// Home / Documentation / Gallery of Distributions / Gamma distribution

Gamma distribution

Shape of Distribution

Basic Properties

  • Two parameters \alpha, \beta are required (How can you get these?)
    \alpha>0,\beta>0
  • Continuous distribution defined on semi-bounded range x \geq 0
  • This distribution is asymmetric.

Probability

Quantile

  • Inverse function of cumulative distribution function cannot be expressed in closed form.
  • GAMMAINV is an excel function.
  • How to compute this on Excel.

     
    1
    2
    3
    4
    5
    6
       
    A B
    Data Description
    0.7 Probability associated with the distribution
    4 Value of parameter Alpha
    2.3 Value of parameter Beta
    Formula Description (Result)
    =GAMMAINV(A2,A3,A4) Inverse of the cumulative distribution function for the terms above

Characteristics

Mean – Where is the “center” of the distribution? (Definition)

  • Mean of the distribution is given as
    \alpha\beta
  • How to compute this on Excel

     
    1
    2
    3
    4
    5
    A B
    Data Description
    4 Value of parameter Alpha
    2.3 Value of parameter Beta
    Formula Description (Result)
    =NTGAMMAMEAN(A2,A3) Mean of the distribution for the terms above
  • Function reference : NTGAMMAMEAN

Standard Deviation – How wide does the distribution spread? (Definition)

  • Variance of the distribution is given as
    \alpha\beta^2

    Standard Deviation is a positive square root of Variance.

  • How to compute this on Excel

     
    1
    2
    3
    4
    5
       
    A B
    Data Description
    4 Value of parameter Alpha
    2.3 Value of parameter Beta
    Formula Description (Result)
    =NTGAMMASTDEV(A2,A3) Standard deviation of the distribution for the terms above
  • Function reference : NTGAMMASTDEV

Skewness – Which side is the distribution distorted into? (Definition)

  • Skewness of the distribution is given as
    \frac{2}{\sqrt{\alpha}}
  • How to compute this on Excel

     
    1
    2
    3
    4
    A B
    Data Description
    4 Value of parameter Alpha
    Formula Description (Result)
    =NTGAMMASKEW(A2) Skewness of the distribution for the terms above
  • Function reference : NTGAMMASKEW

Kurtosis – Sharp or Dull, consequently Fat Tail or Thin Tail (Definition)

  • Kurtosis of the distribution is given as
    \frac{6}{\alpha}
  • This distribution can be leptokurtic or platykurtic.
  • How to compute this on Excel

     
    1
    2
    3
    4
    A B
    Data Description
    4 Value of parameter Alpha
    Formula Description (Result)
    =NTGAMMAKURT(A2) Kurtosis of the distribution for the terms above
  • Function reference : NTGAMMAKURT

Random Numbers

  • How to generate random numbers on Excel.
     
    1
    2
    3
    4
    5
       
    A B
    Data Description
    4 Value of parameter Alpha
    2.3 Value of parameter Beta
    Formula Description (Result)
    =NTRANDGAMMA(100,A2,A3,0) 100 gamma deviates based on Mersenne-Twister algorithm for which the parameters above

    Note The formula in the example must be entered as an array formula. After copying the example to a blank worksheet, select the range A5:A104 starting with the formula cell. Press F2, and then press CTRL+SHIFT+ENTER.

  • Function reference : NTRANDGAMMA

NtRand Functions

  • If you already have parameters of the distribution
  • If you know mean and standard deviation of the distribution

Reference

 

Comments are closed.