From cbfd8db15c96f79ebe6e2e69d42cc85ebef5f9b4 Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Sun, 14 Sep 2014 21:22:00 -0700 Subject: [PATCH] Fixed errors in probability density function. For some reason I was calling the PDF the probability, when of course it is the probability density. --- Chapter04_Gaussians/Gaussians.ipynb | 216 +++++++----- .../Gaussians_Animations.ipynb | 322 ++++++++++++++++++ Chapter04_Gaussians/gaussian_animate.gif | Bin 0 -> 772194 bytes code/stats.py | 66 +++- 4 files changed, 515 insertions(+), 89 deletions(-) create mode 100644 Chapter04_Gaussians/Gaussians_Animations.ipynb create mode 100644 Chapter04_Gaussians/gaussian_animate.gif diff --git a/Chapter04_Gaussians/Gaussians.ipynb b/Chapter04_Gaussians/Gaussians.ipynb index 34e55c2..1c14191 100644 --- a/Chapter04_Gaussians/Gaussians.ipynb +++ b/Chapter04_Gaussians/Gaussians.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:f06623f9c65b72eaaa654d00719496d1826c6c5a76a1cb6ee583c4b4844b2cf2" + "signature": "sha256:00a931decd323bc4f252540ee5dd36a369b885268e890c562b4a210ea2fff34b" }, "nbformat": 3, "nbformat_minor": 0, @@ -257,13 +257,13 @@ ], "metadata": {}, "output_type": "pyout", - "prompt_number": 12, + "prompt_number": 3, "text": [ - "" + "" ] } ], - "prompt_number": 12 + "prompt_number": 3 }, { "cell_type": "heading", @@ -290,7 +290,7 @@ "input": [ "from stats import plot_gaussian\n", "\n", - "plot_gaussian(mean=100, variance=15*15, xlabel='IQ', ylabel='percent')" + "plot_gaussian(mean=100, variance=15*15, xlabel='IQ')" ], "language": "python", "metadata": {}, @@ -298,13 +298,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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RxEJUpF4dH+4e2A6AV77/S+doRGkkeQi7euuXDeQXFDGiZwvaNJYlZoXlpo7s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\nhBBCCCGELv4fDKN3j0zi4+cAAAAASUVORK5CYII=\n", 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/pb+ViohNOX3+GlMW/QTAuwPCVaLFZo3p25q7fD3ZcvAMizYnGB1HRAygIi0i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\nt80gfe7cOezt7TGZTMydO5dly5YRFBREampqm0H67NmzjBw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"text": [ - "" + "" ] } ], - "prompt_number": 13 + "prompt_number": 4 }, { "cell_type": "markdown", @@ -359,7 +359,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "

Don't be dissuaded by the equation if you haven't seen it before; you will not need to memorize or manipulate it. The computation of this function is stored in stats.py. \n", + "

Don't be dissuaded by the equation if you haven't seen it before; you will not need to memorize or manipulate it. The computation of this function is stored in `stats.py` with the function `gaussian(x, mean, var)`.\n", "\n", "> **Optional:** Let's remind ourselves how to look at a function stored in a file by using the *%load* magic. If you type *%load -s gaussian stats.py* into a code cell and then press CTRL-Enter, the notebook will create a new input cell and load the function into it.\n", "\n", @@ -384,11 +384,53 @@ "cell_type": "code", "collapsed": false, "input": [ - "from stats import gaussian\n", - "plot_gaussian(22,4,mean_line=True,xlabel='$^{\\circ}C$',ylabel=\"Percent\")\n", + "from stats import gaussian, norm_cdf\n", + "plot_gaussian(22, 4, mean_line=True, xlabel='$^{\\circ}C$')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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b16BSoD+HTyUwZ8U+03FE5CaoLIvIDTl2OoGZS3djWTDs4Yam44g4FHc3F4Y8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\nYTK4QhEREelKsK8Hv77zeu5OS+HFD79gxdZc3tu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+ "text": [ + "" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So what does this curve *mean*? Assume for a moment that we have a thermometer, which reads 22$\\,^{\\circ}C$. No thermometer is perfectly accurate, and so we normally expect that thermometer will read $\\pm$ that temperature by some amount each time we read it. Furthermore, a theorem called **Central Limit Theorem** states that if we make many measurements that the measurements will be normally distributed. So, when we look at this chart we can *sort of* think of it as representing the probability of the thermometer reading a particular value given the actual temperature of 22$^{\\circ}C$. However, that is not quite accurate mathematically. \n", "\n", - "print('Probability of 22 is %.2f' % (gaussian(22,22,4)*100))\n", - "print('Probability of 24 is %.2f' % (gaussian(24,22,4)*100))" + "Recall that we said that the distribution is *continuous*. Think of an infinitly long straight line - what is the probability that a point you pick randomly is at, say, 2.0. Clearly 0%, as there is an infinite number of choices to choose from. The same is true for normal distributions; in the graph above the probability of being *exactly* 22$^{\\circ}C$ is 0% because there are an infinite number of values the reading can take.\n", + "\n", + "So what then is this curve? It is something we call the *probability density function.* Later we will delve into this in greater detail; for now just understand that the area under the curve at any region gives you the probability of those values. So, for example, if you compute the area under the curve between 20 and 22 the result will be the probability of the temperature reading being between those two temperatures." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So how do you compute the probability, or area under the curve? Well, you integrate the equation for the Gaussian \n", + "\n", + "$$ \\int^{x_1}_{x_0} \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{1}{2}{(x-\\mu)^2}/\\sigma^2 } dx$$\n", + "\n", + "I wrote `stats.norm_cdf` which computes the integral for you. So, for example, we can compute" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print('Probability of value in range 21.5 to 22.5 is {:.2f}%'.format(\n", + " norm_cdf((21.5, 22.5), 22,4)*100))\n", + "print('Probability of value in range 23.5 to 24.5 is {:.2f}%'.format(\n", + " norm_cdf((23.5, 24.5), 22,4)*100))" ], "language": "python", "metadata": {}, @@ -397,27 +439,17 @@ "output_type": "stream", "stream": "stdout", "text": [ - "Probability of 22 is 19.95\n", - "Probability of 24 is 12.10\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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5CdHQpFCIGnvvh32AeTqjr7eH4jTCGU0Z2J7wYH+S0/NYvStFdRyXJ4VC1MiB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\nvopq1ZQHJnbn5kFSIIQQlQt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- "text": [ - "" + "Probability of value in range 21.5 to 22.5 is 19.74%\n", + "Probability of value in range 23.5 to 24.5 is 12.10%\n" ] } ], - "prompt_number": 14 + "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "So what does this curve *mean*? Assume for a moment that we have a thermometer, which reads 22$\\,^{\\circ}C$. No thermometer is perfectly accurate, and so we normally expect that thermometer will read $\\pm$ that temperature by some amount each time we read it. Furthermore, a theorem called **Central Limit Theorem** states that if we make many measurements that the measurements will be normally distributed. If that is true, then this chart can be interpreted as a continuous curve depicting our belief that the temperature is any given temperature. In this curve, we assign a probability of the temperature being exactly 22$^{\\circ}C$ is $19.95\\%$. Looking to the right, we assign the probability that the temperature is 24$^{\\circ}C$ is $12.10\\%$. Because of the curve's symmetry, the probability of 20$^{\\circ}$C is also $12.10\\%$.\n", - "\n", "So the mean ($\\mu$) is what it sounds like - the average of all possible probabilities. Because of the symmetric shape of the curve it is also the tallest part of the curve. The thermometer reads $22^{\\circ}C$, so that is what we used for the mean. \n", "\n", "> *Important*: I will repeat what I wrote at the top of this section: \"A Gaussian...is completely described with two parameters\"\n", @@ -426,13 +458,42 @@ "\n", "$$temp = \\mathcal{N}(22,4)$$\n", "\n", - "This is an **extremely important** result. Gaussians allow me to capture an infinite number of possible values with only two numbers! With the values $\\mu=22$ and $\\sigma^2=4$ I can compute the probability of the temperature being $22\\,^{\\circ}C$, $20\\,^{\\circ}C$, $87.34\\,^{\\circ}C$, or any other arbitrary value.\n", - "\n", + "This is an **extremely important** result. Gaussians allow me to capture an infinite number of possible values with only two numbers! With the values $\\mu=22$ and $\\sigma^2=4$ I can compute the distribution of measurements for over any range." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "###### The Variance\n", "\n", - "Since this is a probability distribution it is required that the area under the curve always equals one. This should be intuitively clear - the area under the curve represents all possible occurences, which must sum to one.\n", - "\n", - "This leads to an important insight. If the variance is small the curve will be narrow. To keep the area equal to 1, the curve must also be tall. On the other hand if the variance is large the curve will be wide, and thus it will also have to be short to make the area equal to 1.\n", + "Since this is a probability density distribution it is required that the area under the curve always equals one. This should be intuitively clear - the area under the curve represents all possible occurences, which must sum to one. We can prove this ourselves with a bit of code. (If you are mathematically inclined, integrate the Gaussian equation from $-\\infty$ to $\\infty$)" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print(norm_cdf((-1e8, 1e8), mu=0, var=4))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1.0\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This leads to an important insight. If the variance is small the curve will be narrow. this is because the variance is a measure of *how much* the samples vary from the mean. To keep the area equal to 1, the curve must also be tall. On the other hand if the variance is large the curve will be wide, and thus it will also have to be short to make the area equal to 1.\n", "\n", "Let's look at that graphically:" ] @@ -457,19 +518,19 @@ { "metadata": {}, "output_type": "display_data", - "png": 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vAIuB64GXBihbBxQAc4DrgJd9OL8QIa20dgsaHZScSiBMSRny6yXGhLPjQCqq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\nDRc5cQuJsl66AHZfure3h0o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EZEgDK8r+C8rhxjBS4lyn8zW2a1VZRAJLQVlERIbkWVGO91/rxbnvp/YLEQk0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\nT4nZ+oaiEwYWRTxMqGUuJ2r/l2ZbEXtL/oW5IXczP+Qe9Dp1XBC+foj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"text": [ - "" + "" ] } ], - "prompt_number": 15 + "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "So what is this telling us? The blue gaussian is very narrow. It is saying that we believe $x=23$, and that we are very sure about that $(90%)$. In contrast, the red gaussian also believes that $x=23$, but we are much less sure about that $(18%)$. Our believe that $x=23$ is lower, and so our belief about the likely possible values for $x$ is spread out - we think it is quite likely that $x=20$ or $x=26$, for example. The blue gaussian has almost completely eliminated $22$ or $24$ as possible value - their probability is almost $0\\%$, whereas the red curve considers them nearly as likely as $23$.\n", + "So what is this telling us? The blue gaussian is very narrow. It is saying that we believe $x=23$, and that we are very sure about that. In contrast, the red gaussian also believes that $x=23$, but we are much less sure about that. Our believe that $x=23$ is lower, and so our belief about the likely possible values for $x$ is spread out - we think it is quite likely that $x=20$ or $x=26$, for example. The blue gaussian has almost completely eliminated $22$ or $24$ as possible value - their probability is almost $0\\%$, whereas the red curve considers them nearly as likely as $23$.\n", "\n", "If we think back to the thermometer, we can consider these three curves as representing the readings from three different thermometers. The blue curve represents a very accurate thermometer, and the red one represents a fairly inaccurate one. Green of course represents one in between the two others. Note the very powerful property the Gaussian distribution affords us - we can entirely represent both the reading and the error of a thermometer with only two numbers - the mean and the variance.\n", "\n", @@ -499,13 +560,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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xwMjBLUzniDilFy9dyzp52V6Op2YYrhGRv6LBKmKnxs+KJb/QyoD2tagfEWw6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\nB/f2jOLeng0ICtClAs5Kg9UJHUtJZ9K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LMp0kRcSyLMY+0B4/H09mrT3Aqp3JppNExIVpsIpIscjLtzHi2zUAPHFTY2qFBRsukqJW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\nM6WEabC6kYuZuUxYuIvxC+JIy8wFoEe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ygCbcfUHPoCNJgWlUJ4vnb+xHRloyr4+eyZPvTw46kqQKZBmWtJ2Skii/fWIU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\nvxM4/o63mDRnOY3qZPH8jf1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mUI4B4CrlOhya9dM+jf9mk1LSsuTladFTdzbTY7c3lbe1ZD/MWsxmdb6xujrfWF3xSec1\nesYvit6VqJc+W6s50fv19oPt1aR2RaNjAsB1U7IftQGghNsRf0ovfbZWOw+eliR1ubG6xg5pq1rB\n7rdkWp2QcvrqxUj9uPGgXpu1XtviTum2MQs0pFsjjerbUgE2Y6aDAMD1RDkGgCtwzp6pd7/ZrC9+\n2iOnU6pSwVdjB7dRz5trufXKDyaTSb1a11GnptU0cd5WfRq1W58v26NFGw7qtYG36K62YW79+wFA\nYcyFbwIAuMjpdGrumlh1fP5bzVyxRxazSY/d3lTR7/VVZMvapaY4+vlY9erAWxQ17m7dXC9Yp86n\n68kPf1a/t35UbOLZwncAAG6KI8cAUET7j57Ry5//ovX78tYqbt0gRG892E4Nq1co5J7u64YaQZr/\n6h36dk2Mxs7eoHV7jqvbP+fpH7c31bN3NZePF08jAEoXHtUAoAj+u2q//vn5WmXlOBQU4K0xA1rr\n3vb1Ss2R4oKYzSb179hA3W6qqXe+2aSvVu7TfxZu19LNh/TZyO4lbiUOALgaTKsAgAJk5zg0ZuY6\njZy2Wlk5Dt3fqYFWT+invh3ql4li/HsV/L317kMdtPD13qpXNVCxx86p15gFWrXziNHRAKDYUI4B\n4DLOXMjQgPGL9dmy32T1MOv94RGaMDxCgb5eRkczVIt6wVr0xp3qeXNNnU/L0qB3l+rjH3fK6XQa\nHQ0ArhrlGAD+wp7DybptzHyt23NclQN99O3oXrqvUwOjY5UYfj5WTXumm57rc5McTqfGzt6gpz9a\npfSsHKOjAcBVoRwDwB8s2hCv3q8v1JFTqWpWp5IWj81bsQGXMptNGnlPC017tqtsXh6a98sB9Xnj\nBx1LTjU6GgBcMcoxALg4HE69++1m/ePfPyk9M0f3tK+r78b0UpUKvkZHK9Fua1lbC1+/UzUq+Wvn\nwdO6bcwCbdqfZHQsALgilGMAkHQhLUsPTVquDxZsk9lk0msP3KIPHu1U4k//XFI0qlFBP469S+0a\nV9Wp8+nqO+5Hzf55n9GxAOBvoxwDKPPik87rjte+17KtCQr09dJXL/bUI5FNytxqFFergr+3Zr8Y\nqYd6his716EXPl2jV2b8ouwch9HRAKDIKMcAyrRVO4+o15gFij12TvVDA7XojTsV0aSa0bHclofF\nrDcGtdHERyJk9TBrxvI9uv+dxUpOSTc6GgAUCeUYQJn1zeoYDXp3qc6nZalHi5r64V93qjYntCgW\n/Ts20NzRvVQ50Ee/7j2uO177XkdPXTA6FgAUinIMoEz6auU+PTc1Wg6nU0/d2UyfPttNfj5Wo2OV\nKi3qBWvx2LvVpFZFJZy8oHveXKSEkylGxwKAAlGOAZQ5M5bv0ajpa+R0Sq/c10ov9Wsps5n5xddC\nlQq++uaV23VT3co6ejpV94xdpPik80bHAoDLohwDKFOmLdmlV2b8Ikl6/YFb9PgdNxqcqPQLsFk1\n+8VItWoQrONn7Lp37CIdOHbO6FgA8JcoxwDKjI8W7dDrX66XJI0b0lbDI5sYnKjs8LdZ9eWoSLVp\nVEUnzqXpnrGLtO/IGaNjAcCfUI4BlAkfLNimN7/eKJNJevehDhravbHRkcocX29PzXqhpzqEh+p0\nSt5ayL8lJBsdCwAuQTkGUKo5nU5NmLtF7367WSaT9P7wjhrYpaHRscosHy8PzRjZXV1urK4zFzLU\nb9yP2nnwlNGxACAf5RhAqeV0OvXON5s1af5WmU0m/fuxzurfsb7Rsco8b6uHPh3RTd1uqqFz9kz1\nf2uxth44aXQsAJBEOQZQSjmdTo2dvUH/WbhdFrNJU57srD7t6hodCy5enhZNfaarbmtZSylpWbr/\n7cXatD/J6FgAQDkGUPo4nU69+sWv+mTxLnlazPrk6VvV+5Ywo2PhD6weFn345K3qfUsdpWZka8D4\nJVq/97jRsQCUcZRjAKWKw+HUPz//RZ8t+01WD7OmPttVkS1rGx0Ll+HpYdb/PZ53VD8tM0cD312i\nNbsTjY4FoAyjHAMoNZxOp16dtU6zftorb0+LPnuuu7rfVNPoWCiEh8WsyY92VP+O9ZWRlauhE5Zq\nI1MsABiEcgyg1PhgwTZ9vmyPrB5mff58D3W+sbrRkVBEFrNZEx6O0P2dGigjO68g7z3MOsgArr9C\ny3FSUpIGDRqkZs2aqU+fPoqNjf1b/8DQoUPVsWPHKw4IAEXx5cq9em/uFplM0n+e6KKI8FCjI+Fv\nMptNGv9Qe0XeXEvn07L0wLtLdPTUBaNjAShjCi3HY8aMUYMGDbRx40ZFRkZqxIgRRd754sWLZbfb\nZTKZriokABRk8aaD+udneaeEfvvB9rq9FXOM3ZXFbNZ/nuisNo2qKOlsmu4fv0TJKelGxwJQhhRY\njlNTU7Vu3ToNHz5cVqtVQ4YMUWJiomJiYgrdsd1u17Rp0/Too4/K6XQWW2AA+L1f9x7Xk1N+lsPp\n1PP3tNCgWxsZHQlXydvqoc+e664balRQ/PHzGvzeUtkzso2OBaCMKLAcJyQkyGq1ymazacCAATp6\n9Khq1Kih+Pj4Qnc8ZcoU9e/fX35+fsUWFgB+b/ehZD34/lJlZudqaLcb9OzdzY2OhGISYLPqy1GR\nqlHJX9vjT+nhScuVlZNrdCwAZYBHQTemp6fL19dXdrtdcXFxSklJka+vr9LTC36LKy4uTuvXr9cL\nL7ygjRs3FhoiKCjo76WG4Tw9PSUxdu6qNIxf/PFzGjxhqS6kZ+ueDg015dleslhK/2eMS8PYFVVQ\nUJCWjB+gzs/N0urdiXrx8/WaMeoOmc3uO1WvLI1facT4ua+LY1cUBZZjHx8f2e12hYSEaMOGDZLy\npkvYbLYCd/rmm29qxIgRRZ5rPHbs2PzLERERfIAPQIFOnLWr18v/1YmzdnVuVlOfvVA2inFZFFa1\nvL4f20/dX5ytb1btUaVyPprwaFc+ywKgUNHR0Vq9erUkyWKxKCIiokj3M+3fv/+yE4JTU1PVqlUr\n/fzzzwoODlZWVpZat26tOXPmqH79+pfdacuWLXXhwqWfMDaZTNq0adOfplkcOXJEjRoxR9DdXHzV\nnJycbHASXAl3Hr8LaVm6d9wi7T6UrCa1Kmru6Nvl52M1OtZ1485jdzXW/paoQe9GKSvHoRf73ayn\n73TPKTRldfxKC8bPfQUFBWnt2rWqXr3wJT4LPNTi5+en9u3ba+rUqcrMzNSMGTMUGhp6STEeNGiQ\nJkyYcMn9Nm3apH379mnfvn364osvFBwcrL179zL/GMBVyczO1UOTl2v3oWTVCg7Ql6N6lqliXJa1\nbxyq/3u8s0wmafw3mzX7531GRwJQShX6PuQbb7yhmJgYtWrVSlFRUZo0adIltycmJhb4CsrpdPL2\nF4Crlutw6KkPf9Yvvx1T5UAfff1SpCqW8zE6Fq6jXq3raNzQdpKkF6evVdTmQ8YGAlAqFTjnWJJC\nQkI0a9asy96+cuXKAu/funVrrVq16m8HA4CLnE6nRs9cpx83HpS/j2feKgaVA4yOBQMM6XqDTp9P\n18R5W/X4f1Zq9ouRuqVRFaNjAShF+AQLgBLvgwXb9MWKvfLytGjGyB5qXJNPipdlz/W5SYNubaTM\n7Fw9OHGZ9h3hNNMAig/lGECJ9v2vcfmnhZ7yRGeOEkImk0njhrbVbS1rKyUtS0MmLNWp82lGxwJQ\nSlCOAZRYm2NPaMQn0ZKk1x9oo8iWnBYaeSxms/79eCc1D6uso6dTNWzicqVn5RgdC0ApQDkGUCId\nPpmiYROXKTM7V4O7NtJDPRobHQkljI/VQ5+P7KZqFf209cBJPfdJtByOy65OCgBFQjkGUOKct2dq\n8HtLlZySoY5NQjV2cFtWvcFfqlTOppnP95Cft6cWro/XhO+2GB0JgJujHAMoUbJzHHr03z8p9tg5\nNahWXh8/3VUenP0OBWhYvYI+eeZWWcwmfbBgm75dE2N0JABujGccACVG3pJtv2j17kRVDPDRzOd7\nKMDGST5QuE5Nq2vskLaSpBemrdH6vccNTgTAXVGOAZQYU5fs0pcr98nb06LPnuum6pX8jY4ENzKk\n6w16uGe4snMdemjycsUnnTc6EgA3RDkGUCIs3XxIY2dvkCRNerSjWtQLNjgR3NGrA1ura/MaOpea\nqcHvRelsaobRkQC4GcoxAMPtOnhaT3z4s5xOaVTfm9X7ljCjI8FNWcxmffhkF91Qo4IOJqVo+OQV\nysrJNToWADdCOQZgqONn7Br6/lKlZ+bo3g719PSdzYyOBDfn6+2pGc/3UHCgTb/uPa6XPlsrp5Ml\n3gAUDeUYgGHsGdka+v5SJZ1N0y0NQ/TuQx1Ysg3FIjTITzOe7y4fLw/NiY7RlB92GB0JgJugHAMw\nRK7DoSen/Kzdh5JVKzhA057tJi9Pi9GxUIo0rV1J/3m8s0wm6e05m7RoQ7zRkQC4AcoxAEOM+3qj\nlm1NUKCvl754oYcq+HsbHQmlUM+ba2n0/a0lSc98tErb4k4anAhASUc5BnDd/XfVfn2yeJc8LCZN\ne7arwqoEGh0Jpdg/bmuigZ0bKiM7Vw9NXK7jZ+xGRwJQglGOAVxXG/cn6aXP1kqS3n6wvdreUNXg\nRCjtTCaT3hzaVm0aVdGJc2l6aNIypWfmGB0LQAlFOQZw3Rw5dUEPT16u7FyHHu4ZrgGdGxodCWWE\n1cOiqc90Vc3K/toRf1rPTY1mBQsAf4lyDOC6sGdk68H3lyk5JUOdmlbTmAGtjY6EMqaCv7c+H9ld\nft6eWrg+Xh8s2GZ0JAAlEOUYwDXncDj11Ic/a++RMwqrUk4fPtlFHhYefnD9NahWQVOe7CKTSXpv\n7hYt3nTQ6EgAShienQBcc+/O3aylW/JWppjxfA+V8/UyOhLKsK7Na+SvYPH0R6u0+1CywYkAlCSU\nYwDX1PxfDuj/vt8ui9mkj56+VXVCyhkdCdA/bmuivh3qKT0zRw9OXKpT59OMjgSghKAcA7hmtsWd\n1MhpqyVJbwxqo4jwUIMTAXlMJpPGP9RBLepV1rFkux6atFyZ2blGxwJQAlCOAVwTx5JTNWziMmVm\n52rQrY00pNsNRkcCLuHladH0Ed1UNchXW2JPatT0NaxgAYByDKD4pWfm6KFJy3XyXLraNKqisYPb\nymQyGR0L+JNK5Wz6/Lke8vHy0Nw1sfpk8S6jIwEwGOUYQLFyOp0a8Um0dh48rVrBAZr6TFd5evBQ\ng5IrvFaQ/v1YJ0nSm19v0PKtCcYGAmAonrEAFKvJ87fphw3x8vfx1IyR3VXB39voSEChbmtZW6P6\n3iynU3piys/ad+SM0ZEAGIRyDKDYLNoQrwnfbZHZZNKHT96qeqHljY4EFNnTdzbTnW3C8k9Yc+ZC\nhtGRABiAcgygWOw6eFrPfhItSRo9oJW6NKtucCLg7zGZTHr/kQjdWKeiDp+6oOGTlysrhxUsgLKG\ncgzgqp04m6ah7y9TemaO+nesr0cimxgdCbgiPlYPffZcd4WUt2n9viS9/PkvrGABlDGUYwBXJT0r\nR8MmLlPSWbtaNwjR2w+2Z2UKuLWQ8r767Lnu8rZa9PWq/ZoWtdvoSACuI8oxgCvmdDr13CfR2h5/\nSjUq+Wvas13l5WkxOhZw1W6sU0mTH+0kSRr71Qat2HbY2EAArhvKMYArNnn+Ni1cHy8/b0/NeL67\nggJ8jI4EFJs7WtfR8/e2kMPp1BP/WckKFkAZQTkGcEUWro/738oUT3VRg2oVjI4EFLtn72quO9uE\nKTUjW0PfX6rklHSjIwG4xijHAP627XGnNOLjvJUpxgxsrVub1TA4EXBtXFzBolmdSjpyKlUPT16u\nzGxWsABKM8oxgL/l+Bm7hk1cpozsXA3o1EDDe4YbHQm4pv63goWvNu4/oZc+W8sKFkApRjkGUGTp\nmTl68P1lOnEuTW0aVdG4B9uxMgXKhODyNs18vrt8vDz0zeoYffzjTqMjAbhGKMcAisThcOqZj1dp\n16HTqhUcoKnPdJXVg5UpUHaE16qofz/WSZI07r8btWxLgrGBAFwTlGMARfL+vC36ceNB+ft4asbI\n7qrg7210JOC6u61lbb3Y72Y5ndITU1Zqz+FkoyMBKGaUYwCFmv/LAU2ev01mk0kfPXWr6oWWNzoS\nYJinejdMyKJHAAAgAElEQVRTn3Z1lZaZo6ETlunU+TSjIwEoRpRjAAXaeuCkRk5bLUl6/YFb1PnG\n6gYnAoxlMpn03sMd1DysshKTU/XQpOXKyMoxOhaAYkI5BnBZR09d0EOTlikzO1cPdGmoYT0aGx0J\nKBG8rR767Lluqhrkqy2xJ/XCp2tYwQIoJSjHAP7SeXumBk9YqpPn0tX2hip6cwgrUwC/VznQphkj\ne8jm5aF5vxzQhO+2GB0JQDGgHAP4k6ycXA3/YIX2Hz2r+qGB+vTZbvL04OEC+KPGNYP08dO3ymwy\nafL8bZoTvd/oSACuEs92AC7hdDr14vS1+uW3Y6pUzkdfvNBT5Xy9jI4FlFi3NquhcUPbSpJGTV+j\n1bsTDU4E4GpQjgFcYvKCbfpmdYx8vDw08/keql7J3+hIQIk3uOsNeuz2psrJdeqRycu178gZoyMB\nuEKUYwD55q6J1YS5W2Q2mfThE110Y51KRkcC3MbL97VSr9a1dSE9W4Pei1LSWbvRkQBcAcoxAEnS\nL78d0/OuJdveGNxG3VvUNDgR4F7MZpMmP9pJN9cL1rFku4ZMWCp7RrbRsQD8TZRjAIo5elYPT16u\n7FyHhkeG68HuLNkGXAkfq4c+H9ldtYIDtPtQsh77v5+Uk+swOhaAv4FyDJRxJ8+ladB7UUpJy1Lk\nzbU0ZkBroyMBbq2Cv7dmjeqp8n5e+mn7EY35Yh1rIANuhHIMlGFpGdka+v5SHT2dquZhlfR/j3eW\nxczDAnC16oSU0+fPdZeXp0VfrNirTxbvMjoSgCLiWRAoo3JzHXpiys/aEX9aNSr5a8bIHvLx8jA6\nFlBqtGwQokn/6ChJGjt7gxZtiDc4EYCioBwDZdSoqT9p2dYEBfp6adaonqpYzsfoSECpc2ebML1y\nXytJ0tMfrdKve44anAhAYSjHQBn0nwWbNOX7LbJ6mDV9RDfVrRpodCSg1HqsV1M90KWhMrNz1fdf\n3ynu2FmjIwEoAOUYKGN+2BCvFz75SZI08ZGOuqVRFYMTAaWbyWTSuKHt1LlpNZ0+n67eo7/RqfNp\nRscCcBmUY6AMid55VE9N+VlOp/SvoRG6u11doyMBZYKHxayPn75VzcKCFXfsrAaOj9J5e6bRsQD8\nBcoxUEZsjj2hh1xrGT99d0uN6t/G6EhAmeLnY9XCcf1UL7SCfktI1tD3lyo9M8foWAD+gHIMlAF7\nD5/RkPfynoj7RdTXO8O7yGQyGR0LKHMqB/pq0Vv9VaWCrzbuP6FH/r1C2TmcJAQoSYpUjpOSkjRo\n0CA1a9ZMffr0UWxsbKH3iY6O1j333KMWLVqoU6dO+uijj646LIC/L+FkigaMX6xz9kz1vLmm3nu4\ng8xmijFglJrB5fT1S5Eq7+ellduPaMQnq+RwcJIQoKQoUjkeM2aMGjRooI0bNyoyMlIjRowo9D5p\naWl6/vnntX79es2ZM0cLFy7UwoULrzowgKI7cTZN97+9WCfPpavtDVU05Yku8rDwhhFgtHqh5fXV\ni5Hy9fbU/HVxnEUPKEEKfZZMTU3VunXrNHz4cFmtVg0ZMkSJiYmKiYkp8H6RkZFq06aNPD09FRwc\nrA4dOmj79u3FFhxAwc7ZMzXgncVKOHlBN9apqM+f6y5vKyf5AEqKG+tUyj+L3ozlezThuy1GRwKg\nIpTjhIQEWa1W2Ww2DRgwQEePHlWNGjUUH//3zvSzfft2NWzY8IqDAii6tIxsDX4vSvuOnlXdqoH6\nclSk/HysRscC8AftGlfVh092kdlk0uT52/Rp1G6jIwFlXqGHkdLT0+Xr6yu73a64uDilpKTI19dX\n6enpRf5HvvrqK2VnZ+vuu+/+y9uDgoKKnhglgqenpyTGriTKys7V0IlztSX2pKpXDtCS8QNUvVLA\nJdswfu6LsXNvfzV+A3sEKdfkqUcmLtZrs35VaHAFPdC1iVERUQD+/tzXxbErikLLsY+Pj+x2u0JC\nQrRhwwZJkt1ul81mK9I/EB0drenTp2v27NmXDTZ27Nj8yxEREerYsWOR9g3gUrm5Dg177wct33JQ\nlcrZtPit+/5UjAGUPIO7N9W51AyNmrpS/5i4WIG+3urVpp7RsQC3Fh0drdWrV0uSLBaLIiIiinS/\nQstxzZo1lZmZqRMnTig4OFhZWVk6fPiwateuXejOt27dqldffVXTp09XSEjIZbd7/PHHL/k5OTm5\nCNFhpIuvmhmrksPpdOqlz9Zq7up98vfx1KwXeqiCj/Mvx4jxc1+MnXsraPwGdgxT4smz+mDBNg18\na4G+HNVTbW+oer0jogD8/bmX8PBwhYeHS8obu7Vr1xbpfoXOOfbz81P79u01depUZWZmasaMGQoN\nDVX9+vXztxk0aJAmTJhwyf327dunZ555RpMnT1bdupyFC7jW3vlms75cuU/enhbNGNlDTWpXNDoS\ngL/phXtbaEjXG5SZnasH31+mnQdPGR0JKHOKtKbTG2+8oZiYGLVq1UpRUVGaNGnSJbcnJib+6VXU\nzJkzdfbsWQ0bNkzNmzdX8+bN9cgjjxRfcgD5PliwTf9ZuF0Ws0kfPX2rbmlUxehIAK6AyWTSm0Pa\n6s42YUrNyNaAd5botwSOUgLXk2n//v2GLqx45MgRNWrUyMgIuAK8tVQyOJ1OTZq3Ve/P2yqTSfrg\n0U66p33h8xQZP/fF2Lm3oo5fVk6uHp60XD9tP6JAPy/996XbeDeoBODvz31dnFZRvXr1QrflbACA\nm3I6nXpv7ha9P2+rzCaT/v1Y5yIVYwAln9XDomnPdlO3m2roXGqm+r/1o3bEM8UCuB4ox4Abcjqd\nenvOJn2wYJssZpP+80Rn9WnH3H6gNPHytGjqM13V8+aaOp+WpfveXqytB04aHQso9SjHgJtxOp0a\nO3uDpvywQx4Wkz58sovubBNmdCwA14DVw6KPn+qq21rWVkpalu5/e7E2xZwwOhZQqlGOATfidDr1\n2pfr9cniXfK0mPXxU7eqV+s6RscCcA15epj14ZNd1PuWOkrNyNbA8Uu0Yd9xo2MBpRblGHATDodT\nr8xYp+lRu2X1MGvqs10V2bLw9cYBuD9PD7P+7/G86VP2jGwNfDdK6/YcMzoWUCpRjgE34HA49c/P\n12rmij3y8rTo0xHd1P2mmkbHAnAdeVjMmvxoR93boZ7SM3M06L0ordmdaHQsoNShHAMlnMPh1Kjp\na/JP8PHZc910a7MaRscCYACL2ayJj0Tovo71lZGVq6ETlmrVziNGxwJKFcoxUILlOhx6bmq0vl61\nX95Wiz5/voc6NS18jUYApZfFbNZ7D0doYJeGysjO1bCJy/XT9sNGxwJKDcoxUELl5Dr07MfR+nZN\nrHy8PDTrhZ6KCA81OhaAEsBsNumdB9vnn2r64UnLtWxrgtGxgFKBcgyUQOmZOXr03z9p3i8HZPPy\n0FejeqrtDVWNjgWgBDGbTRo3tK0e6hmurByHhk9errlrYo2OBbg9yjFQwiSnpKvvuB+1ZPMhBdis\nmv1ipFo3rGJ0LAAlkMlk0r8euEWP3d5UOblOPfPxKk2ev1VOp9PoaIDbohwDJUh80nn1fn2htsWd\nVGiQnxa8dodaNggxOhaAEsx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"text": [ - "" + "" ] }, { "metadata": {}, "output_type": "pyout", - "prompt_number": 17, + "prompt_number": 10, "text": [ "" ] } ], - "prompt_number": 17 + "prompt_number": 10 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, if you are reading this in an IPython Notebook, here is an animation of a Gaussian. First, the mean is being shifted to the right. Then the mean is centered at $\\mu=5$ and the variance is modified.\n", + "\n", + "" + ] }, { "cell_type": "heading", @@ -582,11 +652,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Recall how our discrete Bayesian filter worked. We had a vector implemented as a numpy array representing our belief at a certain moment in time. When we performed another measurement using the `sense()` function we had to multiply probabilities together, and when we performed the motion step using the `update()` function we had to shift and add probabilities. I've promised you that the Kalman filter uses essentially the same process, and that it uses Gaussians instead of histograms, so you might reasonable expect that we will be multiplying, adding, and shifting Gaussians in the Kalman filter.\n", + "Recall how our discrete Bayesian filter worked. We had a vector implemented as a numpy array representing our belief at a certain moment in time. When we performed another measurement using the `update()` function we had to multiply probabilities together, and when we performed the motion step using the `predict()` function we had to shift and add probabilities. I've promised you that the Kalman filter uses essentially the same process, and that it uses Gaussians instead of histograms, so you might reasonable expect that we will be multiplying, adding, and shifting Gaussians in the Kalman filter.\n", "\n", "A typical textbook would directly launch into a multipage proof of the behavior of Gaussians under these operations, but I don't see the value in that right now. I think the math will be much more intuitive and clear if we just start developing a Kalman filter using Gaussians. I will provide the equations for multiplying and shifting Gaussians at the appropriate time. You will then be able to develop a physical intuition for what these operations do, rather than be forced to digest a lot of fairly abstract math.\n", "\n", - "The key point, which I will only assert for now, is that all the operations are very simple, and that they preserve the properties of the Gaussian. This is somewhat remarkable, in that the Gaussian is a nonlinear function, and typically if you multiply a nonlinear equation with itself you end up with a different equation. For example, the shape of `sin(x)sin(x)` is very different from `sin(x)`. But the result of multiplying two Gaussians is yet another Gaussian. This is a fundamental property, and the key reason why Kalman filters are possible." + "The key point, which I will only assert for now, is that all the operations are very simple, and that they preserve the properties of the Gaussian. This is somewhat remarkable, in that the Gaussian is a nonlinear function, and typically if you multiply a nonlinear equation with itself you end up with a different equation. For example, the shape of `sin(x)sin(x)` is very different from `sin(x)`. But the result of multiplying two Gaussians is yet another Gaussian. This is a fundamental property, and a key reason why Kalman filters are possible." ] }, { @@ -626,13 +696,13 @@ ] } ], - "prompt_number": 18 + "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The call `norm(2,3)` creates what scipy calls a 'frozen' distribution - it creates and returns an object with a mean of 2 and a standard deviation of 3. You can then use this object multiple times to get the probability of various values, like so:" + "The call `norm(2,3)` creates what scipy calls a 'frozen' distribution - it creates and returns an object with a mean of 2 and a standard deviation of 3. You can then use this object multiple times to get the probability density of various values, like so:" ] }, { @@ -640,9 +710,9 @@ "collapsed": false, "input": [ "n23 = norm(2,3)\n", - "print ('probability of 1.5 is %.4f' % n23.pdf(1.5))\n", - "print ('probability of 2.5 is also %.4f' % n23.pdf(2.5))\n", - "print ('whereas probability of 2 is %.4f' % n23.pdf(2))" + "print ('probability density of 1.5 is %.4f' % n23.pdf(1.5))\n", + "print ('probability density of 2.5 is also %.4f' % n23.pdf(2.5))\n", + "print ('whereas probability density of 2 is %.4f' % n23.pdf(2))" ], "language": "python", "metadata": {}, @@ -651,13 +721,13 @@ "output_type": "stream", "stream": "stdout", "text": [ - "probability of 1.5 is 0.1311\n", - "probability of 2.5 is also 0.1311\n", - "whereas probability of 2 is 0.1330\n" + "probability density of 1.5 is 0.1311\n", + "probability density of 2.5 is also 0.1311\n", + "whereas probability density of 2 is 0.1330\n" ] } ], - "prompt_number": 19 + "prompt_number": 12 }, { "cell_type": "markdown", @@ -676,18 +746,7 @@ ], "language": "python", "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[ 0.38741053 -4.91803911 -2.00879426 -1.15175952 2.63354369 -0.96097707\n", - " 2.45698146 4.22587531 3.69924957 -0.27811435 -0.94132557 4.96510082\n", - " 3.43324112 4.09462176 0.6446632 ]\n" - ] - } - ], - "prompt_number": 20 + "outputs": [] }, { "cell_type": "markdown", @@ -705,16 +764,7 @@ ], "language": "python", "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "0.5\n" - ] - } - ], - "prompt_number": 21 + "outputs": [] }, { "cell_type": "markdown", @@ -733,18 +783,7 @@ ], "language": "python", "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "variance is 9.0\n", - "standard deviation is 3.0\n", - "mean is 2.0\n" - ] - } - ], - "prompt_number": 23 + "outputs": [] }, { "cell_type": "markdown", @@ -771,7 +810,8 @@ "* They express a continuous probability distribution\n", "* They are completely described by two parameters: the mean ($\\mu$) and variance ($\\sigma^2$)\n", "* $\\mu$ is the average of all possible values\n", - "* $\\sigma^2$ represents how much our measurements vary from the mean" + "* The variance $\\sigma^2$ represents how much our measurements vary from the mean\n", + "* The standard deviation ($\\sigma$) is the square root of the variance ($\\sigma^2$)" ] }, { diff --git a/Chapter04_Gaussians/Gaussians_Animations.ipynb b/Chapter04_Gaussians/Gaussians_Animations.ipynb new file mode 100644 index 0000000..79d5a7a --- /dev/null +++ b/Chapter04_Gaussians/Gaussians_Animations.ipynb @@ -0,0 +1,322 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:c37d0ec0133c79aa5807b6f8cb1fc339f0365aa42cb11bfe3a91cba980759b23" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division, print_function\n", + "%matplotlib inline\n", + "import sys\n", + "sys.path.insert(0,'../code') # allow us to format the book\n", + "\n", + "# use same formatting as rest of book so that the plots are\n", + "# consistant with that look and feel.\n", + "import book_format\n", + "book_format.load_style()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n" + ], + "metadata": {}, + "output_type": "pyout", + "prompt_number": 1, + "text": [ + "" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from gif_animate import animate\n", + "from stats import gaussian\n", + "\n", + "def plt_g (mu, variance):\n", + " xs = np.arange(2,8,0.05)\n", + " ys = [gaussian (x, mu, variance) for x in xs]\n", + " plt.plot (xs, ys)\n", + " plt.ylim((0,1))\n", + "\n", + " \n", + "mu = 2\n", + "sigma = 0.6\n", + "def ganimate(frame):\n", + " global mu, sigma\n", + " if frame < 25:\n", + " mu += .2\n", + " elif frame == 25:\n", + " mu = 5\n", + " elif frame < 37:\n", + " sigma -= 0.05\n", + " else:\n", + " sigma += 0.05\n", + " \n", + " plt.cla()\n", + " plt_g(mu,sigma)\n", + "\n", + "animate('gaussian_animate.gif', ganimate, frames=80, interval=50)\n", + "animate??" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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YQkERERFDKCgiImIIBUVERAyhoIiIiCEUFBERMYSCIiIihlBQRETEEAqKiIgYQkERERFD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\npt7ejhcnB+Li6GD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z0NEFMG_ZUVlZ8{#0}7yqYRH9D_<40eF7( z00s^~fw%W5UNC%T_$lM}EKq=o4N!`*XN$Lpi@B(ayU2^Z=!?GyjKL_3!$^$9XpF~* zjLE2s%gBt)=#0+@jnOEL(@2fgXpPs1joGM;+sKXG=#Ae9j^QYd<4BI>XpZNIj_Ih5 z>&TAn=#K9QkMSsv^GJ{NXpi@ZkNK#N`^b;|=s%DD2#^6OkON7O1!<56iI54YkPFF> u4e5{%36T*gkrPRg6={(diIEwpksHa89qExD36dcxk|RlyB^i5x0029#5g#=G literal 0 HcmV?d00001 diff --git a/code/stats.py b/code/stats.py index d0e8be9..7565ca6 100644 --- a/code/stats.py +++ b/code/stats.py @@ -22,6 +22,7 @@ import matplotlib.pyplot as plt import scipy.sparse as sp import scipy.sparse.linalg as spln import scipy.stats +from scipy.stats import norm from matplotlib.patches import Ellipse _two_pi = 2*math.pi @@ -325,9 +326,72 @@ def do_plot_test(): +def norm_cdf (x_range, mu, var=1, std=None): + """ computes the probability that a Gaussian distribution lies + within a range of values. + + Paramateters + ------------ + + x_range : (float, float) + tuple of range to compute probability for + + mu : float + mean of the Gaussian + + var : float, optional + variance of the Gaussian. Ignored if std is provided + + std : float, optional + standard deviation of the Gaussian. This overrides the var parameter + + + Returns + ------- + probability : float + probability that Gaussian is within x_range. E.g. .1 means 10%. + + """ + + if std is None: + std = math.sqrt(var) + return abs(norm.cdf(x_range[0], loc=mu, scale=std) - + norm.cdf(x_range[1], loc=mu, scale=std)) + + + +def test_norm_cdf(): + + # test using the 68-95-99.7 rule + + mu = 5 + std = 3 + var = std*std + + std_1 = (norm_cdf((mu-std, mu+std), mu, var)) + assert abs(std_1 - .6827) < .0001 + + std_1 = (norm_cdf((mu+std, mu-std), mu, std=std)) + assert abs(std_1 - .6827) < .0001 + + std_1half = (norm_cdf((mu+std, mu), mu, var)) + assert abs(std_1half - .6827/2) < .0001 + + std_2 = (norm_cdf((mu-2*std, mu+2*std), mu, var)) + assert abs(std_2 - .9545) < .0001 + + std_3 = (norm_cdf((mu-3*std, mu+3*std), mu, var)) + assert abs(std_3 - .9973) < .0001 + + + +test_norm_cdf() + if __name__ == '__main__': - from scipy.stats import norm + + + test_norm_cdf () do_plot_test()