# \[ANN\]: PhaseTypeDistributions.jl, PhaseTypeDistributionsFitting.jl (and FixedSparsityMatrices.jl)
**URL:** https://discourse.julialang.org/t/ann-phasetypedistributions-jl-phasetypedistributionsfitting-jl-and-fixedsparsitymatrices-jl/137631
**Category:** Package Announcements
**Tags:** statistics, linearalgebra, matrices, probability
**Created:** [June 15, 2026, 4:58am UTC](https://discourse.julialang.org/t/ann-phasetypedistributions-jl-phasetypedistributionsfitting-jl-and-fixedsparsitymatrices-jl/137631 "2026-06-15T04:58:19Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@yoninazarathy](https://discourse.julialang.org/u/yoninazarathy)
#### Post date: [June 15, 2026, 4:58am UTC](https://discourse.julialang.org/t/ann-phasetypedistributions-jl-phasetypedistributionsfitting-jl-and-fixedsparsitymatrices-jl/137631/1 "2026-06-15T04:58:19Z")
We’re happy to announce two new packages for phase-type (PH) distributions, plus a supporting third package for structured matrices (which may be useful in its own right).
A phase-type distribution is the distribution of the time until absorption of a finite-state continuous-time Markov chain. This semi-parametric family can approximate any non-negative distribution arbitrarily well, and it appears throughout queueing theory, reliability, and survival analysis. See [Wikipedia: Phase-type distribution](https://en.wikipedia.org/wiki/Phase-type_distribution).
The packages:
- **[PhaseTypeDistributions.jl](https://github.com/Julia-Matrix-Analytic-Probability/PhaseTypeDistributions.jl)** — PH distributions (and their competing-risks generalization,
MAPH) as first-class `Distributions.jl` types: `pdf`, `cdf`, `rand`, moments, and more.
- **[PhaseTypeDistributionsFitting.jl](https://github.com/Julia-Matrix-Analytic-Probability/PhaseTypeDistributionsFitting.jl)** — maximum-likelihood fitting of PH and MAPH
distributions from data, via the EM algorithm.
- **[FixedSparsityMatrices.jl](https://github.com/yoninazarathy/FixedSparsityMatrices.jl)** – a supporting utility: dense arrays with a _fixed sparsity pattern_, so structural zeros are preserved exactly through linear-algebra operations.
Prior (not currently maintained) Julia work in this space is [EMpht.jl](https://github.com/Pat-Laub/EMpht.jl), which fits univariate PH distributions via EM.
Feedback and contributions welcome!
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### Author:  [@tp2750](https://discourse.julialang.org/u/tp2750)
#### Post date: [June 25, 2026, 10:27am UTC](https://discourse.julialang.org/t/ann-phasetypedistributions-jl-phasetypedistributionsfitting-jl-and-fixedsparsitymatrices-jl/137631/2 "2026-06-25T10:27:55Z")
Very nice. Thanks for sharing!