Phase-type distribution

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Phase-type distribution topic overview

The analysis highlights Characters, Characterization and Special cases as prominent areas in the source structure around Phase-type distribution.

Related topics: 21
Source areas: 6
Connected nodes: 27
Extracted relationships: 75
Concept neighborhoods: 19
Bridge connections: 27

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Overview · 9 topics

Special cases · 4 topics

Approximating other distributions · 2 topics

Characterization · 2 topics

Definition · 2 topics

Fitting a phase type distribution to data · 2 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Key facts & relationships

High-confidence facts extracted from structured source data. Use them as anchors for further research.

CDF: 1 − α e x S 1 {\displaystyle 1-{\boldsymbol {\alpha }}e^{xS}{\boldsymbol {1}}}
CF: − α ( i t I + S ) − 1 S 0 + α 0 {\displaystyle -{\boldsymbol {\alpha }}(itI+S)^{-1}{\boldsymbol {S}}^{0}+\alpha _{0}}
Mean: − α S − 1 1 {\displaystyle -{\boldsymbol {\alpha }}{S}^{-1}\mathbf {1} }
Median: no simple closed form
MGF: − α ( t I + S ) − 1 S 0 + α 0 {\displaystyle -{\boldsymbol {\alpha }}(tI+S)^{-1}{\boldsymbol {S}}^{0}+\alpha _{0}}
Mode: no simple closed form

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Probability distribution
Exponential distributions Exponential distribution
Poisson processes Poisson process
Sequence
Stochastic process
Random variable
States Markov process
Discrete-time Discrete time
Discrete phase-type distribution

Definition

Characterization

Special cases

Approximating other distributions

Fitting a phase type distribution to data

Heavy-tailed distributions Heavy-tailed distribution
Expectation–maximization algorithm

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Phase-type distribution connects Entity context

The extracted context around Phase-type distribution shows recurring relationship patterns in the source. For example, Phase-type distribution → Algorithmic Approach, ASA SIAM, Chapter, Characterization, Communication, Communications, Dover Publications Inc, Emeritus, Florin, In Liber Amicorum Prof, Introduction, Latouche, Louvain, Matrix Analytic Methods, Matrix-Geometric Solutions, Neuts, O'Cinneide, Pages, PH Distributions, Phase Type Another extracted example is Phase-type distribution → Coxian, Degenerate, Deterministic, Erlang, Exponential, Hyperexponential, Hypoexponential, Note, The. Use these groups to spot repeated connection types before inspecting the individual relationships.

Top relations

related to References · 29

Phase-type distribution → Algorithmic Approach, ASA SIAM, Chapter, Characterization, Communication, Communications, Dover Publications Inc, Emeritus, Florin, In Liber Amicorum Prof, Introduction, Latouche, Louvain, Matrix Analytic Methods, Matrix-Geometric Solutions, Neuts, O'Cinneide, Pages, PH Distributions, Phase Type

related to Special cases · 9

Phase-type distribution → Coxian, Degenerate, Deterministic, Erlang, Exponential, Hyperexponential, Hypoexponential, Note, The

related to Approximating other distributions · 8

Phase-type distribution → Any, Approximating, BuTools, Erlang, In, Markovian, Mathematica, MATLAB

related to Fitting a phase type distribution to data · 6

Phase-type distribution → Fitting, HyperStar, It, Java, Methods, PhFit

related to Definition · 4

Phase-type distribution → Consider, Further, Markov, The

is a · 3

Phase-type distribution → distribution of time from the above process's starting until absorption in the absorbing state.This process can be written in the form of a transition rate matrix, exponential distribution of parameter λ, probability distribution constructed by a convolution or mixture of exponential distributions

related to Erlang distribution · 3

Phase-type distribution → For, The Erlang, This

see also · 2

Phase-type distribution → Discrete, Markov

CDF · 1

Phase-type distribution → 1 − α e x S 1 {\displaystyle 1-{\boldsymbol {\alpha }}e^{xS}{\boldsymbol {1}}}

CF · 1

Phase-type distribution → − α ( i t I + S ) − 1 S 0 + α 0 {\displaystyle -{\boldsymbol {\alpha }}(itI+S)^{-1}{\boldsymbol {S}}^{0}+\alpha _{0}}

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

distribution phase-type phase distributions phases type process probability erlang exponential state absorbing mixture sequence matrix fitting random stochastic time markov

Phase-type distribution relationships Subject–Predicate–Object triples

TTTA extracted 75 structured relationships around Phase-type distribution. Examples in this analysis include Phase-type distribution → CDF → 1 − α e x S 1 {\displaystyle 1-{\boldsymbol {\alpha }}e^{xS}{\boldsymbol {1}}} and Phase-type distribution → CF → − α ( i t I + S ) − 1 S 0 + α 0 {\displaystyle -{\boldsymbol {\alpha }}(itI+S)^{-1}{\boldsymbol {S}}^{0}+\alpha _{0}}. The table shows each extracted connection, where it came from and its confidence.

Subject	Predicate	Object	Confidence	Src
Phase-type distribution	CDF	1 − α e x S 1 {\displaystyle 1-{\boldsymbol {\alpha }}e^{xS}{\boldsymbol {1}}}	1.00	infobox
Phase-type distribution	CF	− α ( i t I + S ) − 1 S 0 + α 0 {\displaystyle -{\boldsymbol {\alpha }}(itI+S)^{-1}{\boldsymbol {S}}^{0}+\alpha _{0}}	1.00	infobox
Phase-type distribution	Mean	− α S − 1 1 {\displaystyle -{\boldsymbol {\alpha }}{S}^{-1}\mathbf {1} }	1.00	infobox
Phase-type distribution	Median	no simple closed form	1.00	infobox
Phase-type distribution	MGF	− α ( t I + S ) − 1 S 0 + α 0 {\displaystyle -{\boldsymbol {\alpha }}(tI+S)^{-1}{\boldsymbol {S}}^{0}+\alpha _{0}}	1.00	infobox
Phase-type distribution	Mode	no simple closed form	1.00	infobox
Phase-type distribution	Parameters	S , m × m {\displaystyle S,\;m\times m} subgenerator matrix α {\displaystyle {\boldsymbol {\alpha }}} , probability row vector	1.00	infobox
Phase-type distribution	PDF	α e x S S 0 {\displaystyle {\boldsymbol {\alpha }}e^{xS}{\boldsymbol {S}}^{0}} See article for details	1.00	infobox
Phase-type distribution	Support	x ∈ [ 0 ; ∞ ) {\displaystyle x\in [0;\infty )\!}	1.00	infobox
Phase-type distribution	Variance	2 α S − 2 1 − ( α S − 1 1 ) 2 {\displaystyle 2{\boldsymbol {\alpha }}{S}^{-2}\mathbf {1} -({\boldsymbol {\alpha }}{S}^{-1}\mathbf {1} )^{2}}	1.00	infobox
Phase-type distribution	is a	probability distribution constructed by a convolution or mixture of exponential distributions	0.90	text
Phase-type distribution	is a	distribution of time from the above process's starting until absorption in the absorbing state.This process can be written in the form of a transition rate matrix	0.90	text
Phase-type distribution	is a	exponential distribution of parameter λ	0.90	text

Related concept clusters Concept neighborhoods

The concept neighborhoods around Phase-type distribution bring nearby vocabulary together. In this analysis, examples include Phase-type, Distributions and Erlang. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

Phase-type distribution
- Phase-type
- Distributions
- Erlang
- Fitting
- Phases
- Exponential
- State
- Continuous
- Discrete
- Probability
- Distributed
- Absorbing
phase-type distribution
- Phase-type
- Distributions
- Phase
- Erlang
- Type
- Exponential
- Fitting
- State
- Phases
- Probability
- Continuous
- Discrete
probability distribution
- Phase-type
- Phase
- Erlang
- Α0
- Type
- Exponential
- State
- Zero
- Starting
- Distributions
- Phases
- Process
exponential distributions
- Mixture
- Also
- Hyperexponential
- Phase-type
- Fitting
- Variables
- Random
- Type
- Probability
- Phase
- Ph
- Distributed
stochastic process
- Markov
- Absorbing
- State
- States
- Also
- Approximating
- Form
- Vector
- Α0
- Distributed
- Ph
- Probability
discrete phase-type distribution
- Phase-type
- Distributions
- Phase
- Erlang
- Fitting
- Type
- Exponential
- Also
- Continuous
- Data
- State
- Phases
continuous-time markov process
- States
- Also
- Markov
- One
- Process
- Absorbing
- Random
- State
- Fitting
- See
- Approximating
- Form
matrix exponential
- Mixture
- Also
- Hyperexponential
- Variables
- Random
- Given
- Distributed
- Markov
- Ph
- Phase
- Erlang
- Probability

Connections between topic areas Semantic bridges

For Phase-type distribution, one of the stronger structural bridges in this analysis connects Phase-type distribution with Overview. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3

Phase-type distribution — Overview · splits 18 ⟂ 10

Phase-type distribution — Special cases · splits 23 ⟂ 5

Phase-type distribution — Definition · splits 25 ⟂ 3

Phase-type distribution — Characterization · splits 25 ⟂ 3

Phase-type distribution — Approximating other distributions · splits 25 ⟂ 3

Phase-type distribution — Fitting a phase type distribution to data · splits 25 ⟂ 3

Map overview Semantic statistics

Phase-type distribution

Nodes28

Edges27

Triples75

Avg. degree1.93

Density0.071429

Components1

Source & methodology

TTTA analyzes the structure around Phase-type distribution to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Characters, Characterization & Special cases, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Phase-type distribution · EN edition · Analysis: TopicsToTalkAbout