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Sjoerd C. de Vries
Sjoerd C. de Vries
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Defining and evaluating new continuous distributiionsdistributions based on Mathematica's distributions

A number of functions operate with Mathematica's set of distributions e.g.

Through[{Mean, StandardDeviation, Variance}[UniformDistribution[{umin,umax}]]]

which returns the correct result

    {(umax + umin)/2, (umax - umin)/(2 Sqrt[3]), 1/12 (umax - umin)^2}

However, when I add two continuous distributions, thus creating a kind of annular distribution, it will not be evaluated.

Through[{Mean, StandardDeviation, Variance}[
  UniformDistribution[{umin, umax}] - 
   UniformDistribution[{\[Epsilon] umin, \[Epsilon] umax}]]]

I think I had a very good look at the Mathematica documentation but I simply could not find any indication of how to define "my own distribution".

Please note, that I know how to handle such functions, iei.e., how to calculate the Mean ... The issue of this question is, are there ways in Mathematica, I have missed, that allow me to use Mathematica's functionality on distributions with my distributions I have defined using Mathematica's distributions.

Defining and evaluating new continuous distributiions based on Mathematica's distributions

A number of functions operate with Mathematica's set of distributions e.g.

Through[{Mean, StandardDeviation, Variance}[UniformDistribution[{umin,umax}]]]

which returns the correct result

    {(umax + umin)/2, (umax - umin)/(2 Sqrt[3]), 1/12 (umax - umin)^2}

However, when I add two continuous distributions, thus creating a kind of annular distribution, it will not be evaluated.

Through[{Mean, StandardDeviation, Variance}[
  UniformDistribution[{umin, umax}] - 
   UniformDistribution[{\[Epsilon] umin, \[Epsilon] umax}]]]

I think I had a very good look at the Mathematica documentation but I simply could not find any indication of how to define "my own distribution".

Please note, that I know how to handle such functions, ie how to calculate the Mean ... The issue of this question is, are there ways in Mathematica, I have missed, that allow me to use Mathematica's functionality on distributions with my distributions I have defined using Mathematica's distributions.

Defining and evaluating new continuous distributions based on Mathematica's distributions

A number of functions operate with Mathematica's set of distributions e.g.

Through[{Mean, StandardDeviation, Variance}[UniformDistribution[{umin,umax}]]]

which returns the correct result

    {(umax + umin)/2, (umax - umin)/(2 Sqrt[3]), 1/12 (umax - umin)^2}

However, when I add two continuous distributions, thus creating a kind of annular distribution, it will not be evaluated.

Through[{Mean, StandardDeviation, Variance}[
  UniformDistribution[{umin, umax}] - 
   UniformDistribution[{\[Epsilon] umin, \[Epsilon] umax}]]]

I think I had a very good look at the Mathematica documentation but I simply could not find any indication of how to define "my own distribution".

Please note, that I know how to handle such functions, i.e., how to calculate the Mean ... The issue of this question is, are there ways in Mathematica, I have missed, that allow me to use Mathematica's functionality on distributions with my distributions I have defined using Mathematica's distributions.

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Ernst Stelzer
Ernst Stelzer
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Defining and evaluating new continuous distributiions based on Mathematica's distributions

A number of functions operate with Mathematica's set of distributions e.g.

Through[{Mean, StandardDeviation, Variance}[UniformDistribution[{umin,umax}]]]

which returns the correct result

    {(umax + umin)/2, (umax - umin)/(2 Sqrt[3]), 1/12 (umax - umin)^2}

However, when I add two continuous distributions, thus creating a kind of annular distribution, it will not be evaluated.

Through[{Mean, StandardDeviation, Variance}[
  UniformDistribution[{umin, umax}] - 
   UniformDistribution[{\[Epsilon] umin, \[Epsilon] umax}]]]

I think I had a very good look at the Mathematica documentation but I simply could not find any indication of how to define "my own distribution".

Please note, that I know how to handle such functions, ie how to calculate the Mean ... The issue of this question is, are there ways in Mathematica, I have missed, that allow me to use Mathematica's functionality on distributions with my distributions I have defined using Mathematica's distributions.