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Chi square distribution

Shape of Distribution

Basic Properties

  • One parameter N is 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
    N
  • How to compute this on Excel
     
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    Data Description
    9 Value of parameter N
    Formula Description (Result)
    =NTCHISQMEAN(A2,A3) Mean of the distribution for the terms above
  • Function reference : NTCHISQMEAN

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

  • Variance of the distribution is given as
    2N

    Standard Deviation is a positive square root of Variance.

  • How to compute this on Excel
     
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    Data Description
    9 Value of parameter N
    Formula Description (Result)
    =NTCHISQSTDEV(A2) Standard deviation of the distribution for the terms above
  • Function reference : NTCHISQSTDEV

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

  • Skewness of the distribution is given as
    \sqrt{\frac{8}{N}}
  • How to compute this on Excel
     
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    Data Description
    9 Value of parameter Alpha
    Formula Description (Result)
    =NTCHISQSKEW(A2) Skewness of the distribution for the terms above
  • Function reference : NTCHISQSKEW

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

  • Kurtosis of the distribution is given as
    \frac{12}{N}
  • This distribution can be leptokurtic or platykurtic.
  • How to compute this on Excel
     
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    Data Description
    9 Value of parameter N
    Formula Description (Result)
    =NTCHISQKURT(A2) Kurtosis of the distribution for the terms above
  • Function reference : NTCHISQKURT

Random Numbers

  • How to generate random numbers on Excel.
     
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    Data Description
    9 Value of parameter N
    Formula Description (Result)
    =NTRANDCHISQ(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 : NTRANDCHISQ

NtRand Functions

Reference

 

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