SimTally

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

Bases: EventBasedTally, SimStatisticsInterface

The SimTally receive the observations in the same way as the EventBasedTally 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 SimTally 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 SimTally 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 SimTally is a statistics object that calculates descriptive statistics for a number of observations, such as mean, variance, minimum, maximum, skewness, 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.

The mean of the SimTally is calculated with the formula:

\[\mu = \sum_{i=1}^{n} {x_{i}} / n\]

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

Example

In discrete-event simulation, the SimTally can be used to calculate statistical values for waiting times in queues, time in system of entities, processing times at a server, and throughput times of partial processes. When objects such as Servers or Entities are EventProducers, they can easily feed the EventBasedTally when their internal state changes.

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

• _sum (float) – the sum of the observation values

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

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

• _m1, _m2, _m3, _m4 (float) – the 1st to 4th moment of the 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 SimTally 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 SimTally is a a statistics object that calculates descriptive statistics for a number of observations, such as mean, variance, minimum, maximum, skewness, etc.

Given the fact that the SimTally 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 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 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.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 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 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.DATA_EVENT and the payload should be a single float. This value will be registered by the tally.

A second event to which the SimTally 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 float 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 DATA_EVENT’s payload is not a float

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

confidence_interval(alpha: float) → Tuple[float]

Return the confidence interval around the mean with the provided alpha. When fewer than two observations were registered, (NaN, NaN) is returned.

Parameters:

alpha (float) – Alpha is the significance level used to compute the confidence level. The confidence level equals \(100 * (1 - alpha)\%\), or in other words, an alpha of 0.05 indicates a 95 percent confidence level.

Returns:

The confidence interval around the mean, or (NaN, NaN) when fewer than two observations were registered.

Return type:

(float, float)

Raises:

• TypeError – when alpha is not a float

• ValueError – when alpha is not between 0 and 1, inclusive

excess_kurtosis(biased: bool = True) → float

Return the excess kurtosis of the registered data. The kurtosis value of the normal distribution is 3. The (biased) excess kurtosis is the kurtosis value shifted by -3 to be 0 for the normal distribution. The biased excess kurtosis needs three observations; if fewer observations were registered, NaN is returned.

The formula for the biased (population) excess kurtosis is:

\[ExcessKurt_{biased} = Kurt_{biased} - 3\]

The unbiased (sample) excess kurtosis is the sample-corrected value of the biased excess kurtosis. When fewer than four observations were registered, NaN is returned for the unbiased excess kurtosis. Several formulas exist to calculate the sample excess kurtosis from the biased excess kurtosis. Here we use:

\[ExcessKurt_{unbiased} = \frac{n - 1}{(n - 2) (n - 3)} \left( (n + 1) ExcessKurt_{biased} + 6 \right)\]

This is the excess kurtosis that is calculated by, for instance, SAS, SPSS and Excel.

Parameters:

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

Returns:

The excess kurtosis of all observations since the initialization, or NaN when too few observations were registered.

Return type:

float

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.

kurtosis(biased: bool = True) → float

Return the kurtosis of all observations since the statistic initialization. The biased (sample) kurtosis calculation needs three observations, and the unbiased (population) calculation needs four observations. When too few observations were registered, NaN is returned.

The formula for the biased (population) kurtosis is:

\[kurt_{biased} = \frac{\sum{(x_{i} - \mu)^4}}{n.\sigma^4}\]

where \(\sigma^2\) is the population variance. So the denominator is equal to \(n . pop\_var^2\).

The formula for the unbiased (sample) kurtosis is:

\[kurt_{unbiased} = \frac{\sum{(x_{i} - \mu)^4}}{(n-1).S^4}\]

where \(S^2\) is the sample variance. So the denominator is equal to \((n - 1) . sample\_var^2\).

Parameters:

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

Returns:

The kurtosis of all observations since the initialization, or NaN when too few observations were registered.

Return type:

float

max() → float

Return the 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

mean() → float

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

The mean of the Tally is calculated with the formula:

\[\mu = \sum_{i=1}^{n} {x_{i}} / n\]

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

Returns:

The mean, or NaN when no observations were registered.

Return type:

float

min() → float

Return the 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

Return the name of this statistics object.

Returns:

The name of this statistics object.

Return type:

str

register(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 records a single observation value, and calculate all statistics up to and including the last value (mean, standard deviation, minimum, maximum, skewness, etc.).

Parameters:

value (float) – The value of the observation.

Raises:

• TypeError – when value is not a number

• ValueError – when value is NaN

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 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.

skewness(biased: bool = True) → float

Return the skewness of all observations since the statistic initialization. For the biased (population) skewness, at least two observations are needed; for the unbiased (sample) skewness, at least three observations are needed. If there are too few observations, NaN is returned. The method returns the biased (population) skewness as the default.

The formula for the biased (population) skewness is:

\[Skew_{biased} = \frac{ \sum{(x_{i} - \mu)^3} }{n . \sigma^3}\]

where \(\sigma^2\) is the biased (population) variance. So the denominator is equal to \(n . population\_var^{3/2}\).

There are different formulas to calculate the unbiased (sample) skewness from the biased (population) skewness. Minitab, for instance calculates unbiased skewness as:

\[Skew_{unbiased} = Skew_{biased} {\left( \frac{n - 1}{n} \right)} ^{3/2}\]

whereas SAS, SPSS and Excel calculate it as:

\[Skew_{unbiased} = Skew_{biased} \sqrt{\frac{n (n - 1)}{n - 2} }\]

Here we follow the last mentioned formula. All formulas converge to the same value with larger n.

Parameters:

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

Returns:

The skewness of all observations since the initialization, or NaN when too few observations were registered.

Return type:

float

stdev(biased: bool = True) → float

Return the standard deviation of all observations since the initialization. The sample standard deviation is defined as the square root of the variance. The biased standard deviation needs at least 1 observation, the unbiased version needs at least 2.

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

\[\sigma = \sqrt{ {\frac{1}{n}} \left( \sum{x_{i}^2} - \left( \sum{x_{i}} \right)^2 / n \right) }\]

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

\[S = \sqrt{ {\frac{1}{n - 1}} \left( \sum{x_{i}^2} - \left( \sum{x_{i}} \right)^2 / n \right) }\]

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 (unbiased) sample standard deviation of all observations since the initialization, or NaN when not enough observations were registered.

Return type:

float

sum() → float

Return the sum of all observations since the statistic initialization.

Returns:

The sum of the observations.

Return type:

float

variance(biased: bool = True) → float

Return the variance of all observations since the statistic initialization. By default, the biased (population) variance is returned. The biased variance needs at least 1 observation, the unbiased variance needs at least 2.

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

\[\sigma^2 = { {\frac{1}{n}} \left( \sum{x_{i}^2} - \left( \sum{x_{i}} \right)^2 / n \right) }\]

The formula for the unbiased (or sample) variance is:

\[S^2 = { {\frac{1}{n-1}} \left( \sum{x_{i}^2} - \left( \sum{x_{i}} \right)^2 / n \right) }\]

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 biassed or unbiased variance of all observations since the initialization, or NaN when too few observations were registered.

Return type:

float