17.2.4 Probability Plot and QQ PlotProbPlotQQPlot
The probability plot is used to test whether a dataset follows a given distribution. It shows a graph with an observed cumulative percentage on the X axis and an expected cumulative percentage on the Y axis. If all the scatter points are close to the reference line, we can say that the dataset follows the given distribution.
A QQ (QuantileQuantile) plot is another graphic method for testing whether a dataset follows a given distribution. It differs from the probability plot in that it shows observed and expected values instead of percentages on the X and Y axes. If all the scatter points are close to the reference line, we can say that the dataset follows the given distribution.
Origin supports four given distributions (Normal, Lognormal, Exponential, and Weibull), and five methods for plotting percentile approximations (Blom, Benard, Hazen, Van der Waerden, and KaplanMeier).
Creating Probability Plot or QQ Plot
To create a probability plot or QQ plot:
 Highlight one Y column.
 Open the probability/QQ plot dialog:
 For a probability plot: In Origin's main menu, click Plot, then point to Probability, and then click Probability Plot. Alternatively, you can click the Probability Plot button on the 2D Graphs toolbar.
 For a QQ plot: In Origin's main menu, click Plot, then point to Probability, and then click QQ Plot. Alternatively, you can click the QQ Plot button on the 2D Graphs toolbar.
 In the plot_prob XFunction dialog, specify the distribution and method.
 Click OK to create a probability plot or a QQ plot.
The Dialog of plot_prob XFunction
Input Data

Specify the input data.

Distribution

Select a distribution type for your data. For more information about distributions, please refer to Distributions section.
 Distribution
 Four distributions are available.
 Normal
 Lognormal
 Exponential
 Weibull
 Gamma
 Estimate from Data
 Specify whether to estimate distribution parameters from input data. If not, parameters can be specified manually.
 mu
 Mean of the normal distribution.
 sigma
 Standard deviation of Normal distribution.
 shape
 Shape of the specified distribution. Available in both Lognormal, Weibull and Gamma distributions.
 scale
 Scale of the specified distribution. Available in Lognormal, Exponential, Weibull and Gamma distributions.

Score Method

Select a method for plotting percentile approximations. For more information about methods, please refer to Score Methods section.
 Blom
 Benard
 Hazen
 Van der Waerden
 KaplanMeier

Confidence Band

Specify whether to output the confidence band in probability plot. For computation details, see Algorithms.

Confidence Level(%)

Only available when Confidence Band is selected. Specify the confidence level in percentage for the chosen distribution.

Exchange XY Axes

Specify whether to switch X and Y axis positions.

X Minimum X Maximum

Auto values are X Minimum = 1 and X Maximum = 99.5. If Auto is cleared, use the minimum and maximum values of the Reference Line column in the output.
When X Minimum is greater than the Auto value, we calculate Percentile value p1 for the X Minimum, and the Percentile column should only include p1, and values greater than p1, in the default list. If X Maximum is less than the Auto value, we calculate the Percentile value p2 for the X Maximum, and the Percentile column should only include p2, and values less than p2, in the default list.
When X Minimum is less than the Auto value, we calculate the Percentile value p1 for the X Minimum. If p1<1e5, p1=1e5, we then find the minimum value 10^(m) which is larger than p1 and the Percentile column includes p1, 10^(m), 10^(m+1), ,,,,1, 2,...
If X Maximum is greater than the Auto value, we calculate the Percentile value p2 for the X Maximum. If p2>99.99, p2=99.99, we then find the maximum value which is less than p2 from the list (99.9, 99.99) and the Percentile column includes 99, 99.5, 99.9,..p2.

Output Range

This determines where the calculated data for the graph is stored.

Distributions
Origin includes four distributions for Probability and QQ plots. The following table lists their density functions:
Distribution

Density Function p(x)

Range

Parameters

Normal


all

,mean,is the location parameter
,standard deviation, is the scale parameter

Lognormal



is the shape scale parameter
is the scale parameter.

Exponential



is the scale parameter.

Weibull



is the scale parameter
is the shape parameter

Gamma



is the scale parameter
is the shape parameter

Details for Constructing Probability Plot
To construct a probability plot, sort the observed dataset from smallest to largest:
 , is the total number of the observed dataset.
The sorted observed values are represented on the plot by points whose Xcoordinates are and whose Ycoordinates are calculated using the Score Method.
Scale types of probability plot are different according to the distributions
Distribution

X Scale Type

Y Scale Type

Normal

Linear

Probability

Lognormal

Ln

Probability

Exponential

Ln

Double Log Reciprocal

Weibull

Log10

Double Log Reciprocal

Gamma

Log10

Probability

Details for Constructing QQ Plot
To construct a QQ plot,sort the observed dataset from smallest to largest:
 , where is the total number of observed values.
The Y values are the inverse cumulative distribution functions of the score method used.
Score Methods
Input data is ordered from smallest to largest, and then the serial number of the sorted data is scored using one of the methods listed below. In this table, is the serial number and is the total number of the nonmissing input data.
Methods

Plotting Position

Blom


Benard


Hazen


Van der Waerden


KaplanMeier


Reference
 Samuel Kotz , Campbell B. Read , N. Balakrishnan, Brani Vidakovic, 2005. Encyclopedia of statistical sciences., NewYork: John Wiley & Sons, Inc.
 Thode, Henry C. 2002, Testing for Normality, CRC Press
