Manuals/calci/KURT

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KURT(n1,n2,…)


  • , are values to calculate kurtosis.

Description

  • This function gives the value of Kurtosis of a given set.
  • Kurtosis is the peak or flatness of a frequency distribution graph especially with respect to the concentration of values near the Mean as compared with the Normal Distribution.
  • A normal distribution has a Kurtosis of 3.
  • Distributions having higher Kurtosis have flatter tails or more extreme values that phenomenon called 'leptokurtosis' also it is the positive excess Kurtosis , and those with lower Kurtosis have fatter middles or fewer extreme value that phenomenon called 'Platykurtosis' also it is the negative excess Kurtosis.
  • Example for positive Kurtosis(leptokurtosis) is Exponential distribution, Poisson distribution, Laplace Distribution.
  • Example for Negative Kurtosis(platykurtosis) is Bernoulli distribution, Uniform distribution.
  • Kurtosis has no units.
  • Kurtosis is defined by:
  • Kurtosis=:

, where is the Sample Standard Deviation. is the Arithmetic Mean.

  • In this function arguments may be any type like numbers,names,arrays or references that contain numbers.
  • We can give logical values and text references also directly.
  • Suppose the referred argument contains any null cells, logical values like that values are not considered.
  • This function will return the result as error when
1.Any one of the argument is non-numeric.
2.Suppose the number of data points are less than four or the standard deviation of the sample is zero
3.The referred arguments could not convert
  in to numbers.
  • When calculating kurtosis, a result of +3.00 indicates the absence of kurtosis (distribution is mesokurtic).
  • For simplicity in its interpretation, some statisticians adjust this result to zero (i.e. kurtosis minus 3 equals zero), and then any reading other than zero is referred to as excess kurtosis.
  • Negative numbers indicate a platykurtic distribution and positive numbers indicate a leptokurtic distribution.
  • The below table is listing the Kurtosis excess for the number of common distributions:
Spreadsheet
Distribution Kurtosis excess
Bernoulli distribution
Beta distribution
Binomial distribution
Chi squared distribution
Exponential distribution 6
Gamma distribution
Log normal distribution
Negative binomial distribution
Normal distribution 0
Poisson distribution
Student's t distribution

ZOS

  • The syntax is to calculate KURTOSIS in ZOS is
    • , are values to calculate kurtosis.
  • For e.g., kurt([-1..-10,20..25..0.5])
KURTOSIS

Examples

Spreadsheet
A B C D E
1 14 11 23 54 38
2 6 7 8 9 10
3 1898 1987 1786 1947
4 26 16 12
5
  1. =KURT(A1:E1) = -0.8704870491886512
  2. =KURT(A2:E2) = -1.199999999
  3. =KURT(A3:D3) = 0.8709011137293157
  4. =KURT(A4:C4) = NAN

Related Videos

Kurtosis

See Also

References

Kurtosis


List of Main Z Functions

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