Difference between revisions of "Manuals/calci/KURT"

 
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<div style="font-size:30px">'''KURT(n1,n2,…)'''</div><br/>
+
<div style="font-size:30px">'''KURT()'''</div><br/>
*<math>n1</math>,<math>n2</math> are values to calculate kurtosis.
+
*Parameters are any values to calculate kurtosis.
 +
**KURT(), returns the kurtosis of a data set.
 +
 
 
==Description==
 
==Description==
 
*This function gives the value of Kurtosis of a given set.
 
*This function gives the value of Kurtosis of a given set.
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*Kurtosis is defined by:
 
*Kurtosis is defined by:
 
*Kurtosis=:
 
*Kurtosis=:
<math>{\frac{n(n+1)}{(n-1)(n-2)(n-3)}*\sum[(xi-\bar{x})/s]^4}-3(n-1)^2/(n-2)(n-3)</math>, where <math>s</math> is the sample standard deviation.x(bar) is the arithmetic mean.
+
<math>\frac{n(n+1)}{(n-1)(n-2)(n-3)} \frac{\sum (x_{i}-\bar{x})^4}{s}- \frac{3(n-1)^2}{(n-2)(n-3)}</math>, where <math>s</math> is the Sample Standard Deviation.<math>\bar{x}</math> is the Arithmetic Mean.
 
*In this function arguments may be any type like numbers,names,arrays or references that contain numbers.
 
*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.
 
*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.
 
*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  
 
*This function will return the result as error when  
#Any one of the argument is non-numeric.
+
1.Any one of the argument is non-numeric.
#suppose the number of data points are less than four or the standard deviation of the sampleis zero
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2.Suppose the number of data points are less than four or the standard deviation of the sample is zero
#The referred arguments could not convert
+
3.The referred arguments could not convert
in to numbers.
+
  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:
 +
{| class="wikitable"
 +
|+Spreadsheet
 +
! Distribution !! Kurtosis excess
 +
|-
 +
| Bernoulli distribution || <math>\frac{1}{1-p}+\frac{1}{p}-6</math>
 +
|-
 +
| Beta distribution ||<math>\frac{6[a^3+a^2(1-2b)+b^2(1+b)-2ab(2+b)]}{ab(2+a+b)(3+a+b)}</math>
 +
|-
 +
| Binomial distribution || <math>\frac{6p^2-6p+1}{np(1-p)}</math>
 +
|-
 +
| Chi squared distribution || <math>\frac{12}{r}</math>
 +
|-
 +
| Exponential distribution || 6
 +
|-
 +
| Gamma distribution || <math> \frac {6}{a}</math>
 +
|-
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| Log normal distribution ||<math>e^{4S^2}+2e^{3S^2}+3e^{2S^2}-6</math>
 +
|-
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| Negative binomial distribution ||<math>\frac{6-p(6-p)}{r(1-p)}</math>
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|-
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| Normal distribution || 0
 +
|-
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| Poisson distribution || <math>\frac{1}{v}</math>
 +
|-
 +
| Student's t distribution ||<math>\frac{6}{n-4}</math>
 +
|}
 +
 
 +
==ZOS==
 +
*The syntax is to calculate KURTOSIS in ZOS is <math>KURT()</math>
 +
**Parameters are any values to calculate kurtosis.
 +
*For e.g., KURT([-1..-10,20..25..0.5])
 +
{{#ev:youtube|YqusfrKpWEA|280|center|KURTOSIS}}
  
 
==Examples==
 
==Examples==
1.DATA
+
{| class="wikitable"
14
+
|+Spreadsheet
11
+
|-
23
+
! !! A !! B !! C !! D!! E
54
+
|-
38
+
! 1
KURT(C1:C5)=-0.8704870492
+
| 14 || 11 || 23 || 54 || 38
2. DATA={6,7,8,9,10}
+
|-
KURT(A1:A5)=-1.199999999
+
! 2
3.DATA={1898,1987,1786,1947}
+
| 6 || 7 || 8 || 9 || 10
KURT(B1:B4)=0.870901113729
+
|-
4.DATA={26,16,12}
+
! 3
KURT(D1:D3)=NAN
+
| 1898  || 1987  || 1786  ||1947 ||
 +
|-
 +
! 4
 +
| 26 ||16  || 12  || ||
 +
|}
 +
# =KURT(A1:E1) = -0.8704870491886512
 +
# =KURT(A2:E2) = -1.199999999
 +
# =KURT(A3:D3) = 0.8709011137293157
 +
# =KURT(A4:C4) = NAN
 +
 
 +
==Related Videos==
 +
 
 +
{{#ev:youtube|HnMGKsupF8Q|280|center|Kurtosis}}
 +
 
 
==See Also==
 
==See Also==
 
*[[Manuals/calci/SKEW  | SKEW ]]
 
*[[Manuals/calci/SKEW  | SKEW ]]
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==References==
 
==References==
[http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient Correlation]
+
[http://en.wikipedia.org/wiki/Kurtosis Kurtosis]
 +
 
 +
 
 +
*[[Z_API_Functions | List of Main Z Functions]]
 +
 
 +
*[[ Z3 |  Z3 home ]]

Latest revision as of 17:22, 7 August 2018

KURT()


  • Parameters are any values to calculate kurtosis.
    • KURT(), returns the kurtosis of a data set.

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  
    • Parameters are any 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
  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