# Manuals/calci/KURT

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:
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

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

Kurtosis