---
myst:
    substitutions:
        bloc:
            stocha:
                python: 6-16
                cpp: 5-15
            trunc:
                python: "18"
                cpp: "17"
        code:
            python: "addDistribution(statt, weight=1.)"
            cpp: "int addDistribution(URANIE::DataServer::TStochasticAttribute *statt, double weight=1.);"
---
```{include} /../core/dataserver/attribute/introducing_tstochastic_attribute/compose_equation.md
```

{{ uranie }} code to simulate a composition of three normally-distributed laws (with their 
own statistical properties):

{{
    "```{literalinclude} " + parent_dir 
    + "/roottest/uranie/doc/dataserver/attribute/" + language + "/compose." + extension + "\n"
    + ":language: " + language + "\n"
    + ":lines: " + bloc["stocha"][language] + "\n"
    + "```"
}}


```{include} /../core/dataserver/attribute/introducing_tstochastic_attribute/compose_figure.md
```

Is it also possible to set boundaries to the infinite span of this distribution, if it is created 
from at least one infinite-based law, to create a truncated composed law. This can be done by 
calling the following method:

{{
    "```{literalinclude} " + parent_dir 
    + "/roottest/uranie/doc/dataserver/attribute/" + language + "/compose." + extension + "\n"
    + ":language: " + language + "\n"
    + ":lines: " + bloc["trunc"][language] + "\n"
    + "```"
}}

The resulting PDF, CDF and inverse CDF, with and without truncation, can be seen, in this case, in 
{numref}`dataserver_tcompose_trunc_distribution` for a given set of parameters and various boundaries.

{{
    "```{" "figure" "} " + parent_dir +
        "/usermanual/dataserver/figures/TComposedNormalTruncatedDistribution.png\n"
    ":align: center\n"
    ":name: dataserver_tcompose_trunc_distribution\n"
    + figure_scale + "\n"
    "\n"
    "Example of PDF, CDF and inverse CDF for a truncated composed distribution made out of three 
    normal distributions with respective weights.\n"
    "```"
}}

The only specific method that is new for the composition is the `addDistribution` method whose 
signature is the following one:

{{
    "```{code} " + language + "\n"
    + code[language] + "\n"
    + "```"
}}

The first element is a pointer to a `TStochasticAttribute` (so any object that is an instance of a 
class that derives form it). The second one is the weight (which is 1 by default) and which is the 
$\omega$ constant written in the formula above.

```{warning}
The theoretical element (mean, standard deviation and mode) can not always be measured for certain 
stochastic distribution (see the Cauchy's one for instance).
- If one wants to add such a distribution in a composed law, a warning exception should pop-up to 
state that theoretical properties can not be estimated.              
- As for the mode, several distributions prevent from having a single-point mode estimation 
(for instance the Uniform distribution). The mode estimation should then be taken with great care.
```