Cumulative Distribution Function

Cumulative Distribution Function

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 Cumulative Distribution Function.


Properties of Cumulative Distribution Function

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



The table below describes the different fields present on the Properties pane of the 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.

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 CDF 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 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.

Advanced Options

The table below describes these two parameters.

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.


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.

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.
  • The value for mean lies in the range from − ∞ to ∞ (minus infinity to infinity).

Standard Deviation

  • The default value is 1.0.
  • You can select any real number strictly 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.

Discrete

Bernoulli

Probability

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

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 (as any value above 0 can be selected as 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.

Hypergeometric

Population Size

  • The default value is 10.
  • You can select the minimum value as zero (0).
  • Any natural number can be selected as population size.

Number of successes

  • The default value is 5.
  • You can select the minimum value as zero (0).
  • You can select any value up to the population size as the maximum value.

Number of draws

  • The default value is 5.
  • You can select the minimum value as zero (0).
  • You can select any value up to the population size as the maximum value.

Poisson

lambda

  • The default value is 5.
  • You can select any value greater than zero as the minimum value.
  • You can select any float value (above the minimum value) as the maximum value (as any value above 0 can be selected as maximum value)

Discrete Uniform

Lower Limit

The default value is 1.

Upper Limit

The default value is 2.


Example of Cumulative Distribution Function

Consider the Iris dataset with columns of Sepal length, Sepal Width, Petal width and Species. A snippet of input data is shown in the figure below.


The selected values for properties and Advanced options for the Cumulative Distribution Function are given in the table below.

PropertyValue

Input Column

Petal Width

Distribution type

Discrete

Distribution

Binomial

Number of Trials

10

Probability

0.5

The Result page of the Cumulative Distribution Function is displayed in the figure below. The graph shows the variation in Cumulative Probability Output values for the given variable values (Petal Width) in the dataset.

For example, the Petal Width value of 1.9 has a Cumulative Probability Output value of 0.0107.


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



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