---
title: "Method 4"
canonical: "https://modelassist.epixanalytics.com/space/EA/26575276/Method%204"
format: markdown
---
# **Create a distribution from a set of points on a curve**

####  

#### Situation

We have a set of co-ordinates that we wish to use to construct a distribution:

  


1. {x, f(x)} for a continuous distribution where f(x) is (or is proportional to) the probability density at value x;

2. {x, F(x)} a continuous distribution where F(x) is the cumulative probability (P(X<=x)) at value x; or

3. {x, p(x)} for a discrete distribution where p(x) is (or is proportional to) the probability of value x.

#### Uses

There are many uses of this technique. For example:

  


- Converting the results of a [constructed Bayesian inference](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575383/) calculation into a distribution; or
- Constructing a [spliced](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575624/) or [mixed](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26574993/) distribution by averaging, or manipulating probability density functions for the component distributions; or
- knowing the [pdf](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26574888/) or [pmf](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26574887/) of a specific distribution not available in your software

  


#### Application

We can use the same techniques as explained in [Method 3](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575275/) to create distributions from a set of points:

  


If the data set is of the form of {x, f(x)}, we can use a [General distribution](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575232)

If the data set is of the form {x, F(x)}, we can use the [Cumulative distribution](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575222) 

If the data set is of the form {x, p(x)}, we can use the <u>[Discrete distribution](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575205/)</u>

  


The {x} values must be in ascending order for the General and Cumulative distribution because they construct a distribution shape. For the Discrete distribution this is unnecessary because it is simply a list of values.

  


  


  


  


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