# 2.13.1.6 diststats

## Contents

Minimum Origin Version Required: 8.0 SR6

## Command Line Usage

 

diststats iy:=col(3) percent:=col(4) quantile:=col(5); 

## Variables

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

Input

XYRange

<active>
Specify the input data.
Percent of Integral Area percent

Input

vector

<unassigned>
This variable is related to quantile. Assign a vector to this variable. Then for each value k in the vector, the kth percentile will be output.
Peak Direction dir

Input

int

1
This X-Function assumes that there is a peak in the input data. It will locate it. The user is required to specify the direction of the peak.

Option list:

• neg:negative
This means that the peak is a negative one. When this option is chosen, the data point that has the minimum Y value will be regarded as the peak.
• pos:Positive
This means that the peak is a positive one. When this option is chosen, the data point that has the maximum Y value will be regarded as the peak.
Index of Peak ipeak

Output

int

<unassigned>
Specify the output of the index of the data point which is the peak in the input data.
X Peak xpeak

Output

double

<unassigned>
Specify the output of the X value of the data point which is the peak in the input data.
Y Peak ypeak

Output

double

<unassigned>
Specify the output of the Y value of the data point which is the peak in the input data.
Mean mean

Output

double

<unassigned>
Specify the output of the mean of the input dataset. See its computation in the Algorithm part.
Median median

Output

double

<unassigned>
Specify the output of the mean of the input dataset. See its computation in the Algorithm part.
Quantile quantile

Output

vector

<unassigned>
Specify the output of the quantiles correspond to the values in the vector that is assigned to the percent variable.

## Description

This function can be used to execute distribution statistics on an XY range. The input data's X values should be monotonically increasing and the Y values should be greater than 0. Otherwise, the X-Function cannot be used.

## Example

fname$= system.path.program$ + "Samples\Curve Fitting\Gaussian.dat";
newbook;
impasc;
dataset aa={0,0.01,25,50,99.99,100};
col(4)=aa;
diststats iy:=col(2) percent:=aa quantile:=col(5);

## Algorithms

Mean

The weighted arithmetic mean is calculated: $mean = \frac{\sum_{i=1}^n{y_i \cdot x_i}}{\sum_{i=1}^n {y_i}}$ where $x_i$ and $y_i$ is the X and Y values of the ith data point in the input dataset.

Median

First the sum of Y value of all data points is calculated:

$S=\sum_i^ny_i$

We suppose there is an M=0.5*S, for your data, the formula below is always coming into existence:

$\sum_i^ky_i \le M<\sum_{i=1}^{k+1}y_i$

And the median we want is Median=X[K].

Quantile

Integration is performed on the whole input data to calculate the absolute area. Then for each value k in the vector assigned to the percent variable, the function finds a value m so that if one integrates the input curve from the first X value to m, the absolute area of this section will be of k percent of the total area.