Manuals/calci/KURT

KURT(n1,n2,…)

• $n1$,$n2$ 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=:

${\frac {n(n+1)}{(n-1)(n-2)(n-3)}}{\frac {\sum (x_{i}-{\bar {x}})^{4}}{s}}-{\frac {3(n-1)^{2}}{(n-2)(n-3)}}$, where $s$ is the Sample Standard Deviation.${\bar {x}}$ 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.

• The below table is listing the Kurtosis excess for the number of common distributions:

Spreadsheet

	Distribution	Kurtosis excess
Bernoulli distribution	<math>\frac{1}{1-p}+\frac{1}{p}-6 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 =KURT(A1:E1) = 0.870901113729 =KURT(A2:E2) = -1.199999999 =KURT(A3:D3) = 0.870901113729 =KURT(A4:C4) = NAN See Also SKEW STDEV STDEVP References Kurtosis