2.2.5. Skewness
Skewness its a simmetry measure of data from the probability distribution of a variable. A normal curve presents skewness equal to '0', here the utility of this measure to compare other distributions with a gaussian or with a normal.
A negative measure indicates the distribution negative tail its longer and a positive measure indicates that the distribution positive tail its longer. In other words, a negative value indicates data moved to right (negative long tail) and positive values indicates data moved to left to the left (postive long tail).
There is many form of skewness (default, Pearson and others) which will not ever return the same result. Only equal forms of skewness must be compared!
2.2.5.1. Function MX.SKEW
Access:
- Menu - Insert | Function | Metrixus
 -Default | Metrixus Toolbar
Description:
Returns the data skewness or from the quotation return, according to the parameters informed. Allows to calculate the sample or population and also other forms of skewness from Karl Pearson. if the amount of valid data its lesser than 3, return ERRO.
For assets quotation, its interesting determines the simmetry of quotations return and not the simmetry in the quotations. This allows to infer about the type of an asset return distribution, in example.
Call: MX.SKEW (Data, Returns, Sample, Type, Intervals)
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 2 contiguous cells with data.
|
Returns |
boolean |
Optional. Indicates if the data represents quotations and the result presented is the skewness from this quotations returns. Insert 0 (default) for data and 1 for quotations return.
|
Sample |
boolean |
Optional. Indicates if the data refer to a sample (insert 0) or population (1). The default value is sample (0).
|
Type |
integer |
Optional. Indicates which type of skewness must be returned. It can be the standard form (insert 0), first coefficient of the Pearson skewness (insert 1) or second coefficient of Pearson skewness (insert 2). The default is the standard form of skewness (or 0).
|
Intervals |
integer |
Optional. A number bigger than 1 which indicates the amount of classes created to the first coefficient of the Pearson skewness. If TYPE is equal 1, this number is obligatory and can't be bigger than half of data amount.
|
Important:
In case of skewness of quotations returns, to the estatistics parameters determination - like mean and standard deviation - it isn't aplied none logarithmic on the quotations returna.
|
Important:
Also in skewness 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!
|
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 skewness the function return is:
- Default format of skewness: Type = 0. The resulted values are between -1 and +1.
- Population:
- Sample:
- 1° coefficient of Pearson skewness: Type = 1. USe the mode from data. If the distribution isn't unimmodal - one mode only - return ERROR.
- Population:
Moda=Mode
- Sample:
Moda=Mode
Important:
The mode value is calculated to contiguous data. On this form, the data are classified in the amount of Intervals which must be obligatory informed. The amount of intervals must be bigger than 1 and not bigger than the half of total data analyzed or the function will return ERROR. The mode is the result of the arithmetic mean between the class and mode limits, if exist (unimodal). If exist more than one modal class, the function will return ERROR. Modifying the intervals parameter can by-pass this error!
|
- 2° coefficient of Pearson skewness: Type = 2. Uses data median.
- Population:
Mediana=Median
- Sample:
Mediana=Median
Important:
The median is the data central value or, if exists two values, the arithmetic mean of it.
|
Where:
- Mean:
Média=Mean
- Standard deviation:
DP=St. Dev.;
Amostra=Sample;
População=Population;
Using data example:
Skewness of data – parameters:
- Data Intervals: P7:S23 (68 data)
- Sample
- 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.SKEW(P7:S23)
Results:
Using quotations example:
Skewness of quotations – parameters:
- Data Intervals: P7:S23 (68 data – 67 returns)
- Returns 1
- Sample 0
- 1° Coefficient of Pearson 1
- Intervals 15
- Data – same data from the last - data sorted by lines and collumns
= MX.SKEW(P7:S23, 1, 0, 1, 15)
Results:
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