// Home / Documentation / Gallery of Distributions / Uniform distribution (Continuous)

Uniform distribution (Continuous)

Where will you meet this distribution?

  • Generating random numbers according to a desired distribution
  • Digital signal processing (dithering) – digital audio, digital video, digital photography, seismology, RADAR, weather forecasting systems and many more

Shape of Distribution

Basic Properties

  • Two parameters are required.

    These parameters are minimum and maximum value of variable respectively.

  • Continuous distribution defined on bounded range
  • This distribution is always symmetric.

Probability

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

     
    1
    2
    3
    4
    5
    6
    7
    A B
    Data Description
    0.5 Value for which you want the distribution
    1 Value of parameter A
    5 Value of parameter B
    Formula Description (Result)
    =(A2-A3)/(A4-A3) Cumulative distribution function for the terms above
    =1/(A4-A3) Probability density function for the terms above

    Sample distribution

Quantile

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

     
    1
    2
    3
    4
    5
    6
    A B
    Data Description
    0.5 Probability associated with the distribution
    1 Value of parameter A
    5 Value of parameter B
    Formula Description (Result)
    =A3+A2*(A4-A3) Inverse of the cumulative distribution function for the terms above

Characteristics

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

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

     
    1
    2
    3
    4
    5
    A B
    Data Description
    8 Value of parameter A
    2 Value of parameter B
    Formula Description (Result)
    =(A2+A3)/2 Mean of the distribution for the terms above

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

     
    1
    2
    3
    4
    5
    A B
    Data Description
    8 Value of parameter A
    2 Value of parameter B
    Formula Description (Result)
    =(A3-A2)/(2*SQRT(3)) Standard deviation of the distribution for the terms above

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

  • Skewness is

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

  • Kurtosis is

Random Numbers

  • Random number x is generated from uniform random U,
  • How to generate random numbers on Excel.
     
    1
    2
    3
    4
    5
       
    A B
    Data Description
    1 Value of parameter A
    5 Value of parameter B
    Formula Description (Result)
    =(A3-A2)*NTRAND(100,A2,A3,0)+A2 100 uniform 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.

NtRand Functions

  • Generating random numbers based on Mersenne Twister algorithm: NTRAND

Reference

 

Comments are closed.