diff --git a/src/fit_em.jl b/src/fit_em.jl
index 53aecb7..f26d0ba 100644
--- a/src/fit_em.jl
+++ b/src/fit_em.jl
@@ -124,9 +124,20 @@ function E_step!(
 ) where {T<:AbstractFloat}
     # evaluate likelihood for each type k
     for k in eachindex(dists)
-        LL[:, k] .= log(α[k]) .+ logpdf.(dists[k], y)
+        logα, distk = log(α[k]), dists[k]
+        if robust
+            isfinite(logα) || continue
+            for n in eachindex(y)
+                logp = logpdf(distk, y[n])
+                isfinite(logp) || continue
+                LL[n, k] = logα + logp
+            end
+        else
+            for n in eachindex(y)
+                LL[n, k] = logα + logpdf(distk, y[n])
+            end
+        end
     end
-    robust && replace!(LL, -Inf => nextfloat(-Inf), Inf => log(prevfloat(Inf)))
     # get posterior of each category
     logsumexp!(c, LL) # c[:] = logsumexp(LL, dims=2)
     γ[:, :] .= exp.(LL .- c)
@@ -143,12 +154,20 @@ function E_step!(
 )
     # evaluate likelihood for each type k
     for k in eachindex(dists)
-        LL[:, k] .= log(α[k])
-        for n in axes(y, 2)
-            LL[n, k] += logpdf(dists[k], y[:, n])
+        logα, distk = log(α[k]), dists[k]
+        if robust
+            isfinite(logα) || continue
+            for n in axes(y, 2)
+                logp = logpdf(distk, y[:, n])
+                isfinite(logp) || continue
+                LL[n, k] = logα + logp
+            end
+        else
+            for n in axes(y, 2)
+                LL[n, k] = logα + logpdf(distk, y[:, n])
+            end
         end
     end
-    robust && replace!(LL, -Inf => nextfloat(-Inf), Inf => log(prevfloat(Inf)))
     # get posterior of each category
     c[:] = logsumexp(LL, dims = 2)
     γ[:, :] = exp.(LL .- c)
diff --git a/src/stochastic_em.jl b/src/stochastic_em.jl
index 4cd4da4..c652c34 100644
--- a/src/stochastic_em.jl
+++ b/src/stochastic_em.jl
@@ -59,8 +59,13 @@ function fit_mle!(
         # M-step
         # using ẑ, maximize (update) the parameters
         α[:] = length.(cat)/N
-        dists[:] = [fit_mle(dists[k], y[cat[k]]) for k = 1:K]
-
+        dists[:] = map(1:K) do k 
+                    if α[k] > 0
+                        fit_mle(dists[k], y[cat[k]])
+                    else
+                        dists[k]
+                    end
+                 end
         # E-step
         # evaluate likelihood for each type k
         E_step!(LL, c, γ, dists, α, y; robust = robust)
@@ -133,7 +138,13 @@ function fit_mle!(
         # M-step
         # using ẑ, maximize (update) the parameters
         α[:] = length.(cat)/N
-        dists[:] = [fit_mle(dists[k], y[:, cat[k]]) for k = 1:K]
+        dists[:] = map(1:K) do k 
+            if α[k] > 0
+                fit_mle(dists[k], y[:, cat[k]])
+            else
+                dists[k]
+            end
+         end
 
         # E-step
         # evaluate likelihood for each type k
diff --git a/test/runtests.jl b/test/runtests.jl
index 6aaccd9..abcfc8e 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -260,3 +260,37 @@ end
     ẑ = predict(m, y)
     @test count(ẑ .== z) / N > 0.85
 end
+
+@testset "Test robustness against dropout issue" begin
+    # See https://github.com/dmetivie/ExpectationMaximization.jl/issues/11 
+    # In this example, one of the mixture weight goes to zero outputing at iteration 3 an
+    # ERROR: PosDefException: matrix is not Hermitian; Cholesky factorization failed.
+    Random.seed!(1234)
+
+    N = 600
+    
+    ctrue = [[-0.3, 1],
+            [-0.4, 0.7],
+            [0.4, -0.6]]
+    X = reduce(hcat, [randn(length(c), N÷3) .+ c for c in ctrue])
+    mix_bad_guess = MixtureModel([MvNormal([1.6, -2.4], [100 0.0; 0.0 1]), MvNormal([-1.1, -0.6], 0.01), MvNormal([0.4, 2.4], 1)])
+    
+    fit_mle(mix_bad_guess, X, maxiter = 1)
+    
+    try # make sure our test case is problematic after two iterations without robust option
+        fit_mle(mix_bad_guess, X, maxiter = 20) #triggers error
+        @test false
+    catch e
+        @test true
+    end
+    begin 
+        #! no error thrown, however the EM converges to some bad local maxima!
+        mix_mle_bad = fit_mle(mix_bad_guess, X, maxiter = 2000, robust = true)
+        @test true
+    end
+    begin 
+        #! no error thrown, however the SEM has one mixture component with zero proba (remaining the same at every iteration)
+        mix_mle_S = fit_mle(mix_bad_guess, X, method = StochasticEM(), maxiter = 2000)
+        @test true
+    end
+end
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