Difference between revisions of "Manuals/calci/KURT"
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(Created page with "<div id="6SpaceContent" class="zcontent" align="left"> '''KURT'''(N'''1''',N2,...) '''Where N1,N2,.... '''are the arguments to calculate the kurtosis. </div> ---- <...") |
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| − | <div | + | <div style="font-size:30px">'''KURT(n1,n2,…)'''</div><br/> |
| + | *<math>n1</math>,<math>n2</math> are values to calculate kurtosis. | ||
| + | ==Description== | ||
| + | *This function gives the value of kurtosis of a given set. | ||
| + | *Kurtosis is the peakedness or flatness of the graph of a frequency distribution 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,possion distribution, Laplace distribution. | ||
| + | *Example for negative kurtosis(platykurtosis) is Bernoulli distribution, Uniform distribution. | ||
| + | *Kurtosis has no units. | ||
| + | *Kurtosis is defined by: | ||
| + | *kurtosis={n(n+1)/(n-1)(n-2)(n-3)*summation[(xi-x(bar)/s]^4}-3(n-1)^2/(n-2)(n-3), wher s is the sample standard deviation.x(bar) is the arithmetic mean. | ||
| + | *In this function argumentsmay 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 | ||
| + | #Any one of the argument is nonnumeric. | ||
| + | #suppose the number of data points are less than four or the standard deviation of the sampleis zero | ||
| + | #The referred arguments could not convert | ||
| + | in to numbers. | ||
| + | ==Examples== | ||
| + | 1.DATA | ||
| + | 14 | ||
| + | 11 | ||
| + | 23 | ||
| + | 54 | ||
| + | 38 | ||
| + | KURT(C1:C5)=-0.8704870492 | ||
| + | 2. DATA={6,7,8,9,10} | ||
| + | KURT(A1:A5)=-1.199999999 | ||
| + | 3.DATA={1898,1987,1786,1947} | ||
| + | KURT(B1:B4)=0.870901113729 | ||
| + | 4.DATA={26,16,12} | ||
| + | KURT(D1:D3)=NAN | ||
| + | ==See Also== | ||
| + | *[[Manuals/calci/SKEW | SKEW ]] | ||
| + | *[[Manuals/calci/STDEV | STDEV ]] | ||
| + | *[[Manuals/calci/STDEVP | STDEVP ]] | ||
| − | + | ==References== | |
| − | + | [http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient Correlation] | |
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Revision as of 01:39, 12 December 2013
KURT(n1,n2,…)
- , are values to calculate kurtosis.
,
are values to calculate kurtosis.Description
- This function gives the value of kurtosis of a given set.
- Kurtosis is the peakedness or flatness of the graph of a frequency distribution 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,possion distribution, Laplace distribution.
- Example for negative kurtosis(platykurtosis) is Bernoulli distribution, Uniform distribution.
- Kurtosis has no units.
- Kurtosis is defined by:
- kurtosis={n(n+1)/(n-1)(n-2)(n-3)*summation[(xi-x(bar)/s]^4}-3(n-1)^2/(n-2)(n-3), wher s is the sample standard deviation.x(bar) is the arithmetic mean.
- In this function argumentsmay 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
- Any one of the argument is nonnumeric.
- suppose the number of data points are less than four or the standard deviation of the sampleis zero
- The referred arguments could not convert
in to numbers.
Examples
1.DATA 14 11 23 54 38 KURT(C1:C5)=-0.8704870492 2. DATA={6,7,8,9,10} KURT(A1:A5)=-1.199999999 3.DATA={1898,1987,1786,1947} KURT(B1:B4)=0.870901113729 4.DATA={26,16,12} KURT(D1:D3)=NAN