Ex1_Power_law.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hTlwCLuex6VA"
      },
      "source": [
        "# Power law"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RAeDliCkx6VC"
      },
      "source": [
        "## Review:\n",
        "### Power law distribution\n",
        "* Special kind of probability distribution\n",
        "$$P(x) = C x^{-\\alpha}\\quad \\text{for} \\quad x \\geqslant x_{min} > 0$$\n",
        "\n",
        "where C is a normalization constant makes $\\int_{x_{min}}^{\\infty} P(x) dx = 1$.\n",
        "\n",
        "With the help of `sympy` (symbolic python, similiar with symbolic toolbox in matlab), we can find out the value of C"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "iosYfKRbx6VD",
        "outputId": "2de29d3b-6aae-49f7-da20-8dbc15f8789f"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$\\displaystyle C x^{- \\alpha}$"
            ],
            "text/plain": [
              "C/x**alpha"
            ]
          },
          "execution_count": 1,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "import sympy\n",
        "x, C, alpha, xmin = sympy.symbols('x C alpha x_{min}', positive=True)\n",
        "P = C * x ** (-alpha)\n",
        "P"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 88
        },
        "id": "WF2-89mYx6VF",
        "outputId": "e1c4638d-a02a-4c31-d0f9-5d40de18f5f1"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$\\displaystyle \\begin{cases} \\frac{C x_{min} x_{min}^{- \\alpha}}{\\alpha - 1} & \\text{for}\\: \\alpha > 1 \\\\\\int\\limits_{x_{min}}^{\\infty} C x^{- \\alpha}\\, dx & \\text{otherwise} \\end{cases}$"
            ],
            "text/plain": [
              "Piecewise((C*x_{min}/(x_{min}**alpha*(alpha - 1)), alpha > 1), (Integral(C/x**alpha, (x, x_{min}, oo)), True))"
            ]
          },
          "execution_count": 2,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "integral_result = sympy.integrate(P, (x, xmin, sympy.oo)) # oo refers to infinity\n",
        "integral_result"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Gk_TznJDx6VF"
      },
      "source": [
        "the result shows when $\\alpha > 1$, the integral is $\\frac{C x_{min}^{1-\\alpha}}{\\alpha - 1}$, otherwise, this integral is diverge."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 58
        },
        "id": "0mq76GqR0m3E",
        "outputId": "aaabdf93-88b7-4592-f7d4-a255435fd797"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$\\displaystyle \\left( \\frac{C x_{min} x_{min}^{- \\alpha}}{\\alpha - 1}, \\  \\alpha > 1\\right)$"
            ],
            "text/plain": [
              "(C*x_{min}/(x_{min}**alpha*(alpha - 1)), alpha > 1)"
            ]
          },
          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "integral_result.args[0]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 56
        },
        "id": "1hCXGuSYx6VG",
        "outputId": "5a8c3063-6b5c-4203-c4ff-6ece7a70a529"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$\\displaystyle \\frac{C x_{min}^{1 - \\alpha}}{\\alpha - 1}$"
            ],
            "text/plain": [
              "C*x_{min}**(1 - alpha)/(alpha - 1)"
            ]
          },
          "execution_count": 4,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "integral_result = integral_result.args[0][0] # get the integral for alpha > 1\n",
        "sympy.simplify(integral_result)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "mjAM-pm5x6VG",
        "outputId": "e7c438f8-69ed-49f7-cb82-9563198bc236"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$\\displaystyle x_{min}^{\\alpha - 1} \\left(\\alpha - 1\\right)$"
            ],
            "text/plain": [
              "x_{min}**(alpha - 1)*(alpha - 1)"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "solution = sympy.solve(integral_result - 1, C)[0] # solve the equation, integral_result - 1 = 0\n",
        "solution"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "sQp87xEnx6VH",
        "outputId": "84013599-5a2a-4096-ce8c-85e0686435f5"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$\\displaystyle x^{- \\alpha} x_{min}^{\\alpha - 1} \\left(\\alpha - 1\\right)$"
            ],
            "text/plain": [
              "x_{min}**(alpha - 1)*(alpha - 1)/x**alpha"
            ]
          },
          "execution_count": 6,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "P = P.subs(C, solution) # substitude the solution\n",
        "P = sympy.simplify(P)\n",
        "P"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XKWR-TAbx6VH"
      },
      "source": [
        "Finally, we find out $C = (\\alpha-1)/x_{min}^{1-\\alpha}$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ygdWjcY_x6VI"
      },
      "source": [
        "### Moments\n",
        "\n",
        "The n-th moment of a distribution is : $\\left< x^k \\right> = \\int_{x_{min}}^{\\infty} x^k P(x) dx$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 88
        },
        "id": "uVrdwX7Px6VI",
        "outputId": "9b580699-94ad-4ec0-c05f-ac59c1aa868c"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$\\displaystyle \\begin{cases} \\frac{x_{min}^{k} \\left(1 - \\alpha\\right)}{- \\alpha + k + 1} & \\text{for}\\: \\alpha - k > 1 \\\\x_{min}^{\\alpha - 1} \\left(\\alpha - 1\\right) \\int\\limits_{x_{min}}^{\\infty} x^{- \\alpha + k}\\, dx & \\text{otherwise} \\end{cases}$"
            ],
            "text/plain": [
              "Piecewise((x_{min}**k*(1 - alpha)/(-alpha + k + 1), alpha - k > 1), (x_{min}**(alpha - 1)*(alpha - 1)*Integral(x**(-alpha + k), (x, x_{min}, oo)), True))"
            ]
          },
          "execution_count": 7,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "k = sympy.Symbol('k', positive=True)\n",
        "moments_k = sympy.integrate(P * x ** k, (x, xmin, sympy.oo))\n",
        "sympy.simplify(moments_k)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q4fk7URIx6VI"
      },
      "source": [
        "$$\\left< x^k \\right> = x^k_{min}\\frac{\\alpha-1}{\\alpha-k-1} \\quad \\text{for} \\quad \\alpha > 1 + k$$\n",
        "otherwise\n",
        "$$\\left< x^k \\right> \\quad \\text{diverge}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L8pdXpGfx6VJ"
      },
      "source": [
        "### Visualize the powerlaw distribution\n",
        "It's convenient to visualize the powerlaw in log-log scale, as\n",
        "\n",
        "$$\\log{P(x)} = -\\alpha \\log{x} + \\log{C}$$\n",
        "Using log-log plot, powerlaw will become a straight  line with sloop equal to $-\\alpha$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YZCZm2wix6VJ"
      },
      "source": [
        "#### From the formula"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "tBvGL6tRx6VJ"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def powerlaw(x, alpha, xmin=1):\n",
        "    assert x.min() >= xmin, f'the minimum x should larger than {xmin}'\n",
        "    C = xmin ** (alpha-1) * (alpha - 1)\n",
        "    return C * x** (- alpha)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 451
        },
        "id": "3sy7iRDqx6VK",
        "outputId": "377185b6-77fd-4a6b-f98d-12e159deb85f"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7e9641a89fc0>"
            ]
          },
          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "xx = np.linspace(1, 10**4, 100)\n",
        "plt.plot(xx, powerlaw(xx, 1.5), label=r\"$\\alpha$=1.5\")\n",
        "plt.plot(xx, powerlaw(xx, 2.5), label=r\"$\\alpha$=2.5\")\n",
        "plt.xscale('log')\n",
        "plt.yscale('log')\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "55ifjvDyx6VK"
      },
      "source": [
        "#### From random numbers\n",
        "\n",
        "In scipy.stats module, there is a class: [pareto](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pareto.html#scipy.stats.pareto) to generate Pareto continuous random variable.\n",
        "\n",
        "> Pareto Distribution: $$P(x, b) = \\frac{b}{x^{b+1}}$$ where $x \\geqslant 1$ and $b>0$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "L8GhCCbNx6VL"
      },
      "outputs": [],
      "source": [
        "from scipy.stats import pareto\n",
        "b = 0.5 # equivalent to alpha = 1.5\n",
        "r = pareto.rvs(b, size=10000) # generate 10000 random numbers from pareto distribution"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ovpyBea3x6VL"
      },
      "source": [
        "Once we have the random numbers, we can compute the histogram of them by using [numpy.histogram](https://numpy.org/doc/stable/reference/generated/numpy.histogram.html)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 457
        },
        "id": "YpzNo9iYx6VM",
        "outputId": "b1db8930-91be-4d96-b59f-429b17776023"
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "hist, bin_edges = np.histogram(r, bins=100, range=(1, 10000), density=True)\n",
        "# with density=True the result is the value of the probability density function at the bin\n",
        "bin_center = (bin_edges[1:] + bin_edges[:-1]) / 2\n",
        "plt.plot(bin_center, hist, label='histogram')\n",
        "plt.title(\"histogram with linear bins\")\n",
        "plt.legend()\n",
        "plt.xscale('log')\n",
        "plt.yscale('log')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x3LN4fsPx6VM"
      },
      "source": [
        "The distribution is noisy in the right-hand end of the distribution because of sampling errors.\n",
        "The power-law distribution dwindles in this region, meaning that each bin only has a few samples in it. So the fractional fluctuations in the bin counts are large and this appears as a noisy curve on the plot.\n",
        "One way to deal with this is to vary the width of the bins in the histogram. The most common choice is to create bins such that each is a fixed multiple wider the one before it. This is known as `logarithmic binning`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5u1XcoBEvPwc",
        "outputId": "f1a49a31-554e-45bd-9a46-0f3c1d6a395e"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0.        , 0.76752836, 1.53505673, 2.30258509, 3.07011346,\n",
              "       3.83764182, 4.60517019, 5.37269855, 6.14022691, 6.90775528])"
            ]
          },
          "execution_count": 39,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "b = np.logspace(0, 3, 10)\n",
        "np.log(b)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "7Moec200x6VN",
        "outputId": "6efd350f-29a2-4796-943e-99d759d74b3a"
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "hist, bin_edges = np.histogram(r, bins=np.logspace(0, 4, 100), density=True)\n",
        "# with density=True the result is the value of the probability density function at the bin\n",
        "bin_center = (bin_edges[1:] + bin_edges[:-1]) / 2\n",
        "plt.plot(bin_center, hist, label='histogram')\n",
        "plt.plot(bin_center, powerlaw(bin_center, 1.5), label=\"power law function\")\n",
        "plt.title(\"histogram with 'logarithmic binning'\")\n",
        "plt.legend()\n",
        "plt.xscale('log')\n",
        "plt.yscale('log')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mE5a3NfJx6VN"
      },
      "source": [
        "## Fit a power law distribution\n",
        "\n",
        "### polynomial fit\n",
        "The simplest way to fit a histogram of power-law distribution is by using a straight line, in other words, fit the relation between log y and log x by a 1 order polynomial."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9og9KRLQvPwf",
        "outputId": "e5128723-daae-4d4b-f35a-888ea67bd547"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([-1.52637682, -0.6033226 ])"
            ]
          },
          "execution_count": 41,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "p = np.polyfit(np.log(bin_center), np.log(hist), deg=1)\n",
        "p"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "id": "j-bWCecbvPwh",
        "outputId": "5f5ea40d-9371-47eb-85b9-73e4b401588c"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f4aca2a9c70>"
            ]
          },
          "execution_count": 46,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(np.log(bin_center), np.log(hist), label='histogram')\n",
        "plt.plot(np.log(bin_center), np.log(bin_center) * p[0] + p[1], label=f\"fitting curve, $\\\\alpha$ = {p[0]:.2f}\")\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tTGq71devPwi"
      },
      "source": [
        "# Maximum likelihood Estimation (MLE)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Kk4LxTdxvPwi"
      },
      "source": [
        "The simplest way to fit a Pareto distribution by MLE is using pareto.fit() directly"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "s-c_ng-bx6VO",
        "outputId": "68a7e5dd-5762-486e-df0d-c32160fa2060"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.49984294417611996"
            ]
          },
          "execution_count": 47,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "b, loc, scale = pareto.fit(r, floc=0, fscale=1)\n",
        "b"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yU-Eu6z3x6VO"
      },
      "source": [
        "In the module scipy.stats, this `fit` function uses Maximum Likelihood Estimation (MLE) as its default estimation method.\n",
        "\n",
        "[Maximum likelihood Estimation](https://en.wikipedia.org/wiki/Maximum_likelihood_estimation) is achieved by maximizing the conditional probability: $L(\\theta | y)$, where $\\theta$ is the parameter we want to estimate, and y is our observation values. This probability is called likelihood function. In other words, this method is going to find out the most likely $\\theta$ under the condition that we have the measurements ${y_1, y_2, y_3, ... y_n}$\n",
        "\n",
        "$$L(\\theta|y) = \\prod_n P(y_n; \\theta)$$\n",
        "\n",
        "To find out the maximum value, it's often convenient to work with the natural logarithm of the likelihood function, called log-likelihood:\n",
        "$$l(\\theta|y) = \\sum_n \\log{ P(y_n; \\theta)}$$\n",
        "Then solve the equation:\n",
        "$$\\frac{\\partial l}{\\partial \\theta}=0$$\n",
        "\n",
        "So for Power law distribution:\n",
        "$$P(x; b) = C x^{-\\alpha}$$\n",
        "where $C=(\\alpha-1)/x_{min}^{1-\\alpha}$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 67
        },
        "id": "YjGSw6C0x6VO",
        "outputId": "843a37d9-d494-4621-ebe2-48a1d930afbc"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$\\displaystyle \\sum_{i=1}^{n} \\log{\\left(x_{min}^{\\alpha - 1} \\left(\\alpha - 1\\right) {y}_{i}^{- \\alpha} \\right)}$"
            ],
            "text/plain": [
              "Sum(log(x_{min}**(alpha - 1)*(alpha - 1)/y[i]**alpha), (i, 1, n))"
            ]
          },
          "execution_count": 48,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "y = sympy.IndexedBase('y', positive=True)\n",
        "i, n, b = sympy.symbols('i n b', positive=True)\n",
        "P = P.subs(x, y[i])\n",
        "log_L = sympy.Sum(sympy.log(P), (i, 1, n)) # l = sum of log(P(x))\n",
        "log_L"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 67
        },
        "id": "iXUnMhCCx6VP",
        "outputId": "2103a293-1d9f-499b-946e-d1c18a81cfa4"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$\\displaystyle \\sum_{i=1}^{n} \\frac{x_{min}^{1 - \\alpha} \\left(x_{min}^{\\alpha - 1} \\left(\\alpha - 1\\right) \\log{\\left(x_{min} \\right)} {y}_{i}^{- \\alpha} - x_{min}^{\\alpha - 1} \\left(\\alpha - 1\\right) \\log{\\left({y}_{i} \\right)} {y}_{i}^{- \\alpha} + x_{min}^{\\alpha - 1} {y}_{i}^{- \\alpha}\\right) {y}_{i}^{\\alpha}}{\\alpha - 1}$"
            ],
            "text/plain": [
              "Sum(x_{min}**(1 - alpha)*(x_{min}**(alpha - 1)*(alpha - 1)*log(x_{min})/y[i]**alpha - x_{min}**(alpha - 1)*(alpha - 1)*log(y[i])/y[i]**alpha + x_{min}**(alpha - 1)/y[i]**alpha)*y[i]**alpha/(alpha - 1), (i, 1, n))"
            ]
          },
          "execution_count": 49,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "dldb = log_L.diff(alpha)\n",
        "dldb"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 67
        },
        "id": "ZwoUKwBJx6VP",
        "outputId": "e70917bf-0847-44a7-d3a8-9ea02b224628"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$\\displaystyle n \\left(\\alpha - 1\\right) \\log{\\left(x_{min} \\right)} + n + \\left(1 - \\alpha\\right) \\sum_{i=1}^{n} \\log{\\left({y}_{i} \\right)}$"
            ],
            "text/plain": [
              "n*(alpha - 1)*log(x_{min}) + n + (1 - alpha)*Sum(log(y[i]), (i, 1, n))"
            ]
          },
          "execution_count": 50,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "dldb = log_L.diff(alpha)\n",
        "dldb = sympy.simplify(dldb * (alpha-1))\n",
        "dldb"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JTbrnp-dx6VP"
      },
      "source": [
        "So:\n",
        "$$\\frac{\\partial l}{\\partial b}=0$$\n",
        "$$n(\\alpha-1)\\log{x_{min}}+n+(1-\\alpha)\\sum_i \\log{y_i} = 0$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 59
        },
        "id": "iF7XXWwMx6VQ",
        "outputId": "443c04d6-855c-435f-e3e8-66197a045f38"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$\\displaystyle \\frac{n \\log{\\left(x_{min} \\right)} - n - \\sum_{i=1}^{n} \\log{\\left({y}_{i} \\right)}}{n \\log{\\left(x_{min} \\right)} - \\sum_{i=1}^{n} \\log{\\left({y}_{i} \\right)}}$"
            ],
            "text/plain": [
              "(n*log(x_{min}) - n - Sum(log(y[i]), (i, 1, n)))/(n*log(x_{min}) - Sum(log(y[i]), (i, 1, n)))"
            ]
          },
          "execution_count": 51,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "sympy.solve(dldb, alpha)[0]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LXlDNVOqx6VQ"
      },
      "source": [
        "Finally we get:\n",
        "$$\\alpha = \\frac{n\\log{x_{min}-n-\\sum_i\\log{y_i}}}{n\\log{x_{min}-\\sum_i \\log{y_i}}} = 1 + \\frac{n}{\\sum_i\\log{y_i}-n\\log{x_{min}}}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QPpCLSLXvPwp"
      },
      "source": [
        "With maximum likelihood, we can get Akaike information criterion (AIC), which is an estimator of prediction error and thereby relative quality of statistical models for a given set of data."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Haqql8wvx6VQ"
      },
      "source": [
        "## Exercise 01\n",
        " ***1.\tAsk ChatGPT to write a 150-200 word summary on an application of power law distribution and then comment/evaluate this answer in your own words in 3-4 sentences based on what you have learned in class. Please also copy the ChatGPT output into the notebook.***"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Rx3zMKMD4tIh"
      },
      "source": [
        "INPUT:  \n",
        "write a 150-200 word summary on the application of power law distribution for the airports.  \n",
        "#-----------------------------#\n",
        "OUTPUT:  \n",
        "Power law distributions are integral to understanding and optimizing airport operations, particularly in analyzing passenger and flight traffic patterns. This distribution typically reveals that a small number of airports handle a vast majority of flights and passengers, while most others manage comparatively fewer. Recognizing this pattern is essential for effective resource allocation and infrastructure planning.\n",
        "\n",
        "For instance, major hubs like Atlanta's Hartsfield-Jackson or London Heathrow handle disproportionately high traffic volumes. By understanding these patterns, airport authorities can better plan for capacity enhancements, security staffing, and gate assignments to accommodate peak traffic efficiently. This helps in minimizing bottlenecks and ensuring smoother operations.\n",
        "\n",
        "Additionally, power law distributions assist in managing the impact of delays and disruptions. Since delays at major hubs can have cascading effects on global networks, airports can develop more robust contingency plans and allocate resources more effectively to mitigate these impacts.\n",
        "\n",
        "Moreover, power law insights aid in strategic investment decisions. Airports can prioritize upgrades and expansions where they will have the most significant impact on overall network efficiency. This application ultimately enhances operational resilience, improves passenger experience, and supports the growth of the global aviation network.\n",
        "#-----------------------------#\n",
        "COMMENT:  \n",
        "The distribution of airports in the real world, such as in the US, follows a power law distribution. Most airports tend to have a small number of airlines connected to them, while a few airports, such as the one in Dallas, Texas, have a large number of airlines connected to them. The answer generated by ChatGPT also reveals this fact by pointing out the existence of hubs. It elucidates the importance of the power law distributions, as delays at major hubs can significantly impact the whole network. This inspires us to pay attention to entities that appear at the tail of a power law distribution."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FE6ge8wpx6VY"
      },
      "source": [
        "***2.Reproduce all three figures on slide 9 using $\\alpha$=1.6,2.2 and 3.1.***\n",
        "> generate random numbers by using scipy.stats.pareto.rvs(b, size)\n",
        "\n",
        "> make a log-log plot\n",
        "\n",
        "> If first and/or second moments exist, draw the theoretical value as dashed line."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 1800x500 with 3 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from scipy.stats import pareto\n",
        "\n",
        "def samples(alpha, size=100):\n",
        "  b = alpha - 1\n",
        "  r = pareto.rvs(b, size=size)\n",
        "\n",
        "  sample_mean = np.mean(r)\n",
        "  sample_variance = np.var(r)\n",
        "  \n",
        "  return sample_mean, sample_variance\n",
        "\n",
        "sizes = np.logspace(1, 6, 100).astype(int)\n",
        "\n",
        "def population_mean(alpha,r):\n",
        "  mean = np.min(r) * (alpha - 1) / (alpha - 1 - 1)\n",
        "  return mean\n",
        "\n",
        "def population_var(alpha, r):\n",
        "  variance = np.min(r) * (alpha - 1) / (alpha - 1 - 2)\n",
        "  return variance\n",
        "\n",
        "\n",
        "def stats(alpha, sizes):\n",
        "\n",
        "  \n",
        "  sample_mean_all, sample_variance_all = [], []\n",
        "  for size in sizes:\n",
        "    r = pareto.rvs(alpha - 1, size=size)\n",
        "\n",
        "    sample_mean_all.append(np.mean(r))\n",
        "    sample_variance_all.append(np.var(r))\n",
        "  \n",
        "  pop_mean = population_mean(alpha,r) if alpha > 1+1 else None\n",
        "  pop_var = population_var(alpha,r) if alpha > 1+2 else None\n",
        "  return sample_mean_all, sample_variance_all, pop_mean, pop_var\n",
        "\n",
        "plt.figure(figsize=(18, 5))\n",
        "for i, alpha in enumerate([1.6, 2.2, 3.1]):\n",
        "  sample_mean_all, sample_variance_all, pop_mean, pop_var = stats(alpha, sizes)\n",
        "  plt.subplot(1, 3, i+1)\n",
        "  plt.scatter(sizes, sample_mean_all, label='sample mean', color='orange')\n",
        "  plt.scatter(sizes, sample_variance_all, label='sample variance',color='blue')\n",
        "  if pop_mean:\n",
        "    plt.axhline(pop_mean, color='r', linestyle='--', label='population mean', linewidth=2)\n",
        "  if pop_var:\n",
        "    plt.axhline(pop_var, color='b', linestyle='--', label='population variance', linewidth=2)\n",
        "  plt.xscale('log')\n",
        "  plt.yscale('log')\n",
        "  plt.legend()\n",
        "  plt.title(f'alpha={alpha}')\n",
        "  plt.ylim(1e-0, 1e10)\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VE8GkflYx6VZ"
      },
      "source": [
        "***3.Reproduce Zipf's law through sample-space-reducing (SSR) processes; fit the histogram to determine the power-law exponent.***\n",
        "\n",
        "**SSR processes**\n",
        " A ball starts at the highest state $i=N$, and may sequentially jump randomly toward any lower state. Once the ball hits the lowest state $i=1$ the process starts again at state $N$. If repeated many times, the probability of visiting states is an exact Zipf's law, $P(i) = \\frac{c}{i}$\n",
        "\n",
        "<!-- The simple sample space reducing (SSR) process could be illustrated by a set of N fair dice with different number of faces. The first has one face, the second has two faces and so on to the N-th that has N faces. To start the process we take the dice with N faces and throw it, getting a result K. Then we throw the dice with K-1 faces getting a new result. Once we reach the dice with one face we restart the process by throwing the N-faced dice again. In an equivalent way, we can interpret the process considering a staircase with N steps: imagine a ball that randomly falls downstairs but never can climb to higher levels. The ball first hits any of the N steps with uniform probability, $P_N(i)=1/N$\n",
        ", $i=1\\dots N$\n",
        ". Then it can only fall down to a lower level with uniform probability and so on until it reaches the bottom step. Once landed on the first step, it restart jumping randomly to any of the steps. -->\n",
        "![SSR](https://media.springernature.com/full/springer-static/image/art%3A10.1038%2Fs41598-017-09836-4/MediaObjects/41598_2017_9836_Fig1_HTML.jpg?as=webp)\n",
        "> Fig 1 in : Corominas-Murtra, B., Hanel, R. & Thurner, S. Sample space reducing cascading processes produce the full spectrum of scaling exponents. Sci Rep 7, 11223 (2017).\n",
        "\n",
        "\n",
        "**Fit the histogram**\n",
        "For checking whether your result obeys $P(i) = \\frac{c}{i}$ or not, please find the exponent by polynomial fit."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 493
        },
        "id": "s0rh5n1pJ949",
        "outputId": "bb885a98-ede7-4b86-9b89-5ad61f910dd0"
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import numpy as np\n",
        "import tqdm\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "def choose_number_infront(i):\n",
        "  '''\n",
        "  Choose a number randomly from 1 to i-1\n",
        "  i: current index\n",
        "  '''\n",
        "  return np.random.choice(np.arange(1, i))\n",
        "\n",
        "index = 20\n",
        "tot_index = []\n",
        "\n",
        "for _ in range(10000):\n",
        "  while index != 1:\n",
        "    index = choose_number_infront(index)\n",
        "    tot_index.append(index)\n",
        "  index = 20\n",
        "tot_index = np.array(tot_index)\n",
        "p = np.bincount(tot_index) / len(tot_index)\n",
        "x = np.arange(1, 20)\n",
        "\n",
        "\n",
        "# Zipf distribution fitting\n",
        "def zipf_fitting(x, y):\n",
        "  k, b = np.polyfit(np.log(x), np.log(y), deg=1)\n",
        "  return x**(k) * np.exp(b), k, b\n",
        "\n",
        "fitted_curve, k, b =  zipf_fitting(x, p[1:])\n",
        "\n",
        "plt.plot(x, p[1:], 'b', label='simulation')\n",
        "plt.plot(x, fitted_curve, 'r', label=f'fitting, k={k:.2f}, b={b:.2f}')\n",
        "plt.xlabel('index')\n",
        "plt.ylabel('probability')\n",
        "plt.title('p distribution')\n",
        "plt.xscale('log')\n",
        "plt.yscale('log')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "\n"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "name": "Lecture1 - Power law.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.11.5"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}