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Modified example to match what the OP gave in an edit.

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edited Oct 28, 2019 at 15:25

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This is an extended comment.

IfI know you believe that the software is misbehaving. However, then please show anyour example using SeedRandom so thatdoes not show a poor fit to the example is repeatabledensity. See below.

SeedRandom[12345];SeedRandom[123456];
x = RandomVariate[WeibullDistribution[84RandomVariate[WeibullDistribution[148.2383, 366653.91, -494781.9]061], 10000];
sol = FindDistributionParameters[x, WeibullDistribution[α, β, μ]]
(* {α -> 67668.9517203, β -> 2942970.6661, μ -> -4223098.73853} *)

Show[Histogram[x, Automatic, "PDF"],
  Plot[{PDF[WeibullDistribution[84PDF[WeibullDistribution[148.2383, 366653.91, -494781.9]061], z],
    PDF[WeibullDistribution[α, β, μ] /. sol, z]},
    {z, Min[x], Max[x]}, PlotLegends -> {"True", "Estimated"}]]

Notice that one can't tell the true from the estimated density.

Now, you say, what about the estimates of the parameters being "far" from the true values? (I'll deal with that after breakfast.)

This is an extended comment.

If you believe the software is misbehaving, then please show an example using SeedRandom so that the example is repeatable.

SeedRandom[12345];
x = RandomVariate[WeibullDistribution[84.2, 366.9, -494.9], 10000];
sol = FindDistributionParameters[x, WeibullDistribution[α, β, μ]]
(* {α -> 67.9517, β -> 294.66, μ -> -422.738} *)

Show[Histogram[x, Automatic, "PDF"],
  Plot[{PDF[WeibullDistribution[84.2, 366.9, -494.9], z],
    PDF[WeibullDistribution[α, β, μ] /. sol, z]},
    {z, Min[x], Max[x]}, PlotLegends -> {"True", "Estimated"}]]

Notice that one can't tell the true from the estimated density.

Now, you say, what about the estimates of the parameters being "far" from the true values? (I'll deal with that after breakfast.)

This is an extended comment.

I know you believe that the software is misbehaving. However, your example does not show a poor fit to the density. See below.

SeedRandom[123456];
x = RandomVariate[WeibullDistribution[148.383, 653.1, -781.061], 10000];
sol = FindDistributionParameters[x, WeibullDistribution[α, β, μ]]
(* {α -> 668.203, β -> 2970.61, μ -> -3098.53} *)

Show[Histogram[x, Automatic, "PDF"],
  Plot[{PDF[WeibullDistribution[148.383, 653.1, -781.061], z],
    PDF[WeibullDistribution[α, β, μ] /. sol, z]},
    {z, Min[x], Max[x]}, PlotLegends -> {"True", "Estimated"}]]

Notice that one can't tell the true from the estimated density.

Now, you say, what about the estimates of the parameters being "far" from the true values? (I'll deal with that after breakfast.)

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created Oct 28, 2019 at 14:39

JimB

42.9k
3
51
108

This is an extended comment.

If you believe the software is misbehaving, then please show an example using SeedRandom so that the example is repeatable.

SeedRandom[12345];
x = RandomVariate[WeibullDistribution[84.2, 366.9, -494.9], 10000];
sol = FindDistributionParameters[x, WeibullDistribution[α, β, μ]]
(* {α -> 67.9517, β -> 294.66, μ -> -422.738} *)

Show[Histogram[x, Automatic, "PDF"],
  Plot[{PDF[WeibullDistribution[84.2, 366.9, -494.9], z],
    PDF[WeibullDistribution[α, β, μ] /. sol, z]},
    {z, Min[x], Max[x]}, PlotLegends -> {"True", "Estimated"}]]

Notice that one can't tell the true from the estimated density.

Now, you say, what about the estimates of the parameters being "far" from the true values? (I'll deal with that after breakfast.)