EventBasedWeightedTally

class pydsol.core.statistics.EventBasedWeightedTally(name: str)[source]

Bases: EventProducer, EventListener, WeightedTally

The EventBasedWeightedTally 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 EventBasedWeightedTally 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 EventBasedTimestampWeightedTally class and 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:

_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

__init__(name: str)[source]

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

Parameters:: name (str) – The name by which the statistics object can be identified.
Raises:: TypeError – when name is not a string

initialize()[source]: 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.

notify(event: Event)[source]

The notify method is the method that is called by the EventProducer to register an observation. The EventType for the observation should be the StatEvents.WEIGHT_DATA_EVENT and the payload should a tuple with two values (weight, value), both floats. This value will be registered by the weighted tally.

Parameters:

event (Event) – The event fired by the EventProducer to provide data to the statistic. The content of the event has to be a tuple with two values (weight, value), both floats.

Raises:

TypeError – when event is not of the type Event
ValueError – when the event’s event_type is not a WEIGHT_DATA_EVENT
TypeError – when the event’s payload is not a tuple
ValueError – when the tuple in the content does not have a length of 2
TypeError – when one of the tuple’s elements is not a number

register(weight: float, value: float)[source]

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

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

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

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