[ANN]: PhaseTypeDistributions.jl, PhaseTypeDistributionsFitting.jl (and FixedSparsityMatrices.jl)

Package Announcements
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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.

The packages:

  • PhaseTypeDistributions.jl — PH distributions (and their competing-risks generalization,
    MAPH) as first-class Distributions.jl types: pdf, cdf, rand, moments, and more.
  • PhaseTypeDistributionsFitting.jl — maximum-likelihood fitting of PH and MAPH
    distributions from data, via the EM algorithm.
  • 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, which fits univariate PH distributions via EM.

Feedback and contributions welcome!

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