GUIskewness

GUIskewness shows the necessary calculations to obtain the variance in a GUI.

Syntax

• out=GUIskewness(x)example
• out=GUIskewness(x, flag)example
• out=GUIskewness(x, flag, w)example

Description

 out =GUIskewness(x) Calculation of biased index of skewness.

 out =GUIskewness(x, flag) Calculation of unbiased index of skewness.

 out =GUIskewness(x, flag, w) Calculation of weighted unbiased index of skewness.

Examples

expand all

Calculation of biased index of skewness.

Vector x contains the expenditure of 20 customers in a supermarket. (See page 178 of [MRZ])

x=[20, 110,  31, 125,  40, 128,  50, 140,  65, 150,  72, 175,...
85, 190,  100, 205,  100, 230,  105 310];
GUIskewness(x)
ans =

21×5 table

i     x_i     (x_i-M)    (x_i-M)^2      (x_i-M)^3
___    ____    _______    __________    ___________

1      20    -101.55         10312    -1.0472e+06
2     110     -11.55         133.4        -1540.8
3      31     -90.55        8199.3    -7.4245e+05
4     125       3.45        11.903         41.064
5      40     -81.55        6650.4    -5.4234e+05
6     128       6.45        41.603         268.34
7      50     -71.55        5119.4    -3.6629e+05
8     140      18.45         340.4         6280.4
9      65     -56.55        3197.9    -1.8084e+05
10     150      28.45         809.4          23028
11      72     -49.55        2455.2    -1.2166e+05
12     175      53.45        2856.9      1.527e+05
13      85     -36.55        1335.9         -48827
14     190      68.45        4685.4     3.2072e+05
15     100     -21.55         464.4         -10008
16     205      83.45        6963.9     5.8114e+05
17     100     -21.55         464.4         -10008
18     230     108.45         11761     1.2755e+06
19     105     -16.55         273.9        -4533.1
20     310     188.45         35513     6.6925e+06
NaN    2431          0    1.0159e+05     5.9765e+06



Calculation of unbiased index of skewness.

Vector x contains the expenditure of 20 customers in a supermarket. (See page 178 of [MRZ])

x=[20, 110,  31, 125,  40, 128,  50, 140,  65, 150,  72, 175,...
85, 190,  100, 205,  100, 230,  105 310];
GUIskewness(x,0)

Calculation of weighted unbiased index of skewness.

Italian grades obtained in a particular university exam by 1000 students. (See page 54 of [CMR])

x=20:29;
% w= vector of frequencies
w=[61    82   102   164   122   122    61   143    82    61];
GUIskewness(x,0,w)

Related Examples

expand all

Calculation of weighted biased index of skewness.

Italian grades obtained in a particular university exam by 1000 students. (See page 54 of [CMR])

x=20:29;
% w= vector of frequencies
w=[61    82   102   164   122   122    61   143    82    61];
GUIskewness(x,1,w)

Input Arguments

x — vector of numeric data. Vector.

Vector containing strictly numerical data.

Data Types: double

flag — flag for unbiasness. Scalar.

If flag=0 the unbiased index is computed.

If flag=1 (default) the biased index is computed, meaning that it tends to differ from the population skewness by a systematic amount based on the sample size.

Example: 1 

Data Types: double

w — weights. Vector.

Vector of the same length of x containing the weights assigned to each observation.

Example: 1:10 

Data Types: double

Output Arguments

out —detailed output to compute the index. Table

Table with n+1 rows (where n is the length of x) containing what is shown in the GUI. Last row contains the totals.

References

Milioli, M.A., Riani, M., Zani, S. (2019), "Introduzione all'analisi dei dati statistici (Quarta edizione ampliata)". [MRZ]

Cerioli, A., Milioli, M.A., Riani, M. (2016), "Esercizi di statistica (Quinta edizione)". [CMR]