SimWeightedTally

class pydsol.core.statistics.SimWeightedTally(key: str, name: str, simulator: SimulatorInterface, *, producer: EventProducer | None = None, event_type: EventType | None = None)

Bases: EventBasedWeightedTally, SimStatisticsInterface

The SimWeightedTally receive the observations in the same way as the EventBasedWeigtedTally statistics class, but this class is also aware of the Simulator. This means they can (a) subscribe to the Simulator’s WARMUP_EVENT taking care that the statistics are initialized appropriately, and (b) register themselves as output statistics in the model. The SimWeightedTally can immediately register itself with an EventProducer for a certain EventType in the model, that will generate the data for the statistics object. The EventProducer and EventTypes to listen to can also be added later with the listen_to method.

The SimWeightedTally can receive its observations by subscribing (listening) to one or more EventProducers that provides the values for the statistic using the EventProducer’s fire(…) method. This way, the statistic gathering and processing is decoupled from the process in the simulation that generates the data: there can be zero, one, or many statistics listeners for each data producing object in the simulation.

This event-based statistic object also fire events with the values of the calculated statistics values, so a GUI-element such as a graph or table can subscribe to this event-based statistics object and be automatically updated when values of the statistic change. Again, this provides decoupling and flexibility where on beforehand it is not known whether zero, one, or many (graphics or simulation) objects are interested in the values that this statistics object calculates.

The SimWeightedTally is a statistics object that calculates descriptive statistics for weighted observations, such as weighted mean, weighted variance, minimum observation, maximum observation, etc.

The initialize() method resets the statistics object. The initialize method can, for instance, be called when the warmup period of the simulation experiment has completed.

In a sense, the weighted tally can be seen as a normal Tally where the observations are multiplied by their weights. But instead of dividing by the number of observations to calculate the mean, the sum of weights times observations is divided by the sum of the weights. Note that when the weights are all set to 1, the WeghtedTally reduces to the ordinary Tally.

Example

In discrete-event simulation, the (event based) WeightedTally is often used with elapsed time as the weights (See the ‘SimPersistent’ class later in this module). This creates a time-weighted statistic that can for instance be used to calculate statistics for (average) queue length, or (average) utilization of a server.

Attributes:

• _key (str) – the key by which the statistics object can be easily found

• _name (str) – the name by which the statistics object can be identified

• _n (int) – the number of observations

• _n_nonzero (int) – the number of non-zero weights

• _sum_of_weights (float) – the sum of the weights

• _weighted_sum (float) – the sum of the observation values times their weights

• _weight_times_variance (float) – the weighted variant of the second moment of the statistic

• _min (float) – the lowest value in the current observations

• _max (float) – the highest value in the current observations

• _simulator (SimulatorInterface) – the simulator

• _event_types (set[EventType]) – the event types from EventProducers to listen to

__init__(key: str, name: str, simulator: SimulatorInterface, *, producer: EventProducer | None = None, event_type: EventType | None = None)

This event-based statistic object also fire events with the values of the calculated statistics values, so a GUI-element such as a graph or table can subscribe to this event-based statistics object and be automatically updated when values of the statistic change. Again, this provides decoupling and flexibility where on beforehand it is not known whether zero, one, or many (graphics or simulation) objects are interested in the values that this statistics object calculates.

The SimWeightedTally statistic object also fire events with the values of the calculated statistics values, so a GUI-element such as a graph or table can subscribe to this event-based statistics object and be automatically updated when values of the statistic change. Again, this provides decoupling and flexibility where on beforehand it is not known whether zero, one, or many (graphics or simulation) objects are interested in the values that this statistics object calculates.

The SimWeightedTally is a a statistics object that calculates descriptive statistics for a number of observations, such as mean, variance, minimum, maximum, sum, etc.

Given the fact that the SimWeightedTally is linked to the Simulator, it is subscribed to the WARMUP_EVENT of the Simulator to initialize the statistics.

Parameters:

• key (str) – The key by which the statistics object can be easily found.

• name (str) – A descriptive name by which the statistics object can be identified.

• simulator (SimulatorInterface) – The simulator for subscribing to the WARMUP_EVENT and accessing the Model to register this output statistic.

• producer (EventProducer (optional)) – A class (often a simulation object such as a Server-type object, a Queue, or an Entity) that extends EventProducer, and is able to fire WEIGHT_DATA_EVENT to its listeners. This statistics object registers itself with the event producer for the specified event_type.

• event_type (EventType (optional)) – The EventType that indicates the type of event we are interested in. By default use the WEIGHT_DATA_EVENT, but when the notify-method is changed to also receive other types of events, the listen_to method can of course also register for these event-types, possibly with a different payload, as well.

Raises:

• TypeError – when key is not a string

• TypeError – when name is not a string

• TypeError – when simulator is not of type SimulatorInterface

• TypeError – if producer is not None, but it is not an EventProducer

• TypeError – if event_type is not None, but it is not an EventType

listen_to(producer: ~pydsol.core.pubsub.EventProducer, event_type: ~pydsol.core.pubsub.EventType = EventType[StatEvents.WEIGHT_DATA_EVENT metadata={self._metadata}])

The statistics objects can register themselves with an EventProducer for a certain EventType in the model, that will generate the data for the statistics object. it is possible to call listen_to multiple time. In that case, the events from all EventProducers where this statistics object is registered, will be processed.

Sending the events with observations is done by the EventProducer’s fire(…) method. This way, the statistic gathering and processing is decoupled from the process in the simulation that generates the data: there can be zero, one, or many statistics listeners for each data producing object in the simulation.

Parameters:

• producer (EventProducer) – A class (often a simulation object such as a Server-type object, a Queue, or an Entity) that extends EventProducer, and is able to fire WEIGHT_DATA_EVENT to its listeners. This statistics object registers itself with the event producer for the specified event_type.

• event_type (EventType) – The EventType that indicates the type of event we are interested in. By default it is the WEIGHT_DATA_EVENT, but when the notify-method is changed to also receive other types of events, the listen_to method can of course also register for these event-types as well.

Raises:

• TypeError – if producer is not an EventProducer

• TypeError – if event_type is not an EventType

property key: str

Return the key by which the statistics object can be easily found.

Returns:

The key by which the statistics object can be easily found.

Return type:

str

property simulator: SimulatorInterface

Return the simulator. The statistic listens to the Simulator for the WARMUP-event.

Returns:

An instance to the simulator to which this statistic is linked.

Return type:

SimulatorInterface

notify(event: Event)

The notify method is the method that is called by EventProducer where this object was added as a listener to register an observation. The EventType for the observation should typically be the StatEvents.WEIGHT_DATA_EVENT and the payload should be a tuple with a float for the weight and a float for the value. The weight-value combination will be registered by the statistic.

A second event to which the SimWeightedTally listens automatically is the WARMUP_EVENT as fired by the Simulator. When that event is received, the statistics are initialized.

Other events are silently skipped.

Parameters:

event (Event) – (1) The event fired by the EventProducer to provide data to the statistic. The event’s content should be a single int with the value. (2) The WARMUP_EVENT as fired by the Simulator. This event has no payload.

Raises:

• TypeError – when event is not of the type Event

• ValueError – when the WEIGHT_DATA_EVENT’s payload is not a tuple

• ValueError – when the WEIGHT_DATA_EVENT’s tuple in the content does not have a length of 2

• TypeError – when one of the WEIGHT_DATA_EVENT’s elements in the tuple is not a number

add_listener(event_type: EventType, listener: EventListener)

Add an EventListener to this EventProducer for a given EventType. If the listener already is registered for this EventType, this will be ignored.

Parameters:

• event_type (EventType) – the EventType for which this listener subscribes

• listener (EventListener) – the subscriber to register for the provided Eventtype

Raises:

EventError – if any of the arguments is of the wrong type

has_listeners() → bool

indicate whether this producer has any listeners or not

initialize()

Initialize the statistics object, resetting all values to the state where no observations have been made. This method can, for instance, be called when the warmup period of the simulation experiment has completed.

max() → float

Return the (unweighted) observation with the highest value. When no observations were registered, NaN is returned.

Returns:

The observation with the highest value, or NaN when no observations were registered.

Return type:

float

min() → float

Return the (unweighted) observation with the lowest value. When no observations were registered, NaN is returned.

Returns:

The observation with the lowest value, or NaN when no observations were registered.

Return type:

float

n() → int

Return the number of observations.

Returns:

The number of observations.

Return type:

int

property name: str

Return the name of this statistics object.

Returns:

The name of this statistics object.

Return type:

str

register(weight: float, value: float)

The event-based classes still have a register method. This method is called by the notify method, but can also be called separately. The method processes one observation.

The method processes one observation value and a corresponding weight, and calculate all statistics up to and including the last weight-value pair (mean, standard deviation, minimum, maximum, sum, etc.). Weight has to be >= 0.

Note

When weight equals zero, the value is counted towards the number of observations, and for the minimum and maximum observation value, but it does not contribute to the other statistics.

Parameters:

• weight (float) – The weight of this observation (has to be >= 0).

• value (float) – The value of the observation.

Raises:

• TypeError – when weight or value is not a number

• ValueError – when weight or value is NaN

• ValueError – when weight < 0

remove_all_listeners(event_type: EventType | None = None, listener: EventListener | None = None)

Remove an EventListener (if given) for a provided EventType (if given) for this EventProducer. It is no problem if there are no matches. There are four situations:

event_type == None and listener == None

all listeners for all event types are removed

event_type == None and listener is specified

the listener is removed for any event for which it was registered

event_type is specified and listener == None

all listeners are removed for the given event_type

event_type and listener are both specified

the listener for the given event type is removed, if it was registered; in essence this is the same as remove_listener

Parameters:

• event_type (EventType, optional) – the EventType for which this listener unsubscribes

• listener (EventListener, optional) – the subscriber to remove for the provided EventType

Raises:

EventError – if any of the arguments is of the wrong type

remove_listener(event_type: EventType, listener: EventListener)

Remove an EventListener of this EventProducer for a given EventType. If the listener is not registered for this EventType, this will be ignored.

Parameters:

• event_type (EventType) – the EventType for which this listener unsubscribes

• listener (EventListener) – the subscriber to remove for the provided Eventtype

Raises:

EventError – if any of the arguments is of the wrong type

classmethod report_footer() → str

Return a string representing a footer for a textual table with a monospaced font that can contain multiple tallies.

classmethod report_header() → str

Return a string representing a header for a textual table with a monospaced font that can contain multiple weighted tallies.

report_line() → str

Return a string representing a line with important statistics values for this tally, for a textual table with a monospaced font that can contain multiple tallies.

weighted_mean() → float

Return the weighted mean. When no observations were registered, NaN is returned.

The weighted mean of the WeightedTally is calculated with the formula:

\[\mu_{W} = \frac{\sum_{i=1}^{n} w_{i}.x_{i}}{\sum_{i=1}^{n} w_{i}}\]

where n is the number of observations, \(w_{i}\) are the weights, and \(x_{i}\) are the observations.

Returns:

The weighted mean, or NaN when no observations were registered.

Return type:

float

weighted_stdev(biased: bool = True) → float

Return the (biased) weighted population standard deviation of all observations since the statistic initialization. The biased version needs at least one observation. For the unbiased version, two observations are needed. When too few observations were registered, NaN is returned.

The formula for the biased (population) weighted standard deviation is:

\[\sigma_{W} = \sqrt{ \frac{\sum_{i=1}^{n}{w_i (x_i - \mu_{W})^2}} {\sum_{i=1}^{n}{w_i}} }\]

where \(w_i\) are the weights, \(x_i\) are the observations, \(n\) is the number of observations, and \(\mu_W\) is the weighted mean of the observations.

For the unbiased (sample) weighted variance (and, hence, for the standard deviation), different algorithms are suggested by the literature. As an example, R and MATLAB calculate weighted sample variance differently. SPSS rounds the sum of weights to the nearest integer and counts that as the ‘sample size’ in the unbiased formula. When weights are used as so-called reliability weights (non-integer) rather than as frequency weights (integer), rounding to the nearest integer and using that to calculate a ‘sample size’ is obviously incorrect. See the discussion at https://en.wikipedia.org/wiki/Weighted_arithmetic_mean#Weighted_sample_variance and at https://stats.stackexchange.com/questions/51442/weighted-variance-one-more-time. Here we have chosen to implement the version that uses reliability weights. The reason is that the weights in simulation study are most usually time intervals that can be on any (non-integer) scale.

The formula used for the unbiased (sample) weighted standard deviation is:

\[S_{W} = \sqrt{ \frac{M}{M - 1} . \sigma^2_{W} }\]

or as a complete formula:

\[S_{W} = \sqrt{ \frac{M}{M - 1} . \frac{\sum_{i=1}^{n}{w_i (x_i - \mu_{W})^2}} {\sum_{i=1}^{n}{w_i}} }\]

where \(w_i\) are the weights, \(x_i\) are the observations, \(n\) is the number of observations, \(M\) is the number of non-zero observations, and \(\mu_W\) is the weighted mean of the observations.

Parameters:

biased (bool) – Whether to return the biased (population) standard deviation or the unbiased (sample) standard deviation. By default, biased is True and the population standard deviation is returned.

Returns:

The weighted standard deviation of all observations since the initialization, or NaN when too few (non-zero) observations were registered.

Return type:

float

weighted_sum() → float

Return the sum of all observations times their weights since the statistic initialization.

Returns:

The sum of the observations times their weights.

Return type:

float

weighted_variance(biased: bool = True) → float

Return the weighted population variance of all observations since the statistic initialization. The biased version needs at least one observation. For the unbiased version, two observations with non-zero weights are needed. When too few observations were registered, NaN is returned.

The formula for the biased (population) weighted variance is:

\[\sigma^{2}_{W} = \frac{\sum_{i=1}^{n}{w_i (x_i - \mu_{W})^2}} {\sum_{i=1}^{n}{w_i}}\]

where \(w_i\) are the weights, \(x_i\) are the observations, \(n\) is the number of observations, and \(\mu_W\) is the weighted mean of the observations.

For the unbiased (sample) weighted variance, different algorithms are suggested by the literature. As an example, R and MATLAB calculate weighted sample variance differently. SPSS rounds the sum of weights to the nearest integer and counts that as the ‘sample size’ in the unbiased formula. When weights are used as so-called reliability weights (non-integer) rather than as frequency weights (integer), rounding to the nearest integer and using that to calculate a ‘sample size’ is obviously incorrect. See the discussion at https://en.wikipedia.org/wiki/Weighted_arithmetic_mean#Weighted_sample_variance and at https://stats.stackexchange.com/questions/51442/weighted-variance-one-more-time. Here we have chosen to implement the version that uses reliability weights. The reason is that the weights in simulation study are most usually time intervals that can be on any (non-integer) scale.

The formula used for the unbiased (sample) weighted variance is:

\[S^{2}_{W} = \frac{M}{M - 1} . \sigma^2_{W}\]

or as a complete formula:

\[S^{2}_{W} = \frac{M}{M - 1} . \frac{\sum_{i=1}^{n}{w_i (x_i-\mu_{W})^2}} {\sum_{i=1}^{n}{w_i}}\]

where \(w_i\) are the weights, \(x_i\) are the observations, \(n\) is the number of observations, \(M\) is the number of non-zero observations, and \(\mu_W\) is the weighted mean of the observations.

Parameters:

biased (bool) – Whether to return the biased (population) variance or the unbiased (sample) variance. By default, biased is True and the population variance is returned.

Returns:

The weighted variance of all observations since the initialization, or NaN when too few (non-zero) observations were registered.

Return type:

float