2.2.6. Excesso of Kurtosis
Kurtosis its a measure of the "peakdness" of the data distribution. Like a gaussian (normal) and a measure equals 3, usually is considered only kurtosis excess relating to the normal distribution.
A negative measure indicates a "peakdness" relating to normal and a positive indicates peaks or prolongs relating to the normal.
Variables with a negative kurtosis excess presents a bigger probability of occurring values far from mean. For positive measures, bigger the probability of values near mean.
Kurtosis also is a normality measure (gaussian) of a distribution.
2.2.6.1. Function MX.KURT
Access:
- Menu - Insert | Function | Metrixus
 -Default | Metrixus Toolbar
Descrição:
Return the excess of kurtosis from data or quotations return relating with a normal distribution or gaussian. Allow to calculate the sample or population. If the valid data amount its lesser than 4, return ERROR.Kurtosis also is a normality measure (gaussian) of a distribution.
Considering the financial assets returns and a negative mean, this are more risky cause it has greater possibility of profits and losses (values away from mean - imagine a flattened bell)!
Call: MX.KURT (Data, Returns, Sample)
Argument |
Type |
Description |
Data |
range |
Contiguous interval of cells containing data to be analyzed. Cell with text or empty are ignored. Must be selected more than 3 contiguous cells with data.
|
Returns |
boolean |
Optional. Indicates if data represents quotations and if the presented result is the excess of kurtosis from this quotations returns. Insert 0 (default) for data and 1 for quotations returns.
|
Sample |
boolean |
Optional. Indicates if the refer to a sample (insert 0) or a population (insert 1). The default is sample (or 0).
|
Important:
In case of excess of kurtosis from quotations returns, for the determination of statistics parameters of data - like mean and standard deviation - its not aplied none logarithmic operator in the quotations return.
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Important:
Also for excess of kurtosis of quotations return, the data must be sorted. Case existsmore than one collumn on cells intervals, the data must be sorted inside the lines and collumns. Any data in collumn A comes before any data in collumn B! Data in line 1 of collumn A come before data in line 2 from collumn A!
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Note 1: Microsoft Excel has limitations for the size of data passed to external functions and its sheets. Its advised to not use external functions calls with big data size from Excel sheets. In a generic form, Microsoft Excel doesn't support a data size bigger than 32.767 fields. More information, see Microsoft Excel Help.
The result for a data amount set n (or data amount n-1 for the excess of kurtosis of quotations return) is:
- Excess of kurtosis: normal curve have mean equals “0”.
- Population:
- Sample:
Where:
- Mean:
Média=Mean
- Standard Deviation:
DP=St. Dev.;
Amostra=Sample;
População=Population;
Using data example:
Excess of kurtosis of data – parameters:
- Data Intervals: P7:S23 (68 data)
- Samples
- Data
| 14.655 | 26.185 | 54.950 | 25.176 |
| 17.990 | 29.249 | 16.395 | 27.815 |
| 22.650 | 33.595 | 19.995 | 31.985 |
| 25.855 | 41.188 | 23.744 | 34.590 |
| 28.950 | 15.605 | 26.680 | 63.500 |
| 32.849 | 19.399 | 30.645 | 17.658 |
| 38.000 | 23.405 | 34.145 | 21.995 |
| 14.799 | 26.268 | 56.000 | 25.540 |
| 19.300 | 29.965 | 16.798 | 27.910 |
| 22.708 | 33.790 | 20.000 | 32.250 |
| 25.999 | 42.660 | 23.920 | 34.618 |
| 29.099 | 15.999 | 27.665 | 17.899 |
| 32.950 | 19.565 | 30.790 | 22.195 |
| 38.175 | 23.651 | 34.500 | 25.810 |
| 14.869 | 26.620 | 56.000 | 28.680 |
| 19.350 | 30.585 | 16.955 | 32.604 |
| 23.240 | 34.145 | 20.600 | 35.550 |
= MX.KURT(P7:S23)
Results:
Using quotations example:
Excess of kurtosis of quotations – parameters:
- Data Intervals: P7:S23 (68 data – 67 returns)
- Returns 1
- Sample 0
- Data - same data from last example - data sorted by lines and columns
= MX.KURT(P7:S23, 1, 0)
Results:
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