T distribution

Shape of Distribution

Basic Properties

  • One parameter is required (Positive integer)
  • Continuous distribution defined on on entire range
  • This distribution is symmetric.

Probability

Characteristics

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

  • Mean of the distribution is defined for and is always 0.
  • How to compute this on Excel

     
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    A B
    Data Description
    8 Value of parameter N
    Formula Description (Result)
    =NTTMEAN(A2) Mean of the distribution for the terms above
  • Function reference : NTTMEAN

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

  • Variance of the distribution is given as

    Standard Deviation is a positive square root of Variance.

  • How to compute this on Excel

     
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    Data Description
    8 Value of parameter N
    Formula Description (Result)
    =NTTSTDEV(A2) Standard deviation of the distribution for the terms above
  • Function reference : NTTSTDEV

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

  • Skewness of the distribution is defined for and is always 0.
  • How to compute this on Excel

     
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    Data Description
    8 Value of parameter N
    Formula Description (Result)
    =NTTSKEW(A2) Skewness of the distribution for the terms above
  • Function reference : NTTSKEW

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

  • Kurtosis of the distribution is given as
  • This distribution can be leptokurtic or platykurtic.
  • How to compute this on Excel

     
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    Data Description
    8 Value of parameter N
    Formula Description (Result)
    =NTTKURT(A2) Kurtosis of the distribution for the terms above
  • Function reference : NTTKURT

Random Numbers

  • How to generate random numbers on Excel.
     
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    Data Description
    9 Value of parameter N
    Formula Description (Result)
    =NTRANDT(100,A2,0) 100 chi square 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 : NTRANDT

NtRand Functions

  • If you already have parameters of the distribution
    • Generating random numbers based on Mersenne Twister algorithm: NTRANDT
    • Computing probability : NTTDIST
    • Computing mean : NTTMEAN
    • Computing standard deviation : NTTSTDEV
    • Computing skewness : NTTSKEW
    • Computing kurtosis : NTTKURT
    • Computing moments above at once : NTTMOM

Reference

 

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