Semi-Markov Process

.github/workflows/ci.yml

@@ -13,7 +13,7 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - '1.5'
+          - '1.8'
           - 'nightly'
         os:
           - ubuntu-latest

.vscode/settings.json

@@ -0,0 +1 @@
+{}

Project.toml

@@ -1,25 +1,32 @@
 name = "MultiStateSystems"
 uuid = "63dd226a-9d27-42a2-9f4c-7f7a071798e0"
 authors = ["Tom Van Acker"]
-version = "0.1.2"
+version = "0.2.0"
 
 [deps]
 AdditionalUnits = "02d9b4f0-7821-44c6-acbd-01a1ab91b72e"
-LightGraphs = "093fc24a-ae57-5d10-9952-331d41423f4d"
+Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
+Interpolations = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Measurements = "eff96d63-e80a-5855-80a2-b1b0885c5ab7"
 Multigraphs = "7ebac608-6c66-46e6-9856-b5f43e107bac"
 OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
+QuadGK = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
+SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
 
 [compat]
+AdditionalUnits = "0.1.4"
+Graphs = "1.9.0"
+Interpolations = "0.14.7"
+Measurements = "2.11.0"
+Multigraphs = "0.3.0"
+OrdinaryDiffEq = "6.58.2"
+QuadGK = "2.9.4"
+SpecialFunctions = "2.3.1"
+Unitful = "1.19.0"
 julia = "1"
-AdditionalUnits = "0.1.2"
-LightGraphs = "1.3.5"
-Measurements = "2.6.0"
-Multigraphs = "0.2.2"
-OrdinaryDiffEq = "5.59.4"
-Unitful = "1.8.0"
 
 [extras]
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

docs/src/distribution.md

@@ -11,55 +11,40 @@ it to allow for weighted distributions as well as the
 ## Distributions
 
 Each distribution has a number of constructors, both based on its full name and
-abbreviation, e.g., `Weibull()` is equivalent to `𝑾()`. Furthermore,
-additional constructors are included for limited input, where all remaining
-parameters are set to their default, e.g., `Weibull(10.0u"hr")` is equivalent
-to `Weibull(10.0u"hr",1.0,1.0)`.
+abbreviation, e.g., `Weibull()` is equivalent to `𝑾()`. The abbreviation 
+constructor is the first letter of the distribution in the `\bi` font.
+Furthermore, additional constructors are included for limited input, where all 
+remaining parameters are set to their default, e.g., `Weibull(10.0u"hr")` is 
+equivalent to `Weibull(10.0u"hr",1.0,1.0)`.
 
-All input parameters are either of the type `Number` or its subtype `Real`:
+All input parameters are either of the type `Number`, its subtype `Real` or a 
+`Function`:
 ```
 Number
  |- Unitful.Quantity, e.g., 10.0u"hr"
  |- Real
      |- AbstractFloat, e.g., 10.0
      |- Integer, e.g., 10
+Function
 ```
 
 All distributions may be scaled using a weight parameter `ω`, where
-`0.0 < ω ≤ 1.0`.
-
-### Dirac Distribution
-
-```@docs
-Dirac
-```
-
-## Uniform Distribution
-
-```@docs
-Uniform
-```
+`0.0 < ω::Real ≤ 1.0` or `0.0 < ω(t)::Fuction ≤ 1.0`.
 
 ## Exponential Distribution
 
 ```@docs
-Exponential
+MultiStateSystems.Exponential
 ```
 
 ## Weibull Distribution
 
 ```@docs
-Weibull
-```
-
-## Raised Cosine Distribution
-
-```@docs
-Cosine
+MultiStateSystems.Weibull
 ```
 
 ## LogNormal Distribution
 
 ```@docs
-LogNormal
+MultiStateSystems.LogNormal
 ```

docs/src/processes.md

@@ -4,12 +4,14 @@
 
 A number of stochastic processes are available to determine the state
 probabilities of an `std`:
-
-* Steady state process `SteadyStateProcess <: AbstractMarkovProcess`
-* Markov chain `:markov_process`
-* Markov process `:markov_process`
-* Semi-Markov process `:semimarkov_process`
-* Van Acker process `:vanacker_process`
+```
+AbstractStochasticProcess
+  |- AbstractMarkovProcess
+      |- SteadyStateProcess
+      |- MarkovProcess
+  |- AbstractSemiMarkovProcess
+      |- SemiMarkovProcess
+```
 
 Solving a stochastic process may be accomplished through:
 ```@docs
@@ -60,6 +62,19 @@ probabilities, given transition rates ρ$_{ij}$(t) and initial values δ$_{i}$:
 dp_i(t)/dt = - ∑_j ρ_{ij}(t)p_i(t) + ∑_j ρ_{ji}(t)p_j(t),  ∀ i ∈ 𝓢.
 ```
 
+## Semi-Markov Process
+
+| Spaces      |             	| Properties  |             |
+| :---------- | :-------------- | :---------- | :---------- |
+| State-space | discrete    	| Renewal     | ✅          |
+| Time-space  | continuous  	| Markov      | ❎          |
+
+A semi-Markov process is described by a random variable $X_t$, where $t$ denotes
+the calendar time. The possible values of $X_t$ are represented by the discrete
+state-space 𝓢 of the state transition diagram `std`.
+
+A semi-Markov process...
+
 ## Van Acker Process
 
 * `T. Van Acker, and D. Van Hertem (2018). Stochastic Process for the