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lines 5-138 of file: xrst/table/density_table.xrst
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{xrst_begin density_table}
{xrst_spell
  cen
  nonsmooth
}

The Density Table
#################

Discussion
**********
The ``density`` table is used to identify densities.
It has the following columns:

density_id
**********
This column has type ``integer``
and is the primary key for this table.
Its initial value is zero, and it increments by one for each row.

density_name
************
This column has type ``text`` .
This column is unique; i.e., each name can only appear ones in this table.
All of the *density_id* values that appear in the
:ref:`prior<prior_table@density_id>` and
:ref:`data<data_table@density_id>` tables
must appear in the density table.
Below is a list of the possible density names
with a link to the corresponding meaning:

uniform
=======
:ref:`statistic@Log-Density Function, D@Uniform`

binomial
========
:ref:`statistic@Log-Density Function, D@Binomial` .
This density is special because it can only be used in the data table.
The data table :ref:`data_table@meas_std` must be null and the
:ref:`data_table@sample_size` must not be null.

.. csv-table:: Binomial Notation
    :widths: auto

    :math:`n`,:ref:`data_table@sample_size` in the data table
    :math:`k`,counts in a binomial sample (need not be an integer)
    :math:`y=k/n`,:ref:`data_table@meas_value` in the data table
    :math:`\mu`,:ref:`average integrand<avg_integrand-name>` is model mean for y.
    :math:`\sqrt{\mu / n}`,approximation used for meas_value standard deviation

gaussian
========
:ref:`statistic@Log-Density Function, D@Gaussian`

cen_gaussian
============
:ref:`statistic@Log-Density Function, D@Censored Gaussian`

log_gaussian
============
:ref:`statistic@Log-Density Function, D@Log-Gaussian`

cen_log_gaussian
================
:ref:`statistic@Log-Density Function, D@Censored Log-Gaussian`

laplace
=======
:ref:`statistic@Log-Density Function, D@Laplace`

cen_laplace
===========
:ref:`statistic@Log-Density Function, D@Censored Laplace`

log_laplace
===========
:ref:`statistic@Log-Density Function, D@Log-Laplace`

cen_log_laplace
===============
:ref:`statistic@Log-Density Function, D@Censored Log-Laplace`

students
========
:ref:`statistic@Log-Density Function, D@Student's-t`

log_students
============
:ref:`statistic@Log-Density Function, D@Log-Student's-t`

Notation
********

Linear
======
We refer to the following densities as linear:
``gaussian`` ,
``cen_gaussian`` ,
``laplace`` ,
``cen_laplace`` ,
``students`` .

Censored
========
We refer to the following densities as censored:
``cen_gaussian`` ,
``cen_log_gaussian`` ,
``cen_laplace`` ,
``cen_log_laplace`` .

Log Scaled
==========
We refer to the following densities as log scaled:
``log_gaussian`` ,
``cen_log_laplace`` ,
``log_laplace`` ,
``log_students`` .

Nonsmooth
=========
We refer to the following densities as nonsmooth:
``laplace`` ,
``cen_laplace`` ,
``log_laplace`` .
{xrst_toc_hidden
    example/table/density_table.py
}
Example
*******
The file :ref:`density_table.py-name`
contains an example ``density`` table.

{xrst_end density_table}