# Truncated Poisson Distribution probs not adding up to one

**URL:** <https://discourse.julialang.org/t/truncated-poisson-distribution-probs-not-adding-up-to-one/61053>\
**Category:** Statistics\
**Tags:** probability\
**Created:** [May 12, 2021, 11:34pm UTC](https://discourse.julialang.org/t/truncated-poisson-distribution-probs-not-adding-up-to-one/61053 "2021-05-12T23:34:30Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Albert\_Zevelev](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/albert_zevelev/32/11844_2.png) [@Albert\_Zevelev](https://discourse.julialang.org/u/Albert_Zevelev)\
**Post date:** [May 12, 2021, 11:34pm UTC](https://discourse.julialang.org/t/truncated-poisson-distribution-probs-not-adding-up-to-one/61053/1 "2021-05-12T23:34:30Z")

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```julia
using Distributions
λ = 2.0; #Poisson parameter
zp = 0.4; #zero prob. 
dpoi = Poisson(λ)
dzip = MixtureModel([Dirac(0.0), dpoi], [zp, 1.0-zp]) #ZeroInflated ZIP
dztp = Truncated(dpoi, 1, Inf) #ZeroTruncated ZTP 
dzmp = MixtureModel([Dirac(0.0), dztp], [zp,1.0-zp]) #ZeroModified ZMP
####
sum(pdf(dpoi, 0:1000)) #1.0
sum(pdf(dzip, 0:1000)) #1.0
sum(pdf(dzmp, 0:1000)) #1.2734073051133634
sum(pdf(dztp, 0:1000)) #1.4556788418556055

```

Shouldn’t the Truncated Poisson distribution be a distribution whose probs add up to one?

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<div class="post-metadata">

**Author:** ![Albert\_Zevelev](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/albert_zevelev/32/11844_2.png) [@Albert\_Zevelev](https://discourse.julialang.org/u/Albert_Zevelev)\
**Post date:** [August 28, 2021, 4:50am UTC](https://discourse.julialang.org/t/truncated-poisson-distribution-probs-not-adding-up-to-one/61053/2 "2021-08-28T04:50:39Z")

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Issue solved by PR:  
[https://github.com/JuliaStats/Distributions.jl/issues/1328#event-5218996744](https://github.com/JuliaStats/Distributions.jl/issues/1328#event-5218996744)