SliceDistribution [proc,t]
represents the distribution of the process state at time t.
SliceDistribution [proc,{t1,…,tk}]
represents the joint distribution of process states at times t1<⋯<tk.
SliceDistribution
SliceDistribution [proc,t]
represents the distribution of the process state at time t.
SliceDistribution [proc,{t1,…,tk}]
represents the joint distribution of process states at times t1<⋯<tk.
Details
- SliceDistribution [proc,t] can be entered as proc[t].
- SliceDistribution [proc,{t1,…,tk}] can be entered as proc[{t1,…,tk}].
- For a random process xproc, its state at time t is a random variable x[t]proc[t], and its state at times t1, …, tk is a random variable {x[t1],…,x[tk]}proc[{t1,…,tk}].
- SliceDistribution will simplify to known special distributions whenever possible.
- SliceDistribution can be used with such functions as Mean , CDF , and RandomVariate , etc.
Examples
open all close allBasic Examples (3)
Find a univariate slice distribution of a PoissonProcess :
Find a bivariate slice distribution of a WienerProcess :
Find a multivariate slice distribution of a moving-average time series:
It does not autoevaluate but behaves like a distribution:
Scope (3)
Slice distribution behaves like a distribution:
Probability density function:
Characteristic function:
Moments:
Generate a set of pseudorandom numbers:
Slice distribution may autoevaluate to known distributions:
Slice distribution for an M/M/ queue:
Probability density function:
Cumulative distribution function:
Mean of the slice distribution:
Find the limit of the mean as t approaches :
This agrees with the mean of the corresponding StationaryDistribution :
As well as the mean system size in the steady state:
Properties & Relations (2)
Slice distribution at infinity is StationaryDistribution :
Use implicit times for computing probabilities:
Obtain the same result using the slice distribution:
Compute an expectation using implicit time in the variable x[t]:
Obtain the same result using the slice distribution:
Possible Issues (1)
For some continuous-time random processes, simulation of a slice distribution is not well defined:
The process path simulation between the origin and the end time depends on the choice of step:
The slice distribution simulations for a few step choices show the approximations of the exact slice distribution:
History
Text
Wolfram Research (2012), SliceDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/SliceDistribution.html.
CMS
Wolfram Language. 2012. "SliceDistribution." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SliceDistribution.html.
APA
Wolfram Language. (2012). SliceDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SliceDistribution.html
BibTeX
@misc{reference.wolfram_2025_slicedistribution, author="Wolfram Research", title="{SliceDistribution}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/SliceDistribution.html}", note=[Accessed: 05-December-2025]}
BibLaTeX
@online{reference.wolfram_2025_slicedistribution, organization={Wolfram Research}, title={SliceDistribution}, year={2012}, url={https://reference.wolfram.com/language/ref/SliceDistribution.html}, note=[Accessed: 05-December-2025]}