gammaden

This function is the gamma distribution’s probability density function. It returns the value of the slope of the cumulative distribution function at the specified argument value.

The Gamma and Beta functions occur frequently in many applications. You can compute their values by writing simple transforms expressed in terms of the gamma density function.

• The Gamma function can be defined by:

  Gamma(x) = 1/(exp(1.0)*gammaden(1,x,1)) 

  
  
• and then the Beta can be defined by:

  Beta(x,y) = Gamma(x)*Gamma(y)/Gamma(x+y)

Syntax

gammaden(x,a,b)

The x argument represents the independent variable and can either be a scalar or a range of numbers. If x is a range, then it must be defined by either using braces { } or by specifying a worksheet column. Any value for x must be real. The a argument is any positive number and is the shape parameter. The b argument is any positive number and is the scale parameter.

Example

The density function can be used to estimate the probability that the values of a gamma distributed random variable G lie in a small interval. If G has shape parameter equal to 3 and scale parameter equal to 1, then to estimate the probability that the values of G lie between 2 and 2.1, multiply the density of G at 2 by the length of the interval .1:

• 
  

  gammaden(2,3,1) * .1 = .027067 

関連情報

• gammadist