司徒頓t分布 | t distribution and gamma distribution
司徒頓t分布(Studentst-distribution),簡稱t分布,在機率論及統計學中用於根據小樣本來估計母體呈常態分布且標準差未知的期望值。若母體標準差已知,或是樣本數足夠大時(依據中央極限定理漸進常態分布),則應使用常態分布來進行估計。其為對兩個樣本期望值差異進行顯著性測試的司徒頓t檢定之基礎。司徒頓t分布機率密度函數累積分布函數母數ν>0{displaystyleu>0!}自由度值域x∈(−∞;+∞){displaystylexin(-infty;+infty)!}機率密度函數Γ((ν+1)/2)νπΓ(ν/2)(1+x2/ν)(ν+1)/2{displaystyle{frac{Gamma((u+1)/2)}{{sqrt{upi}},Gamma...
司徒頓t分布(Students t-distribution),簡稱t 分布,在機率論及統計學中用於根據小樣本來估計母體呈常態分布且標準差未知的期望值。若母體標準差已知,或是樣本數足夠大時(依據中央極限定理漸進常態分布),則應使用常態分布來進行估計。其為對兩個樣本期望值差異進行顯著性測試的司徒頓t檢定之基礎。
司徒頓t 分布機率密度函數
累積分布函數
母數 ν>0{displaystyle u >0!}自由度值域 x∈(−∞;+∞){displaystyle xin (-infty ;+infty )!}機率密度函數 Γ((ν+1)/2)νπΓ(ν/2)(1+x2/ν)(ν+1)/2{displaystyle {frac {Gamma (( u +1)/2)}{{sqrt { u pi }},Gamma ( u /2),(1+x{2}/ u ){( u +1)/2}}}!}累積分布函數 12+xΓ((ν+1)/2)2F1(12,(ν+1)/2;32;−x2ν)πνΓ(ν/2){displaystyle {frac {1}{2}}+{frac {xGamma left(( u +1)/2 ight),_{2}F_{1}left({frac {1}{2}},( u +1)/2;{frac {3}{2}};-{frac {x{2}}{ u }} ight)}{{sqrt {pi u }},Gamma ( u /2)}}}其中:2F1{displaystyle ,_{2}F_{1}}是超幾何函數期望值 ν>1{displaystyle u >1}時為0{displaystyle 0},ν=1{displaystyle u =1}時未定義中位數 0{displaystyle 0}眾數 0{displaystyle 0}變異數 ν>2{displaystyle u >2}時為νν−2{displaystyle {frac { u }{ u -2}}!},否則為無窮大偏度 ν>3{displaystyle u >3}時為0{displaystyle 0}峰...取得本站獨家住宿推薦 15%OFF 訂房優惠
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3 Moments and moment generating functions | t distribution and gamma distribution
If t ≥ 1/β, then the quantity 1 − βt is nonpositive and the integral is infinite. Thus, the mgf of the gamma distribution exists only if t < 1/β. The mean of the gamma ... Read More
Gamma distribution | t distribution and gamma distribution
In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The exponential distribution, Erlang ... Read More
Lecture 6 Gamma distribution, | t distribution and gamma distribution
Lecture 6. Gamma distribution, . 2. -distribution,. Student t-distribution,. Fisher F -distribution. Gamma distribution. Let us take two parameters > 0 and > 0. Read More
Multivariate t | t distribution and gamma distribution
In statistics, the multivariate t-distribution (or multivariate Student distribution) is a multivariate ... generalized Dirichlet · multivariate Laplace · multivariate normal · multivariate stable: multivariate t: normal-inverse-gamma Read More
Noncentral t | t distribution and gamma distribution
As with other probability distributions with noncentrality parameters, the noncentral t-distribution ... where Γ is the gamma function and I is the regularized incomplete beta function. Although there are other forms of the cumulative distribution .. Read More
Relationships among probability distributions | t distribution and gamma distribution
In probability theory and statistics, there are several relationships among probability ... A gamma distribution with shape parameter α = 1 and scale parameter θ is an ... A random variable with a t distribution with one degree of freedom is a ... Read More
Student T Distribution | t distribution and gamma distribution
The Student t distribution (sometimes just called the t distribution) is designed for ... We start by noting that S is a gamma distribution, with probability distribution ... Read More
Student's t distribution | t distribution and gamma distribution
跳到 Relation to the normal and to the Gamma distribution - Relation to the normal and to the Gamma distribution A standard Student's t random variable can be written as a normal random variable whose variance is equal to the reciprocal of a Gamma rand Read More
Student's t Distribution Formula | t distribution and gamma distribution
2018年5月10日 — t Distribution Formula · The symbol Γ is the capital form of the Greek letter gamma. This refers to the gamma function. · These types of ... Read More
Student's t distribution | Properties, proofs | t distribution and gamma distribution
A standard Student's t random variable can be written as a normal random variable whose variance is equal to the reciprocal of a Gamma random variable, as shown ... Read More
Student's t | t distribution and gamma distribution
In probability and statistics, Student's t-distribution is any member of a family of continuous ... -textstyle-frac-Gamma -left(-frac-nu+. CDF ... is the gamma function. Read More
Student's t-Distribution | t distribution and gamma distribution
Student's t -distribution is defined as the distribution of the random variable t which is (very loosely) the ... -infty<t<infty , Gamma(z) is the gamma function, B(a,b) ... Read More
Student | t distribution and gamma distribution
2022年1月25日 — The Student-t distribution is supported on the set of real numbers. Probability density function ... Read More
伽瑪分布 | t distribution and gamma distribution
伽瑪分布(英語:Gamma distribution)是統計學的一種連續機率分布。伽瑪分布中的母數α,稱為形狀母數,β稱為比例母數。 目次. Read More
司徒頓t分布 | t distribution and gamma distribution
司徒顿t分布(Student's t-distribution),簡稱t 分布,在機率論及统计学中用于根据小样本來估計 ... -frac -Gamma ((-nu +1)/2). Read More
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