# openskill.models.weng_lin.common¶

Common functions for the Weng-Lin models.

## Module Contents¶

### Functions¶

 _ladder_pairs(teams) Returns a list of pairs of ranks that are adjacent in the ladder. _unwind(tenet, objects) Retain the stochastic tenet of a sort to revert original sort order. Normal cumulative distribution function. Normal inverse cumulative distribution function. Normal probability density function. v(x, t) The function $$V$$ as defined in Weng and Lin  vt(x, t) The function $$\tilde{V}$$ as defined in Weng and Lin  w(x, t) The function $$W$$ as defined in Weng and Lin  wt(x, t) The function $$\tilde{W}$$ as defined in Weng and Lin 

Returns a list of pairs of ranks that are adjacent in the ladder.

Parameters:

teams (List[Any]) – A list of teams.

Returns:

A list of pairs of teams that are adjacent in the ladder.

Return type:

List[List[Any]]

openskill.models.weng_lin.common._unwind(tenet, objects)[source]

Retain the stochastic tenet of a sort to revert original sort order.

Parameters:
• tenet (List[Union[int, float]]) – A list of tenets for each object in the list.

• objects (List[Any]) – A list of teams to sort.

Returns:

Ordered objects and their tenets.

Return type:

Tuple[List[Any], List[Union[int, float]]]

openskill.models.weng_lin.common.phi_major(x)[source]

Normal cumulative distribution function.

Parameters:

x (Union[int, float]) – A number.

Returns:

A number.

Return type:

float

openskill.models.weng_lin.common.phi_major_inverse(x)[source]

Normal inverse cumulative distribution function.

Parameters:

x (Union[int, float]) – A number.

Returns:

A number.

Return type:

float

openskill.models.weng_lin.common.phi_minor(x)[source]

Normal probability density function.

Parameters:

x (Union[int, float]) – A number.

Returns:

A number.

Return type:

float

openskill.models.weng_lin.common.v(x, t)[source]

The function $$V$$ as defined in Weng and Lin 

Parameters:
Returns:

A number.

Return type:

float

openskill.models.weng_lin.common.vt(x, t)[source]

The function $$\tilde{V}$$ as defined in Weng and Lin 

Parameters:
Returns:

A number.

Return type:

float

openskill.models.weng_lin.common.w(x, t)[source]

The function $$W$$ as defined in Weng and Lin 

Parameters:
Returns:

A number.

Return type:

float

openskill.models.weng_lin.common.wt(x, t)[source]

The function $$\tilde{W}$$ as defined in Weng and Lin 

Parameters:
Returns:

A number.

Return type:

float