F distribution

Shape of Distribution

Basic Properties

  • Two parameters N_1 and N_2 are required (Positive integer)
  • Continuous distribution defined on semi-bounded range x \geq 0
  • This distribution is asymmetric.

Probability

Characteristics

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

  • Mean of the distribution is given as
    \frac{N_2}{N_2-2}\quad (N_2>2)
  • How to compute this on Excel
     
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    Data Description
    8 Value of parameter N2
    Formula Description (Result)
    =NTFMEAN(A2) Mean of the distribution for the terms above
  • Function reference : NTFMEAN

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

  • Variance of the distribution is given as
    \frac{2N_2^2(N_1+N_2-2)}{N_1(N_2-2)^2(N_2-4)}\quad (N_2>4)

    Standard Deviation is a positive square root of Variance.

  • How to compute this on Excel
     
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    Data Description
    4 Value of parameter N1
    30 Value of parameter N2
    Formula Description (Result)
    =NTFSTDEV(A2,A3) Standard deviation of the distribution for the terms above
  • Function reference : NTFSTDEV

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

  • Skewness of the distribution is given as
    \frac{(2N_1+N_2-2)\sqrt{8(N_2-4)}}{\sqrt{N_1(N_1+N_2-2)}(N_2-6)}\quad (N_2>6)
  • How to compute this on Excel
     
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    Data Description
    4 Value of parameter N1
    30 Value of parameter N2
    Formula Description (Result)
    =NTFSKEW(A2,A3) Skewness of the distribution for the terms above
  • Function reference : NTFSKEW

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

  • Kurtosis of the distribution is given as
    \frac{12[(N_2-2)^2(N_2-4)+N_1(N_1+N_2-2)(5N_2-22)]}{N_1(N_2-6)(N_2-8)(N_1+N_2-2)}\quad (N_2>8)
  • This distribution can be leptokurtic or platykurtic.
  • How to compute this on Excel
     
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    Data Description
    4 Value of parameter N1
    30 Value of parameter N2
    Formula Description (Result)
    =NTFKURT(A2,A3) Kurtosis of the distribution for the terms above
  • Function reference : NTFKURT

Random Numbers

  • How to generate random numbers on Excel.
     
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    Data Description
    4 Value of parameter N1
    30 Value of parameter N2
    Formula Description (Result)
    =NTRANDF(100,A2,A3,0) 100 F 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 : NTRANDF

NtRand Functions

  • If you already have parameters of the distribution
    • Generating random numbers based on Mersenne Twister algorithm: NTRANDF
    • Computing probability : NTFDIST
    • Computing mean : NTFMEAN
    • Computing standard deviation : NTFSTDEV
    • Computing skewness : NTFSKEW
    • Computing kurtosis : NTFKURT
    • Computing moments above at once : NTFMOM

Reference

 

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