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zeroinflatedlikelihoods.jl's Introduction

DEPRECATED in favor of ZeroInflatedDistributions.jl!

ZeroInflatedDistributions

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This package defines zero-inflated distributions. It is still under development and has a bias toward non-negative continuous observations with many exact zeros. That said, there is (probably) nothing stopping this being used for e.g. a zero-inflated Poisson distribution, but this is not currently tested. Link functions used for defining models with two processes that jointly model probability of encounter and positive rate are also defined.

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Release notes:

First release; basic functionality including constructing zero-inflated non-negative likelihoods, calculating the log-likelihood of observations, and generating random samples.

Change to ZeroInflatedDistributions.jl?

These are actually distributions, with e.g. mean etc. that can be calculated based on the underlying distributions. Might take some thought about how to deal with discrete zero probability vs continuous density.

Methods to implement:

  • rand(::AbstractRNG, d::UnivariateDistribution)
  • sampler(d::Distribution)
  • pdf(d::UnivariateDistribution, x::Real)
  • logpdf(d::UnivariateDistribution, x::Real)
  • cdf(d::UnivariateDistribution, x::Real)
  • quantile(d::UnivariateDistribution, q::Real)
  • minimum(d::UnivariateDistribution)
  • maximum(d::UnivariateDistribution)
  • insupport(d::UnivariateDistribution, x::Real)

It is also recommended that one also implements the following statistics functions:

  • mean(d::UnivariateDistribution)
  • var(d::UnivariateDistribution)
  • modes(d::UnivariateDistribution)
  • mode(d::UnivariateDistribution)
  • skewness(d::UnivariateDistribution)
  • kurtosis(d::Distribution, ::Bool)
  • entropy(d::UnivariateDistribution, ::Real)
  • mgf(d::UnivariateDistribution, ::Any)
  • cf(d::UnivariateDistribution, ::Any)

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