Distribution reference¶
One section per distribution, from nagasim/core/distributions.py's DISTRIBUTION_REGISTRY. "Arrival" / "Delay" mark whether the distribution is offered for a CREATE inter-arrival time / a delay-bearing block (get_available_distributions).
Bernoulli¶
Yes/no decisions, e.g. reject/accept, pass/fail.
Param: p (success probability) in [0, 1].
Category: special. Arrival: no. Delay: no. Support lower bound: 0.0.
| Parameter | Default | Hint |
|---|---|---|
p |
0.5 |
success probability, in [0, 1] |
Beta¶
Useful for bounded times or probabilities.
Params: alpha, beta > 0; min < max.
Category: continuous. Arrival: yes. Delay: yes. Support lower bound: 0.0. Can be fit from data as Beta (see Input analysis).
| Parameter | Default | Hint |
|---|---|---|
min |
0.0 |
lower bound, < max |
max |
1.0 |
upper bound, > min |
alpha |
1.0 |
shape, > 0 |
beta |
1.0 |
shape, > 0 |
Binomial¶
Fixed-number trials with success/failure outcomes.
Params: n (trials) >= 0, p in [0, 1].
Category: special. Arrival: no. Delay: no. Support lower bound: 0.0. Can be fit from data as Binomial (see Input analysis).
| Parameter | Default | Hint |
|---|---|---|
n |
1.0 |
number of trials, >= 0 |
p |
0.5 |
success probability, in [0, 1] |
BoundedNormal¶
Normal distribution bounded within a range; useful for processes with natural limits, such as delays.
Params: mean (central value), stddev (standard deviation) > 0; min < max.
Category: special. Arrival: no. Delay: yes. Support lower bound: 0.0.
| Parameter | Default | Hint |
|---|---|---|
mean |
0.0 |
central value |
stddev |
1.0 |
standard deviation, > 0 |
min |
0.0 |
lower bound, < max |
max |
1.0 |
upper bound, > min |
Cauchy¶
Heavy-tailed distribution for outlier-sensitive systems (rare); often returns negative values.
Params: x0 (location), gamma (scale) > 0.
Category: special. Arrival: no. Delay: no. Support lower bound: unbounded.
| Parameter | Default | Hint |
|---|---|---|
x0 |
0.0 |
location |
gamma |
1.0 |
scale, > 0 |
ChiSquare¶
Used mostly for statistical diagnostics.
Param: df (degrees of freedom) >= 1.
Category: special. Arrival: no. Delay: no. Support lower bound: 0.0.
| Parameter | Default | Hint |
|---|---|---|
df |
1.0 |
degrees of freedom, >= 1 |
Constant¶
Fixed delay or service time, commonly used for deterministic processes.
Params: value (fixed duration) >= 0.
Category: continuous. Arrival: yes. Delay: yes. Support lower bound: 0.0.
| Parameter | Default | Hint |
|---|---|---|
value |
1.0 |
fixed duration, >= 0 |
CustomExpression¶
Model expression (core/expressions.py grammar).
Param: expression (string, e.g. '2 + EXPO(3)').
Category: continuous. Arrival: yes. Delay: yes. Support lower bound: 0.0.
| Parameter | Default | Hint |
|---|---|---|
expression |
'1' |
model expression, e.g. '2 + EXPO(3)' |
DiscreteUniform¶
Equal chance of integers between bounds.
Params: low (min) <= high (max), integers.
Category: special. Arrival: no. Delay: yes. Support lower bound: 0.0. Can be fit from data as DiscreteUniform (see Input analysis).
| Parameter | Default | Hint |
|---|---|---|
low |
0.0 |
minimum integer, <= high |
high |
1.0 |
maximum integer, >= low |
EmpiricalContinuous¶
Piecewise-uniform continuous sampling from a histogram: picks a bin by weight, then draws uniformly within it (true continuous, not point resampling).
Params: values (float list of bin edges, length = len(probs) + 1), probs (bin weights summing to 1).
Category: continuous. Arrival: yes. Delay: yes. Support lower bound: 0.0.
| Parameter | Default | Hint |
|---|---|---|
values |
[0.0, 1.0] |
bin edges, length = len(probs) + 1 |
probs |
[1.0] |
bin weights, summing to 1 |
EmpiricalDiscrete¶
Samples discrete values (integers) from a list with associated probabilities.
Params: values (int list), probs (weights summing to 1).
Category: discrete. Arrival: yes. Delay: yes. Support lower bound: 0.0.
| Parameter | Default | Hint |
|---|---|---|
values |
[0] |
candidate integer values |
probs |
[1.0] |
weight per value, summing to 1 |
Erlang¶
Sum of k exponential stages (special case of gamma).
Params: k (stages) >= 1, rate (lambda) > 0.
Category: continuous. Arrival: yes. Delay: yes. Support lower bound: 0.0. Can be fit from data as Erlang (see Input analysis).
| Parameter | Default | Hint |
|---|---|---|
k |
1.0 |
number of exponential stages, >= 1 |
rate |
1.0 |
lambda, > 0 |
Exponential¶
Classic model for memoryless interarrival and failure times.
Param: rate (lambda, event rate) > 0.
Category: continuous. Arrival: yes. Delay: yes. Support lower bound: 0.0. Can be fit from data as Exponential (see Input analysis).
| Parameter | Default | Hint |
|---|---|---|
rate |
1.0 |
event rate (lambda), > 0 |
FixedSchedule¶
Step-wise time schedule for entity generation or delays.
Param: schedule (ordered list of times).
Category: continuous. Arrival: yes. Delay: no. Support lower bound: 0.0.
| Parameter | Default | Hint |
|---|---|---|
schedule |
[] |
ordered list of absolute arrival/event times |
Gamma¶
Flexible model for skewed service/process times.
Params: alpha (shape) > 0, beta (scale) > 0.
Category: continuous. Arrival: yes. Delay: yes. Support lower bound: 0.0. Can be fit from data as Gamma (see Input analysis).
| Parameter | Default | Hint |
|---|---|---|
alpha |
1.0 |
shape, > 0 |
beta |
1.0 |
scale, > 0 |
Geometric¶
Models number of trials until first success.
Param: p in (0, 1].
Category: special. Arrival: no. Delay: no. Support lower bound: 0.0. Can be fit from data as Geometric (see Input analysis).
| Parameter | Default | Hint |
|---|---|---|
p |
0.5 |
success probability, in (0, 1] |
Hypergeometric¶
Sampling without replacement (e.g., quality inspection).
Params: N (population) >= K (success states) >= n (sample) >= 0.
Category: special. Arrival: no. Delay: no. Support lower bound: 0.0.
| Parameter | Default | Hint |
|---|---|---|
N |
10.0 |
population size |
K |
5.0 |
number of success states in the population |
n |
3.0 |
sample size |
InverseGaussian¶
Used in detailed modeling of reaction/decision delays.
Params: mu (mean) > 0, lambda (shape) > 0.
Category: continuous. Arrival: yes. Delay: yes. Support lower bound: 0.0. Can be fit from data as InverseGaussian (see Input analysis).
| Parameter | Default | Hint |
|---|---|---|
mu |
1.0 |
mean, > 0 |
lambda |
1.0 |
shape, > 0 |
JohnsonSB¶
For skewed variables bounded in [min, max] (e.g., fill %).
Params: a1, a2 (shape), min < max.
Category: special. Arrival: no. Delay: no. Support lower bound: 0.0.
| Parameter | Default | Hint |
|---|---|---|
a1 |
0.0 |
shape |
a2 |
1.0 |
shape |
min |
0.0 |
lower bound, < max |
max |
1.0 |
upper bound, > min |
JohnsonSU¶
Highly flexible for skewed and kurtotic data fitting; can return negative values.
Params: a, b (shape), loc (center), scale > 0.
Category: special. Arrival: no. Delay: no. Support lower bound: unbounded.
| Parameter | Default | Hint |
|---|---|---|
a |
0.0 |
shape |
b |
1.0 |
shape |
loc |
0.0 |
center |
scale |
1.0 |
scale, > 0 |
LogLogistic¶
Heavy-tailed alternative to lognormal for skewed durations.
Params: c (shape) > 0, scale > 0.
Category: continuous. Arrival: yes. Delay: yes. Support lower bound: 0.0. Can be fit from data as LogLogistic (see Input analysis).
| Parameter | Default | Hint |
|---|---|---|
c |
1.0 |
shape, > 0 |
scale |
1.0 |
scale, > 0 |
Lognormal¶
Right-skewed times like human handling or picking durations.
Params: mu (log-mean), sigma (log-stddev) > 0.
Category: continuous. Arrival: yes. Delay: yes. Support lower bound: 0.0. Can be fit from data as Lognormal (see Input analysis).
| Parameter | Default | Hint |
|---|---|---|
mu |
0.0 |
log-mean |
sigma |
1.0 |
log-stddev, > 0 |
NegativeBinomial¶
Trials until r successes, with success chance p.
Params: r (target successes) >= 1, p in (0, 1].
Category: special. Arrival: no. Delay: no. Support lower bound: 0.0.
| Parameter | Default | Hint |
|---|---|---|
r |
1.0 |
target number of successes, >= 1 |
p |
0.5 |
success probability, in (0, 1] |
Normal¶
Models symmetric variation around a mean (e.g., repair times), can produce negative values unless mean >> 0 and .
Params: mean (central value), stddev (standard deviation) > 0.
Category: special. Arrival: no. Delay: no. Support lower bound: unbounded. Can be fit from data as Normal (see Input analysis).
| Parameter | Default | Hint |
|---|---|---|
mean |
0.0 |
central value |
stddev |
1.0 |
standard deviation, > 0 |
PearsonTypeV¶
Used for inverse-gamma-shaped delays or failures.
Params: a (shape) > 0, scale > 0.
Category: continuous. Arrival: no. Delay: yes. Support lower bound: 0.0.
| Parameter | Default | Hint |
|---|---|---|
a |
1.0 |
shape, > 0 |
scale |
1.0 |
scale, > 0 |
PearsonTypeVI¶
Ratios of gammas (e.g., cost per service); always positive. Can model time if parameters are appropriate.
Params: a, b > 0, scale > 0.
Category: continuous. Arrival: no. Delay: yes. Support lower bound: 0.0.
| Parameter | Default | Hint |
|---|---|---|
a |
1.0 |
shape, > 0 |
b |
1.0 |
shape, > 0 |
scale |
1.0 |
scale, > 0 |
Poisson¶
Number of arrivals/events in a fixed time window.
Param: lambda (average rate) > 0.
Category: discrete. Arrival: yes. Delay: yes. Support lower bound: 0.0. Can be fit from data as Poisson (see Input analysis).
| Parameter | Default | Hint |
|---|---|---|
lambda |
1.0 |
average rate, > 0 |
Rayleigh¶
Models magnitudes like movement noise or energy.
Param: sigma (scale) > 0.
Category: continuous. Arrival: yes. Delay: yes. Support lower bound: 0.0. Can be fit from data as Rayleigh (see Input analysis).
| Parameter | Default | Hint |
|---|---|---|
sigma |
1.0 |
scale, > 0 |
Triangular¶
Used with expert estimates of min, most likely, and max times.
Params: low =< mode =< high.
Category: continuous. Arrival: yes. Delay: yes. Support lower bound: 0.0. Can be fit from data as Triangular (see Input analysis).
| Parameter | Default | Hint |
|---|---|---|
low |
0.0 |
minimum, <= mode |
high |
1.0 |
maximum, >= mode |
mode |
0.5 |
most likely value, between low and high |
Uniform¶
Equal probability within a bounded range; used when only min and max are known.
Params: low (min) =< high (max), both real numbers.
Category: continuous. Arrival: yes. Delay: yes. Support lower bound: 0.0. Can be fit from data as Uniform (see Input analysis).
| Parameter | Default | Hint |
|---|---|---|
low |
0.0 |
minimum, <= high |
high |
1.0 |
maximum, >= low |
Weibull¶
Common for modeling equipment lifetimes and breakdowns.
Params: scale (lambda) > 0, shape (k) > 0.
Category: continuous. Arrival: yes. Delay: yes. Support lower bound: 0.0. Can be fit from data as Weibull (see Input analysis).
| Parameter | Default | Hint |
|---|---|---|
scale |
1.0 |
lambda, > 0 |
shape |
1.0 |
k, > 0 |