Inverse Cumulative Distribution Function

Inverse Cumulative Distribution Function

Inverse Cumulative Distribution Function is located under Model Studio (  ) in Statistical Analysis, in the left task pane. Use the drag-and-drop method to use the algorithm in the canvas. Click the algorithm to view and select different properties for analysis.

Refer to Properties of Inverse Cumulative Distribution Function.


The Inverse Cumulative Distribution Function determines the original value of the randomly selected variable for the given probability value from the dataset.

By default, the data is sorted and then sent to the algorithm. Also, in the output Data tab, the resultant data appears in a sorted manner.

Properties of Inverse Cumulative Distribution Function

The available properties of the Inverse Cumulative Distribution Function are as shown in the figure given below.


The table below describes the different fields present on the Properties pane of the Inverse Cumulative Distribution Function.

Field

Description

Remark

RunIt allows you to run the node.-
ExploreIt allows you to explore the successfully executed node.-
Vertical Ellipses

The available options are

  • Run till node
  • Run from node
  • Publish as a model
  • Publish code
-

Task Name

It is the name of the task selected on the workbook canvas.

You can click the text field to edit or modify the name of the task as required.

Input Column

It allows you to select the variable to be selected as the input attribute.

  • You can select any numerical type of variable.
  • If the data contains missing values, you have to impute the missing values before using the Cumulative Distribution Function.
  • To convert the values beyond the range of 0 to 1 into the required range (between 0 to 1), you can apply the normalization technique in data scaling. (Note: Scaling operation converts the values in the range of -1 to 1.)

Distribution Type

It allows you to select the type of distribution to be applied to the data.

There are two types of Distribution to select from:

  • Continuous
  • Discrete

Distribution

It allows you to select the sub-type of the Distribution selected above.

The sub-types present in Continuous and Discrete Distribution are given in Description of Advanced Options for Distribution Type and Distribution Pairs.

Advanced


Node Configuration

It allows you to select the instance of the AWS server to provide control on the execution of a task in a workbook or workflow.

For more details, refer to Worker Node Configuration.

In the Advanced options, algorithmic parameters for ICDF also appear according to the pair of Distribution Type and Distribution selected. These parameters change according to the Distribution Type and Distribution selected.

For example, when you select the Inverse Cumulative Distribution Function node, the option for Distribution Type is Continuous and that for Distribution is Normal. In this case, the parameters that appear in the Advanced Options are Mean and Standard Deviation.

The table given below describes these two parameters.

Table: Description of Advanced Options for Continuous Distribution Type and Normal Distribution

Field

Description

Remark

Mean

It allows you to select the mean value corresponding to the normal distribution.

  • It appears by default when the Distribution Type is Continuous, and Distribution is Normal.
  • The default value for Mean is 0.0.

Standard Deviation

It allows you to select the value of standard distribution corresponding to the normal distribution.

  • It appears by default when the Distribution Type is Continuous, and Distribution is Normal.
  • The default value for Standard Deviation is 1.0.

Advanced Options

The table below gives the other parameters that appear in advanced options available for individual Distribution Types and Distribution pairs.

Distribution Type

Distribution

Parameter in Advanced Options

Description

Continuous


Chi-squared

Degrees of Freedom

  • The default value is 1.
  • You can select the minimum and maximum values (integers) as 1 and 30, respectively.

Standard Exponential

—

The applicable parameters are already configured.

Exponential

Alpha (α)

You can select any real float value greater than zero.

F-distribution

Degree of Freedom 1

  • The default value for both the Degrees of Freedom is 1.
  • You can select the minimum value as zero (0).
  • Any value above zero can be selected as the maximum value.

Degree of Freedom 2

Gamma

Alpha (α)

  • The default value is 1.
  • You can select any integer value greater than zero.

Standard Normal

—

The applicable parameters are already configured.

Normal

Mean

  • The default value is 0.0.
  • You can select any value in the range from − ∞ to ∞ (minus infinity to infinity).

Standard Deviation

  • The default value is 1.0.
  • You can select any value greater than zero.

t

Degrees of Freedom

  • The default value is 1.
  • You can select the minimum and maximum values (integers) as 1 and 30, respectively.

Standard Uniform

—

The applicable parameters are already configured.

Continuous Uniform

Lower Limit

The default value is 1.

Upper Limit

  • The default value is 2.
  • Upper limit should always be greater than lower limit value.
  • Both the upper and lower limit values lie in the range from − ∞ to ∞ (minus infinity to infinity).

Weibull_min

Shape Parameter

  • The default value is 1.
  • You can select any value greater than zero.

Weibull_max

Shape Parameter

  • The default value is 1.
  • You can select any value greater than zero.

Beta

Alpha

  • The default value is 1.
  • You can select any value greater than zero.

Beta

  • The default value is 1.
  • You can select any value greater than zero.

cauchy

—

The applicable parameters are already configured.

lognormal

Sigma

  • The default value is 1.
  • You can select any value greater than zero.

Discrete

Binomial

Number of trials

  • The default value is 10.
  • You can select the minimum value as zero (0).
  • You can select any real value greater than zero (0) as the maximum value.

Probability

  • The default value is 0.5.
  • You can select the minimum and maximum values (float) as 0 and 1, respectively.

Geometric

Probability

  • The default value is 0.5.
  • You can select the minimum and maximum values (float) as 0 and 1, respectively.

Example of Inverse Cumulative Distribution Function

Consider a dataset of Probability values for various IDs. A snippet of input data is shown in the figure given below.


The selected values for properties of the Inverse Cumulative Distribution Function are given in the table below.

Property

Value

Input Column

Probability

Distribution type

Continuous

Distribution

Exponential

Alpha

1.0

The Result page of the Inverse Cumulative Distribution Function is displayed in the figure below. The graph shows the variation in Quartile values for the probability values in the dataset.

For example, the Probability for the data point 0.7 has a Quartile value of 1.0726.


The Data page of the Inverse Cumulative Distribution Function is displayed in the figure below. It shows a snippet of the X_output values, the Quartile values, corresponding to Probability values in tabular form. By default, the values of Petal Width are sorted and arranged in an ascending order.




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