probability density function.

Beta	beta distribution
Cauchy	Cauchy distribution
ChiSquare	chi-square distribution
Erlang	Erlang distribution
Error	error (exponential power) distribution
Exponential	exponential distribution
FRatio	Fisher f-distribution
Gamma	gamma distribution
Gumbel	Gumbel distribution
InverseGaussian	inverse gaussian (Wald) distribution
Laplace	Laplace distribution
Logistic	logistic distribution
LogNormal	log normal distribution
Maxwell	Maxwell distribution
Moyal	Moyal distribution
NonCentralBeta	noncentral beta distribution
NonCentralChiSquare	noncentral chi-square distribution
NonCentralFRatio	noncentral f-distribution
NonCentralStudentT	noncentral t-distribution
Normal	normal (gaussian) distribution
Pareto	Pareto distribution
Power	power distribution
Rayleigh	Rayleigh distribution
StudentT	Student-t distribution
Triangular	triangular distribution
Uniform	uniform (rectangular) distribution
VonMises	von Mises distribution
Weibull	Weibull distribution

Functions

•	The following functions are used to retrieve information or perform another function on a probability distribution.

AbsoluteDeviation	compute the average absolute deviation
CDF	cumulative distribution function
CentralMoment	central moments
CGF	cumulant generating function
CharacteristicFunction	characteristic function
Cumulant	cumulants
CumulantGeneratingFunction	cumulant generating function
CumulativeDistributionFunction	cumulative distribution function
Decile	deciles
ExpectedValue	compute expected values
FailureRate	hazard (failure) rate
GeometricMean	geometric mean
HarmonicMean	harmonic mean
HazardRate	hazard (failure) rate
InterquartileRange	interquartile range
InverseSurvivalFunction	inverse survival function
Kurtosis	kurtosis
MakeProcedure	generate a procedure for calculating statistical quantities
Mean	arithmetic mean
MeanDeviation	average absolute deviation from the mean
Median	median
MedianDeviation	compute the median absolute deviation
MGF	moment generating function
MillsRatio	Mills ratio
Mode	mode
Moment	moments
MomentGeneratingFunction	moment generating function
OrderStatistic	order statistics
PDF	probability density function
Percentile	percentiles
Probability	compute the probability of an event
ProbabilityDensityFunction	probability density function
ProbabilityFunction	probability function
QuadraticMean	quadratic mean
Quantile	quantiles
Quartile	quartiles
RandomVariable	create new random variables
Skewness	skewness
StandardDeviation	standard deviation
StandardError	standard error of the sampling distribution
StandardizedMoment	standardized moments
Support	support set of a random variable
SurvivalFunction	survival function
Variance	variance
Variation	coefficient of variation