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Poisson distribution

Where do you meet this distribution?

Shape of Distribution

Basic Properties

  • A parameter \nu is required.
    \nu>0

    \nu is mean of the distribution.

  • Discrete distribution defined at non-negative integer x=\{0,1,2,\cdots\}

Probability

  • Cumulative distribution function
    F(x)=\text{e}^{-\nu}\sum_{i=0}^{x}\frac{\nu^i}{i !}
  • Probability mass function
    f(x)=\frac{\nu^x\text{e}^{-\nu}}{x !}
  • How to compute these on Excel.
     
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    Data Description
    3 Value for which you want the distribution
    5 Value of parameter nu
    Formula Description (Result)
    =NTPOISSONDIST(A2,A3,TRUE) Cumulative distribution function for the terms above
    =NTPOISSONDIST(A2,A3,FALSE) Probability mass function for the terms above
  • Function reference : NTPOISSONDIST

Triangular distribution

Characteristics

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

  • Mean is given as \nu

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

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

  • Skewness of the distribution is given as
    \frac{1}{\sqrt{\nu}}
  • How to compute this on Excel
     
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    Data Description
    8 Value of parameter nu
    Formula Description (Result)
    =NTPOISSONSKEW(A2) Mean of the distribution for the terms above
  • Function reference : NTPOISSONSKEW

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

  • Kurtosis of the distribution is given as
    \frac{1}{\nu}
  • How to compute this on Excel
     
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    Data Description
    8 Value of parameter nu
    Formula Description (Result)
    =NTPOISSONKURT(A2) Mean of the distribution for the terms above
  • Function reference : NTPOISSONKURT

Random Numbers

  • How to generate random numbers.
     
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    Data Description
    6 Value of parameter nu
    Formula Description (Result)
    =NTRANDPOISSON(100,A2,0) 100 Poisson 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 A4:A103 starting with the formula cell. Press F2, and then press CTRL+SHIFT+ENTER.

NtRand Functions

Reference

 

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