0028/laplace dist approx.ipynb

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   "source": [
    "using Distributions\n",
    "using StatsPlots\n",
    "using QuadGK"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "850d5df0-2c0a-4e56-b20c-a9b8f82b0b1c",
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    {
     "data": {
      "text/plain": [
       "laplacedistapprox (generic function with 1 method)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function laplacedistapprox(dist)\n",
    "    a = median(dist)\n",
    "    b = quadgk(x -> abs(x - a)*pdf(dist, x), extrema(dist)...)[1]\n",
    "    laplace = Laplace(a, b)\n",
    "end"
   ]
  },
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      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist = Normal()\n",
    "laplace = laplacedistapprox(dist)\n",
    "lnormal = Normal(mean(laplace), std(laplace))\n",
    "plot(dist; label=\"dist\")\n",
    "plot!(laplace; label=\"laplace\", ls=:dash)\n",
    "plot!(lnormal; label=\"lnormal\", ls=:dashdot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "58713a8c-d071-4494-9dd2-5b10c7687f19",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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