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Triangular distribution

Where do you meet this distribution?

Shape of Distribution

Basic Properties

  • Three parameters are required (How can you get these).

    These parameters are minimum value of variable, maximum value of variable and mode of the distribution respectively.

  • Continuous distribution defined on bounded range
  • This distribution can be symmetric or asymmetric.

Probability

  • Cumulative distribution function
  • Probability density function
  • How to compute these on Excel.

     
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    A B
    Data Description
    1.5 Value for which you want the distribution
    1 Value of parameter Min
    3 Value of parameter Max
    1.4 Value of parameter Mode
    Formula Description (Result)
    =NTTRIANGULARDIST(A2,A3,A4,A5,TRUE) Cumulative distribution function for the terms above
    =NTTRIANGULARDIST(A2,A3,A4,A5,FALSE) Probability density function for the terms above
  • Function reference : NTTRIANGULARDIST

Triangular distribution

Quantile

  • Inverse function of cumulative distribution function
  • How to compute this on Excel.

     
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    A B
    Data Description
    0.5 Probability associated with the distribution
    1 Value of parameter Min
    3 Value of parameter Max
    1.4 Value of parameter Mode
    Formula Description (Result)
    =NTTRIANGULARINV(A2,A3,A4,A5) Inverse of the cumulative distribution function for the terms above
  • Function reference : NTTRIANGULARINV

Characteristics

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

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

     
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    A B
    Data Description
    1 Value of parameter Min
    3 Value of parameter Max
    1.4 Value of parameter Mode
    Formula Description (Result)
    =NTTRIANGULARMEAN(A2,A3,A4) Mean of the distribution for the terms above
  • Function reference : NTTRIANGULARMEAN

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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    A B
    Data Description
    1 Value of parameter Min
    3 Value of parameter Max
    1.4 Value of parameter Mode
    Formula Description (Result)
    =NTTRIANGULARSTDEV(A2,A3,A4) Standard deviation of the distribution for the terms above
  • Function reference : NTTRIANGULARSTDEV

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

  • Skewness of the distribution is given as
  • How to compute this on Excel

     
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    A B
    Data Description
    1 Value of parameter Min
    3 Value of parameter Max
    1.4 Value of parameter Mode
    Formula Description (Result)
    =NTTRIANGULARSKEW(A2,A3,A4) Skewness of the distribution for the terms above
  • Function reference : NTTRIANGULARSKEW

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

  • Kurtosis is .

Random Numbers

  • Random number x is generated by inverse function method, which is for uniform random U,
  • How to generate random numbers on Excel.
     
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    A B
    Data Description
    0 Value of parameter A
    3 Value of parameter B
    1.8 Value of parameter C
    Formula Description (Result)
    =NTRANDTRIANGULAR(100,A2,A3,A5,0) 100 triangular 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 A6:A105 starting with the formula cell. Press F2, and then press CTRL+SHIFT+ENTER.

NtRand Functions

Reference

 

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