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Added remaining tables
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Tracy committed Oct 25, 2023
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63 changes: 62 additions & 1 deletion docs/Users_Guide/difficulty_index.rst
Original file line number Diff line number Diff line change
Expand Up @@ -74,9 +74,10 @@ When :math:`\bar{x}` is close to but slightly below the threshold (e.g. between
almost all combinations of probability of exceedance and spread deserve a look, and all values of the
difficulty index for medium and large spread are difficult or nearly difficult.

.. list-table:: Table 1: Example of an obviously easy forecast. :math:`\bar{x}` is very large (e.g. 48 kt) or very small (e.g. 7kt), making :math:`A/2=0.1/2=0.05`.
.. list-table:: Example of an easy forecast where :math:`\bar{x}` is very large (e.g. 48 kt) or very small (e.g. 7kt), making :math:`A/2=0.1/2=0.05`.
:widths: auto
:header-rows: 1
:header-columns: 1

* -
- Small Spread
Expand All @@ -102,3 +103,63 @@ difficulty index for medium and large spread are difficult or nearly difficult.
- 0.05*(0.01+0.5) = 0.026
- 0.05*(0.5+0.5) = 0.05
- 0.05*(1+0.5) = 0.075

.. list-table:: Example of a forecast that could be difficult if the conditions are right, where :math:`\bar{x}` is moderately close to the threshold (e.g. 25kt or 37kt), making :math:`A/2=1/2=0.5`.
:widths: auto
:header-rows: 1
:header-columns: 1

* -
- Small Spread
- Medium Spread
- Large Spread
* - 1
- 0.5*(0.01+0.5) = 0.26
- 0.5*(0.5+0.5) = 0.5
- 0.5*(1+0.5) = 0.75
* - 0.75
- 0.5*(0.01+0.75) = 0.38
- 0.5*(0.5+0.75) = 0.63
- 0.5*(1+0.75) = 0.88
* - 0.5
- 0.5*(0.01+1) = 0.51
- 0.5*(0.5+1) = 0.75
- 0.5*(1+1) = 1.0
* - 0.25
- 0.5*(0.01+0.75) = 0.38
- 0.5*(0.5+0.75) = 0.63
- 0.5*(1+0.75) = 0.88
* - 0
- 0.5*(0.01+0.5) = 0.26
- 0.5*(0.5+0.5) = 0.5
- 0.5*(1+0.5) = 0.75

.. list-table:: Example of a situation that is almost always difficult, where :math:`\bar{x}` is at or slightly below the threshold (e.g. 28kt to 34kt), making :math:`A/2=1.5/2=0.75`.
:widths: auto
:header-rows: 1
:header-columns: 1

* -
- Small Spread
- Medium Spread
- Large Spread
* - 1
- 0.75*(0.01+0.5) = 0.38
- 0.75*(0.5+0.5) = 0.75
- 0.75*(1+0.5) = 1.13
* - 0.75
- 0.75*(0.01+0.75) = 0.57
- 0.75*(0.5+0.75) = 0.94
- 0.75*(1+0.75) = 1.31
* - 0.5
- 0.75*(0.01+1) = 0.76
- 0.75*(0.5+1) = 1.13
- 0.75*(1+1) = 1.5
* - 0.25
- 0.75*(0.01+0.75) = 0.57
- 0.75*(0.5+0.75) = 0.94
- 0.75*(1+0.75) = 1.31
* - 0
- 0.75*(0.01+0.5) = 0.38
- 0.75*(0.5+0.5) = 0.75
- 0.75*(1+0.5) = 1.13

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