乘积性质:\Gamma(a)\Gamma(b) = \Gamma(a+b), \quad a, b > 0,这个性质允许我们简化两个伽玛函数的乘积。 反射公式(Euler's reflection formula):\Gamma(z)\Gamma(1-z) = \frac{\pi}{\sin(\pi z)} 当( z ) 趋向于无穷大时,伽玛函数可以近似为:\Gamma(z) \sim \sqrt{2\pi z}\left(\...
This can be derived using the exponential family formula for the moment generating function of the sufficient statistic, because one of the sufficient statistics of the gamma distribution is ln(x). Information entropy The information entropy is In the k, θ parameterization, the information entropy ...
This article describes the formula syntax and usage of theGAMMAINVfunction in Microsoft Excel. Returns the inverse of the gamma cumulative distribution. If p = GAMMADIST(x,...), then GAMMAINV(p,...) = x. You can use this function to study a variable whose distribution may be skewed. I...
Alpha parameter to the distribution 2 Beta parameter to the distribution Formula Description Result =GAMMADIST(A2,A3,A4,FALSE) Probability density using the x, alpha, and beta values in A2, A3, A4, with FALSE cumulative argument. 0.032639 =GAMMADIST(A2,A3,A4,TRUE) Cumulative distri...
Also, you can type the actualprobability,alphaandbetavalues in the formula as shown below. =GAMMA.INV(4,2,1.5) GAMMA.INV Vs. GAMMA.DIST The Excel GAMMA.INV function is the inverse of the GAMMA.DIST function (when used to calculate the cumulative distribution function, i.e., thecumulative...
Probability distribution functionsFormulas(Mathematics)Analysis of varianceReprintsGamma distributionsGaussian distributionParameter estimationGeneral formulae for minimum variance unbiased estimators of a broad class of functions of the parameters of the Gaussian and gamma distributions are given. The formulae ...
Betais a parameter to the distribution. If beta = 1, GAMMAINV returns the standard gamma distribution. Remarks If any argument is nonnumeric, GAMMAINV returns the #VALUE! error value. If probability < 0 or probability > 1, GAMMAINV returns the #NUM! error value. ...
A note on inference for the mean parameter of the gamma distribution Confidence distribution functionsaddlepoint methodStirling formulaThe two parameter gamma distribution with mean 渭 and shape 蟿 is widely used in reliability ... ACM Wong - 《Statistics & Probability Letters》 被引量: 26发表: 199...
Beta parameter to the distribution Formula Description Result =GAMMA.DIST(A2,A3,A4,FALSE) Probability density using the x, alpha, and beta values in A2, A3, A4, with FALSE cumulative argument. 0.032639 =GAMMA.DIST(A2,A3,A4,TRUE) Cumulative distributuion using the x, alpha, and beta valu...
If cumulative is true, Gamma_Dist returns the cumulative distribution function; if false, it returns the probability density function. Returns Double Remarks If x, alpha, or beta is nonnumeric, Gamma_Dist returns the #VALUE! error value. If x < 0, Gamma_Dist returns the #NUM! error ...