2.13.1.11 mmoments(Pro)

Brief Information

Compute moments on matrix data

Additional Information

This feature is for OriginPro only.

Command Line Usage

1. mmoments im:=MBook1;

2. mmoments im:=MBook1 mean:=mymean;

Variables

Display
Name
Variable
Name
I/O
and
Type
Default
Value
Description
Input Matrix im

Input

MatrixObject

<active>

Specifies the input data range

Mean mean

Output

double

<unassigned>

The variable specifies the output for the arithmetic average.

Standard Deviation sd

Output

double

<unassigned>

The variable specifies the output for the standard deviation, which is a statistical measure of the distance a quantity is likely to lie from the average value of a group of data.

SE of Mean se

Output

double

<unassigned>

The variable specifies the output for the standard error of the mean, which is used to estimate the deviation of the population mean.

Number of Observations n

Output

int

<unassigned>

The variable specifies the output for the number of valid observations

Sum sum

Output

double

<unassigned>

The variable specifies the output for the arithmetic sum of selected dataset

Skewness skewness

Output

double

<unassigned>

The variable specifies the output for skewness, which reveals the symmetry of sample distribution. A positive skewness implies the distribution curve skew to right while a negative value indicates the curve skew to left

Kurtosis kurtosis

Output

double

<unassigned>

The variable specifies the output for kurtosis, which indicates how flat or peaked a distribution is. Negative values correspond to flat distributions, while positive values correspond to peaked distributions.

Coefficient of Variation cv

Output

double

<unassigned>

The variable specifies the coefficient of variation, which gives a measure of how dispersed a dataset is. This measure can be used to compare distributions of different sizes and with different means.

Description

The "moments" command displays the mean, standard deviation, and other summary statistics of a given dataset. moments are used to describe certain basic features of the data in a study.

The X-function of mmoments is used to compute the summary statistics of a Matrix object. It can give out the mean, standard deviation, standard error, kurtosis, skewness, and coefficient of variation of the specified Matrix.

Examples

1. List all input and output results of descriptive statistics of given Matrix
mmoments im:=MBook1;

2. To return the standard deviation of given Matrix from the Command Window, type the following:
mmoments im:=MBook1 sd:=mysd; mysd=

Algorithm

Let Mmoments help English files image002.gif for Mmoments help English files image004.gifdenotes the input value, then:

1. Mean is computed using the following equation: Mmoments help English files image006.gif

2. Standard deviation is computed as follows: Mmoments help English files image008.gif

3. Standard error is computed as: Mmoments help English files image010.gif

4. Sample size is the total number of valid values in a data set

5. Sum is computed using following equation: Mmoments help English files image012.gif

6. Skewness is computed as: Mmoments help English files image014.gif

7. Kurtosis is computed as: Mmoments help English files image016.gif

8. Coefficient of variance is computed as: Mmoments help English files image018.gif

References

Silverman, B.W. (1986), Density Estimation for Statistics and Data Analysis. New York: Chapman and Hall.

Tukey, J.W. (1977), Exploratory Data Analysis. Reading, MA: Addison-Wesley.

Erickson, B.H. and Nosanchuk, T.A. (1992) Understanding Data. Second Edition. Buckingham: Open University Press.

Related X-Functions

stats, quantiles, rowstats, rowquantiles, mquantiles


Keywords:summary statistics, mean, median, standard deviation, skewness, kurtosis