{"nbformat":4,"nbformat_minor":0,"metadata":{"anaconda-cloud":{},"kernelspec":{"display_name":"Python 3","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":"3.7.3"},"colab":{"name":"numpy-05-statistics.ipynb","provenance":[],"collapsed_sections":[]}},"cells":[{"cell_type":"markdown","metadata":{"id":"qCXFQJ3U3l5V","colab_type":"text"},"source":["# Estadística"]},{"cell_type":"code","metadata":{"id":"C-rsKDSm3l5c","colab_type":"code","colab":{}},"source":["import numpy"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"UsDR_vpg3l50","colab_type":"code","outputId":"0bfde628-b24f-4b8b-bad1-cd7c57bdbebc","colab":{"base_uri":"https://localhost:8080/","height":364},"executionInfo":{"status":"ok","timestamp":1589206486223,"user_tz":-120,"elapsed":524,"user":{"displayName":"K&G","photoUrl":"","userId":"11703084203318322732"}}},"source":["x = numpy.random.randn( 100 ) * 5 + 10\n","x"],"execution_count":19,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([12.64817613,  6.7247173 , 14.29127618, 16.19878128,  9.29256514,\n","       11.99753142,  5.27079544, 13.48498339,  7.74326409, 16.76065907,\n","       10.32335627,  6.98482957,  5.41599187,  1.42328176, 16.48727809,\n","        4.96204431, 10.28845788, 10.90963999, 10.63329917, 15.10901747,\n","        1.94830754,  6.30231137, 18.12652284, 18.74178697,  8.72535471,\n","        8.41287592, 11.98331741,  9.42782154, 10.95626054,  1.38719386,\n","       11.59409561, -3.27718354,  8.69413103,  3.58506045, 15.27788775,\n","       -0.94466265,  7.24488802,  8.33291042, 15.5147197 ,  7.92540895,\n","       23.04820037, 10.42153971, 11.19075972,  5.53015795,  8.4882041 ,\n","       17.6947585 , 18.25080826, 11.88177375,  9.79406828,  9.54677956,\n","       13.21649744,  7.48497068, 15.0653455 ,  6.7647108 ,  6.44221805,\n","       11.69024197, 10.14743961, 10.71249902, 13.69407261, 11.03083861,\n","        7.82411209, 14.86175976,  7.09194054, 14.99676981,  8.31249526,\n","       11.00644174, 12.41058243,  7.13880998,  8.64324644,  6.92494043,\n","        3.61222839, 14.39665491,  4.89480758,  6.55989476, 16.54966605,\n","        6.87031749, 12.96329366,  9.63028279,  9.4743312 ,  7.92965018,\n","       14.83007206, 21.04097166,  6.65744869,  2.23620217, 11.31292766,\n","        8.64791579,  6.31235632, 12.2518084 ,  4.5839296 ,  5.65596998,\n","        3.65587694, -0.18117666, 11.18392209, 10.28541326,  3.91281273,\n","        4.57707613, 21.50397277, 15.20296817, 16.97882818,  5.42410792])"]},"metadata":{"tags":[]},"execution_count":19}]},{"cell_type":"code","metadata":{"id":"fn15H0DO3l6Q","colab_type":"code","outputId":"fbc88905-2448-4648-e807-ce0e50f89199","colab":{"base_uri":"https://localhost:8080/","height":34},"executionInfo":{"status":"ok","timestamp":1589206527174,"user_tz":-120,"elapsed":759,"user":{"displayName":"K&G","photoUrl":"","userId":"11703084203318322732"}}},"source":["x.sum()"],"execution_count":20,"outputs":[{"output_type":"execute_result","data":{"text/plain":["987.1704680512217"]},"metadata":{"tags":[]},"execution_count":20}]},{"cell_type":"code","metadata":{"id":"39XHOenQ3l6i","colab_type":"code","outputId":"161da5b9-8083-49a5-a64c-f6848c77d08d","colab":{"base_uri":"https://localhost:8080/","height":34},"executionInfo":{"status":"ok","timestamp":1589206541640,"user_tz":-120,"elapsed":620,"user":{"displayName":"K&G","photoUrl":"","userId":"11703084203318322732"}}},"source":["x.mean()"],"execution_count":21,"outputs":[{"output_type":"execute_result","data":{"text/plain":["9.871704680512217"]},"metadata":{"tags":[]},"execution_count":21}]},{"cell_type":"code","metadata":{"id":"BWIE-Ik03l6x","colab_type":"code","outputId":"e2bf8e2c-ce16-40de-964c-5d87f0abbc9a","colab":{"base_uri":"https://localhost:8080/","height":34},"executionInfo":{"status":"ok","timestamp":1589206550052,"user_tz":-120,"elapsed":561,"user":{"displayName":"K&G","photoUrl":"","userId":"11703084203318322732"}}},"source":["x.std()"],"execution_count":22,"outputs":[{"output_type":"execute_result","data":{"text/plain":["4.97208242158935"]},"metadata":{"tags":[]},"execution_count":22}]},{"cell_type":"code","metadata":{"id":"t3gBh7uE3l7A","colab_type":"code","outputId":"366aabd3-7d04-46dc-cc55-dd7ca471bc79","colab":{"base_uri":"https://localhost:8080/","height":34},"executionInfo":{"status":"ok","timestamp":1589206554517,"user_tz":-120,"elapsed":607,"user":{"displayName":"K&G","photoUrl":"","userId":"11703084203318322732"}}},"source":["x.var()"],"execution_count":23,"outputs":[{"output_type":"execute_result","data":{"text/plain":["24.721603607077817"]},"metadata":{"tags":[]},"execution_count":23}]},{"cell_type":"code","metadata":{"id":"w5oT-13s3l7U","colab_type":"code","colab":{}},"source":["y = numpy.random.randn( 100 ) * 3 - 7\n"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"6nBu_bGX3l7h","colab_type":"code","outputId":"5e1e0fcb-141a-47fc-cfb1-a06aeb05edfb","colab":{"base_uri":"https://localhost:8080/","height":34},"executionInfo":{"status":"ok","timestamp":1589206584132,"user_tz":-120,"elapsed":522,"user":{"displayName":"K&G","photoUrl":"","userId":"11703084203318322732"}}},"source":["xy = numpy.vstack( [ x, y ] )\n","xy.shape"],"execution_count":25,"outputs":[{"output_type":"execute_result","data":{"text/plain":["(2, 100)"]},"metadata":{"tags":[]},"execution_count":25}]},{"cell_type":"code","metadata":{"id":"bCC5dExa3l7t","colab_type":"code","outputId":"26c44dd3-bf26-4b36-90fa-edee3fb79c2d","colab":{"base_uri":"https://localhost:8080/","height":52},"executionInfo":{"status":"ok","timestamp":1589206599978,"user_tz":-120,"elapsed":547,"user":{"displayName":"K&G","photoUrl":"","userId":"11703084203318322732"}}},"source":["numpy.cov(xy)"],"execution_count":26,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[24.97131677,  0.41737244],\n","       [ 0.41737244,  9.52523902]])"]},"metadata":{"tags":[]},"execution_count":26}]},{"cell_type":"code","metadata":{"id":"BDA3zEk13l78","colab_type":"code","colab":{}},"source":["xy = numpy.random.multivariate_normal( [7,5], [[36,-9],[-9,49]], 10) \n","#(media(1*2 ),covarianza(2*2),Ejemplos(1000))"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"vL9ik0KB3l8J","colab_type":"code","outputId":"07b11240-bb90-437e-d560-65c38701d1c5","colab":{"base_uri":"https://localhost:8080/","height":191},"executionInfo":{"status":"ok","timestamp":1589206860664,"user_tz":-120,"elapsed":549,"user":{"displayName":"K&G","photoUrl":"","userId":"11703084203318322732"}}},"source":["xy.shape\n","xy"],"execution_count":33,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[ 9.7030096 ,  6.53880557],\n","       [14.02280161,  1.09176048],\n","       [ 3.81474631,  1.75593363],\n","       [ 7.57090751,  6.53009525],\n","       [ 4.42668944, 17.82815212],\n","       [ 5.16950574, 12.02909847],\n","       [ 1.5113594 ,  8.78705659],\n","       [ 8.26823997,  4.73085008],\n","       [ 7.46483059,  8.42674896],\n","       [ 8.97329924,  6.41049819]])"]},"metadata":{"tags":[]},"execution_count":33}]},{"cell_type":"code","metadata":{"id":"EzKvJdpJ3l8Y","colab_type":"code","outputId":"19fb3f4e-1da1-46ec-c908-e01285657835","colab":{"base_uri":"https://localhost:8080/","height":52},"executionInfo":{"status":"ok","timestamp":1589206866798,"user_tz":-120,"elapsed":503,"user":{"displayName":"K&G","photoUrl":"","userId":"11703084203318322732"}}},"source":["xy.sum(axis=1)"],"execution_count":34,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([16.24181517, 15.11456209,  5.57067994, 14.10100276, 22.25484155,\n","       17.19860421, 10.29841598, 12.99909004, 15.89157955, 15.38379744])"]},"metadata":{"tags":[]},"execution_count":34}]},{"cell_type":"code","metadata":{"id":"bRznGIOm3l8q","colab_type":"code","outputId":"700174d2-05ce-4fad-f81c-d21cab479397","colab":{"base_uri":"https://localhost:8080/","height":34},"executionInfo":{"status":"ok","timestamp":1589206769521,"user_tz":-120,"elapsed":559,"user":{"displayName":"K&G","photoUrl":"","userId":"11703084203318322732"}}},"source":["xy.mean(axis=0)"],"execution_count":31,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([7.17786381, 4.5222496 ])"]},"metadata":{"tags":[]},"execution_count":31}]},{"cell_type":"code","metadata":{"id":"OePj6OCv3l83","colab_type":"code","outputId":"a690dfcb-3f9a-484d-8340-a9cd561aa8a3","colab":{"base_uri":"https://localhost:8080/","height":34},"executionInfo":{"status":"ok","timestamp":1589206407156,"user_tz":-120,"elapsed":2686,"user":{"displayName":"K&G","photoUrl":"","userId":"11703084203318322732"}}},"source":["xy.std(axis=0)"],"execution_count":14,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([5.19412645, 6.00327724])"]},"metadata":{"tags":[]},"execution_count":14}]},{"cell_type":"code","metadata":{"id":"Y0OQhXXC3l9D","colab_type":"code","colab":{"base_uri":"https://localhost:8080/","height":34},"outputId":"45443330-073b-414e-aecd-5352b02b4d1f","executionInfo":{"status":"ok","timestamp":1589206407158,"user_tz":-120,"elapsed":2678,"user":{"displayName":"K&G","photoUrl":"","userId":"11703084203318322732"}}},"source":["xy.var(axis=0)"],"execution_count":15,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([26.9789496 , 36.03933763])"]},"metadata":{"tags":[]},"execution_count":15}]},{"cell_type":"markdown","metadata":{"id":"CDdzQgb63l9P","colab_type":"text"},"source":["## Histograma"]},{"cell_type":"code","metadata":{"id":"a8Al4a8g3l9T","colab_type":"code","outputId":"999da299-bae6-44f5-cc26-16c32a906436","colab":{"base_uri":"https://localhost:8080/","height":52},"executionInfo":{"status":"ok","timestamp":1589206950945,"user_tz":-120,"elapsed":741,"user":{"displayName":"K&G","photoUrl":"","userId":"11703084203318322732"}}},"source":["x = numpy.random.rand( 10000 ) * 100\n","hist,bin_edges = numpy.histogram( x, bins=20, density=False )\n","print( hist )"],"execution_count":35,"outputs":[{"output_type":"stream","text":["[514 527 528 493 472 485 533 503 509 503 521 480 497 476 492 504 497 489\n"," 503 474]\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"OIIdLbT33l9d","colab_type":"code","colab":{"base_uri":"https://localhost:8080/","height":191},"outputId":"603f70ea-d26b-46bf-8890-d0a3d95ef62d","executionInfo":{"status":"ok","timestamp":1589206993735,"user_tz":-120,"elapsed":676,"user":{"displayName":"K&G","photoUrl":"","userId":"11703084203318322732"}}},"source":["hist,bin_edges = numpy.histogram( x, bins=20, density=True )\n","print( hist, hist.sum(), bin_edges[1]-bin_edges[0] )\n","print( bin_edges ) # The same in both cases"],"execution_count":36,"outputs":[{"output_type":"stream","text":["[0.01028247 0.01054253 0.01056254 0.00986237 0.00944227 0.00970233\n"," 0.01066256 0.01006242 0.01018245 0.01006242 0.0104225  0.00960231\n"," 0.00994239 0.00952229 0.00984236 0.01008242 0.00994239 0.00978235\n"," 0.01006242 0.00948228] 0.20004805541872267 4.998798903127999\n","[9.57508767e-03 5.00837399e+00 1.00071729e+01 1.50059718e+01\n"," 2.00047707e+01 2.50035696e+01 3.00023685e+01 3.50011674e+01\n"," 3.99999663e+01 4.49987652e+01 4.99975641e+01 5.49963630e+01\n"," 5.99951619e+01 6.49939608e+01 6.99927597e+01 7.49915586e+01\n"," 7.99903575e+01 8.49891564e+01 8.99879553e+01 9.49867542e+01\n"," 9.99855532e+01]\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"3_Y889FG3l9n","colab_type":"code","colab":{}},"source":[""],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"Z9TkHff83l9w","colab_type":"code","colab":{}},"source":[""],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"89jMrSir3l95","colab_type":"code","colab":{}},"source":[""],"execution_count":0,"outputs":[]}]}