Finden Sie die Verteilung und transformieren Sie sie in die Normalverteilung

Ich habe Daten, die beschreiben, wie oft ein Ereignis während einer Stunde stattfindet ("Anzahl pro Stunde", nph) und wie lange die Ereignisse dauern ("Dauer in Sekunden pro Stunde", dph).

Dies sind die Originaldaten:

nph <- c(2.50000000003638, 3.78947368414551, 1.51456310682008, 5.84686774940732, 4.58823529414907, 5.59999999993481, 5.06666666666667, 11.6470588233699, 1.99999999998209, NA, 4.46153846149851, 18, 1.05882352939726, 9.21739130425452, 27.8399999994814, 15.3750000002237, NA, 6.00000000004109, 9.71428571436649, 12.4848484848485, 16.5034965037115, 20.6666666666667, 3.49999999997453, 4.65882352938624, 4.74999999996544, 3.99999999994522, 2.8, 14.2285714286188, 11.0000000000915, NA, 2.66666666666667, 3.76470588230138, 4.70588235287673, 13.2727272728677, 2.0000000000137, 18.4444444444444, 17.5555555555556, 14.2222222222222, 2.00000000001663, 4, 8.46153846146269, 19.2000000001788, 13.9024390245481, 13, 3.00000000004366, NA, 7.36000000006855, 1.61137440758472, 1.50000000000873, 3.36585365857481, 22.3750000003256, 10.8387096775008, 2.92307692305075, 3.48837209304214, 5.17647058827074, 37.6666666666667, 1.17647058824335, 7.45454545462435, 36.2352941171508, 6.82352941167125, 2.22222222222222, 6.13333333333333, 11.4285714286665, 42.7058823523563, 28.1052631584975, 18.3333333333333, 1.24999999999091, 5.1034482758211, 1.82857142855926, 1.30693069306629, 3.22222222222222, 17.2800000001609, 10.5714285715165, 7.81818181826456, 3.14285714288328, 4.05194805197256, 3.6, 23.0909090904203, 0.249999999998181, 10, 27.3043478258106, 2.49999999998181, 2.00000000001663, 9.14285714293317, 4.74999999996544, 29.3999999996577, 16.9999999998021, 15.7777777777778, 1.74999999998727, 3.46666666666667, 2.45161290324422, 2.05231388331614, 2.60000000001513, 15.4054054053569, 4, 12.2222222222222, 2.46153846151642, 8.15384615399219, 2.23529411761644, 15.1111111111111, 0.23529411764867, 10.5454545455661, 17.5714285715747, 2.3030303030303, 1.37931034481651, 8.32000000007749, 5.1578947368105, 24.1999999997183, 15.4782608694085, 21.8749999998408, 2.74999999997999, 9.91304347823578, 3.86206896548623, 1.16959064328441, 2.84210526319272, 12.857142856929, 4, 3.69230769227463, 2, NA, 1.88888888888889, 15.4285714283148, 0.222222222222222, 6.16666666666667, 13.1034482757569, 3.19999999996275, 4.87499999996453, 2.88000000002682, 5.12499999996271, 26.6666666666667, 9.75000000014188, 17.2048192770602, 1.99999999998545, 1.65517241377981, 3.16666666666667, 2.23529411766237, 6.82352941181143, 2.74999999991996, 2.99999999997817, 11.4929577463281, 1.59999999998137, 8.65116279074452, 5.69230769240964, 13.7777777777778, 0.222222222222222, 10.6000000002468, 13.91304347812, 2.75862068963302, NA, 4.26666666666667, 5.64705882356808, 2.74999999997999, 15.047619047619, 16.6666666666667, 1.49999999998909, 4.62499999996635, 5.71428571428571, 1.83206106868927, 2.44444444444444, 2.4, 3.9999999999709, 2.33333333333333, 3.20000000007451, 5.931034482711, 7.14285714273835, 14.7272727274286, 0.352941176465754, 8.40000000019558, 10.1250000001473, 2.66666666666667, NA, 2.66666666666667, 4.7058823529734, 4.83333333333333, 9.31034482751146, 24.5882352937809, 2.13333333333333, 10.1739130434525, 5.56521739124801, 2.12658227848728, 1.88888888888889, 5.80000000013504, 7.14285714291654, 1.71428571429997, 1.99999999994179, NA, 5.00000000007276, NA, 0.129032258062578, 8.22222222222222, 7.16666666666667, 4.13793103444954, 2.82352941178404, 3.07692307697818, 4.00000000004902, 4.74999999986176, 9.75000000014188, 20.1333333333333, 2.66666666666667, 6.78947368416893, 1.46666666666667, 1.73195876289076, 4.76923076931619, 2.88888888888889, 7.4285714286332, 5.2, 3.384615384676, 4.7727272727399, 6.59999999992317, 11.4545454546667, 1.41176470586302, 11.1999999998696, 6.08000000005662, 4, 4.71428571432492, 5.00000000004158, 6.8, 6.83870967747072, 14.2500000002074, 5.49999999983993, 2.4, 4.71910112354612, 4, 1.72185430463842, 2.44444444444444, 4.30769230776946, 6.30769230780528, 3.53846153852491, 4.35294117641097, NA, 5.99999999990022, NA, NA, 7.42857142857143, 10.1333333333333, 6.79999999992084, 5.54838709681587, 1.83333333333333, 7.06666666666667, 2.9090909091217, 10.8000000001006, NA, 2.13333333333333, NA, 5.09090909090909, 4.21052631570563, 4.00000000003326, 4.28571428571429, 4.28571428574992, 2.49999999998181, 2.76923076928037, 4.99999999985448, 3.87500000005639, NA, NA, 12.2105263159391, 5.44444444444444, 2.6249999999809, 3.74193548389907, 3.28571428574161, 4.88888888888889, 9.33333333333333, 4.21621621620295, NA, 0.8, 4.5306122448549, 4.14285714289159, 3.1137724550985, 0.266666666666667, 5.27272727261567, 1.84615384613731, 8.36363636372488, 2.42857142853104, NA, 2.42857142853104, 8.28571428578318, 1.64705882350685, 8.2, 6.88888888888889, 1.74999999998727, 7.6, 3.33333333333333, 6.24999999995453, 9.56521739120752, 4.93333333333333, 16.4, 2.53333333333333, 7.2, 1.33333333333333, 3.3962264151018, 2, 9.38461538453135, 1.57142857144164, 3.45454545458201, 5.37499999996089, 7.74193548375467, 3.38461538458508, 7, NA, 4.54545454545455, 14.5, 1.93939393939394, 4.33333333333333, 4, 6.58823529402741, 2.90909090902933, 3.32530120480995, 25.6666666666667, 2, 6.54545454545455, 4.4, 3.54378818739119, 1.62499999998818, 4.22222222222222, 2.53333333333333, 14.6666666666667, 2.96296296296296, NA, 3.00000000004366, 16.1999999998114, 1.55555555555556, 3.11111111111111, NA, 4.8, 3.99999999997339, 4, 6.37499999995362, 2.7999999999674, NA, 32.8, 2.49999999998181, 11.0561797754255, NA, 2.75229357793903, 1.7142857142572, 7.66666666666667, 7.28571428577487, 2.36363636358633, 2.14285714287496, 6.27272727274387, 3.62499999997362, 19.6666666666667, 1.71428571427431, 6.60869565210701, 5.57894736838687, 5.84615384610149, 3.03030303030303, 1.33333333333333, 4.87499999996453, 4.71428571432492, 4.74418604653732, 13.0588235292329, 3.12500000004547, NA, 3.37500000004911, 2.41525423729648, 2.37499999998272, 4.54545454550265, 6.28571428576655, 2.55555555555556, 3.17647058819179, 5.59999999993481, 5.85714285719156, 7.42857142844789, NA, 4.83333333333333, 5.33333333333333, 4.48484848484848, 2.93333333333333, 3.83333333333333, 5.52941176474375, 9.33333333333333, 5.16666666666667, 18, 2.82352941178404, 5.54838709681587, 3.55555555555556, 1.25237191650965, 2, 2.16666666666667, 7.16666666666667, 3.00000000002495, 2.83333333333333, 2.48275862068966, 4.42857142860825, 11.1428571426718, NA, 5.52380952380952, 34.3448275859312, 4.75000000006912, 3.26315789471685, 10.2857142857998, 10.5555555555556, 5.00000000004158, 19.0843373493441, 20.6153846152, 2.24999999998363, 8.59259259259259, 4.25806451616101, 2.85714285716014, 5.1578947368105, 8.66666666666667, 3.14285714280487, 6.30769230763582, 6.79999999992084, 8.07692307663376, 5.73333333333333, 8.46153846146269, 2.34482758618807, 4.31999999991953, 4.57142857135254, 2.87500000004184, 2.28571428567627, 0.857142857149985, 10.2352941175069, 3.26086956520914, NA, 13.3333333333333, 2.75000000004002, 6.45161290312889, 3.61290322575218, 1.48854961831995, 3.37499999997544, 4.0540540540413, 5.73333333333333, 3.85714285707871, 3, 6.31578947364551, 1.55555555555556, 7.84615384608358, 0.4, 7.66666666666667, NA, 7.85185185185185, 2.59090909091595, 7.28571428577487, 5.74999999995816, 3.28571428574161, 16.043478260829, 15.8000000003679, 2.50000000003638, NA, 2.06451612904776, 1.82163187855948, 0.874999999993634, 13.2000000001229, 6.92307692301493, 3.7142857143166, 3.00000000001343, 5.83333333333333, 3.86666666666667, 9.39999999989057, 2.49999999998181, 6.24000000005811, 4.58823529414907, 3.72413793109428, 3.21428571427235, 6.85714285719988, 8.42857142864151, 5.23076923086291, 10.5454545455661, 14.1428571429747, 4.00000000005821, 4.08791208795393, 8.47058823517811, 3.94422310755509, 3.62500000005275, 6.0000000001397, 1.33333333333333, 3.73333333333333, 6.31578947352942, NA, 4.53333333333333, 8.46153846169001, 0.470588235287673, 2.28571428571429, 22.7142857144746, 8.00000000012846, 2.8108108108285, 4.57142857146658, 5.87500000008549, 6.42857142862488, 19.2258064513241, 13.4666666666667, 3.46666666666667, 4.90322580648844, 3.51515151515152, 1.56862745098755, 1.53846153844776, 3.63636363636364, 4.71428571432492, 3.06666666666667, 4.61538461546728, NA, 2.83333333333333, 5.53846153841194, 1.80645161287609, 9.14285714285714, 2.42857142853104, 3.2, 5.00000000007276, 4.42857142860825, 6.12500000008913, 3.24999999990541, 4.16326530608288, 14.6666666666667, 5.37499999996089, 7.43478260867684, 9.93548387104236, 3.73205741626378, 2.24999999998363, 13.7777777777778, 4.74074074074074, 7.4285714286332, 3.61904761904762, 7.13513513511269, 5.28571428575824, 5, 2.5882352940822, 11.5000000001673, 27.1249999998026, 2.875, 2.81081081077544, 9.42857142864983, 7.05882352931509, 3.83333333333333, 16.8695652172205, 16.7692307690806, 10.1333333333333, 5.45454545455989, 7.8750000001146, 1.6883116883219, 2.66666666666667, 11.7857142856653, 3.33333333333333, 6.33333333333333, 7.39999999991385, 12.5882352942039, 4.00000000003326, 6.72727272734392, 3.03030303030303, 6, 30.6666666666667, 3.74999999997272, 3.00000000003011, 8.00000000006652, 8.00000000006009, 2.57142857144995, 10.695652173886, 14.2666666666667, 7.75000000011278, 2.51162790697674, 6.33333333333333, 3.28125000004775, 1.88888888888889, 10.4000000002421, 4.87499999996453, 13.7142857143998, 8.5, NA, 4.87499999996453, 8.181818181645, 1.24999999999091, 4.38095238095238, 27.1764705878631, 2.37499999998272, 2.94117647060838, 11.7142857143831, 5.99999999996324, 2.37499999998272, 14.7637795275455, 14.313253012008)
dph <- c(3.12500000004547, 6.69473684199041, 4.3106796117187, 11.6937354988146, 103.882352941888, 10.9999999998719, 7.33333333333333, 20.3529411761918, 5.23076923072239, NA, 4.61538461534328, 47.5555555555556, 2.94117647054795, 18.9565217389385, 44.3199999991745, 28.5000000004147, NA, 10.4705882353658, 19.000000000158, 25.8181818181818, 43.2167832173461, 51.5555555555556, 8.37499999993906, 6.91764705878563, 9.37499999993179, 5.64705882345207, 4.53333333333333, 27.4285714286627, 14.4285714286914, NA, 1.6, 5.76470588227399, 4.70588235287673, 55.2727272733122, 2.11764705883803, 30.8888888888889, 41.2222222222222, 23.4444444444444, 2.42857142859162, 6.2, 17.0769230767702, 21.2800000001982, 40.8292682931466, 14.5, 6.25000000009095, NA, 15.0400000001401, 5.68720379147547, 2.40000000001397, NA, 26.3750000003838, 18.0645161291679, 3.99999999996418, 6.13953488375417, 8.47058823535212, 128.666666666667, 2.23529411766237, 34.1818181821799, 115.999999998411, 5.99999999991782, 5.77777777777778, 10.6666666666667, 15.4285714286997, 54.8235294110138, 81.315789475428, 42.3333333333333, 1.74999999998727, 7.99999999993577, 4.34285714282825, 1.90099009900552, 5.22222222222222, 39.840000000371, 25.1428571430662, 7.81818181826456, 8.57142857149985, 15.2727272728196, 6.4, 93.0909090889387, 0.374999999997272, 23.1666666666667, 29.3913043475286, 0.874999999993634, 1.71428571429997, 13.5714285715414, 5.49999999995998, 134.799999998431, 77.7999999990943, 18, 2.24999999998363, 5.73333333333333, 3.09677419357165, 2.29376257547098, 5.70000000003318, 23.1891891891162, 14, 13.5555555555556, 1.69230769229254, 9.23076923093455, 4.35294117641097, 48.6666666666667, 0.352941176473005, 16.0000000001693, 56.7142857147573, 1.81818181818182, 1.37931034481651, 19.6800000001833, 6.63157894732779, 134.999999998428, 41.0434782604541, 26.8749999998045, 3.62499999997362, 16.5652173912624, 10.3448275861238, 1.28654970761285, 2.94736842108875, 13.4285714283481, 7.6, 3.2307692307403, 2, NA, 3.44444444444444, 93.1428571413081, 0.111111111111111, 13.6666666666667, 28.1379310342568, 2.39999999997206, 7.8749999999427, 4.00000000003725, 6.99999999994907, 60, 26.8750000003911, 30.5060240963, 3.12499999997726, 3.17241379307798, 4.83333333333333, 9.29411764712247, 12.7058823530282, 4.24999999987631, 6.99999999994907, 9.97183098578469, 2.39999999997206, 8.93023255818789, 15.3846153848909, 94, 0.111111111111111, 21.4000000004983, 29.9130434779581, 1.24137931033486, NA, 15.8666666666667, 7.17647058828444, 1.49999999998909, 37.9047619047619, 27.6666666666667, 1.74999999998727, 9.37499999993179, 17.3333333333333, 11.603053435032, 5.33333333333333, 2.8, 7.99999999994179, 3.5, 1.60000000003725, 7.31034482752751, 6.42857142846452, 56.7272727278731, 0, 21.6000000005029, 28.8750000004202, 1.6, NA, 4.5, 5.64705882356808, 7.16666666666667, 36.2068965514334, 40.235294117096, 4.8, 22.3043478260305, 8.86956521730152, 3.94936708861923, 3.33333333333333, 12.6000000002934, 20.0000000001663, 1.28571428572498, 0.749999999978172, NA, 6.25000000009095, NA, 0.258064516125156, 18.6666666666667, 17, 5.51724137926605, 2.58823529413537, 11.0769230771215, 5.26315789480134, 11.4999999996653, 34.1250000004966, 42.4, 6.53333333333333, 33.1578947366389, 4.4, 4.9484536082593, 11.2307692309704, 5.11111111111111, 23.8571428573412, 0.4, 2.30769230773364, 6.81818181819986, 8.19999999990454, 26.7272727275556, 0.352941176465754, 24.1999999997183, 7.04000000006557, 2.5, 7.14285714291654, 11.4285714286665, 12.1333333333333, 2.83870967744068, 42.7500000006221, 4.99999999985448, 3.33333333333333, 10.112359550456, 16.8, 4.23841059603303, 2.22222222222222, 14.4615384617975, 15.6923076925887, 3.23076923082709, 1.05882352939726, NA, 7.42857142844789, NA, NA, 16.952380952381, 12.4, 6.29999999992666, 85.4193548393512, 4.33333333333333, 11.8666666666667, 6.0000000000635, 19.6800000001833, NA, 3.46666666666667, NA, 13.0909090909091, 12.6315789471169, 5.14285714289991, 9.14285714285714, 12.1428571429581, 2.87499999997908, 1.692307692338, 10.2499999997017, 5.00000000007276, NA, NA, 19.578947368661, 10.4444444444444, 1.74999999998727, 4.77419354842295, 8.57142857149985, 9.66666666666667, 13.5238095238095, 7.29729729727434, NA, 1.6, 9.18367346930048, 6.85714285719988, 4.5508982036055, 0.666666666666667, 10.90909090886, 2.61538461536119, 6.1818181818836, 1.57142857140244, NA, 1.99999999996674, 24.4285714287746, 0.941176470575345, 16.6, 17.6666666666667, 0.999999999992724, 10.2666666666667, 7.5, 11.2499999999181, 11.9999999998785, 12.8, 29.7333333333333, 5.33333333333333, 13.6, 1.84615384615385, 12.7924528302168, 2.4, 23.6923076920955, 2.42857142859162, 4.90909090914286, 3.62499999997362, 11.4193548385381, 4.92307692303284, 17, NA, 16.9090909090909, 20.8333333333333, 0.96969696969697, 8, 11.8333333333333, 10.2352941175069, 5.81818181805867, 6.07228915660947, 39.3333333333333, 4.13333333333333, 9.6969696969697, 11.2, 7.94297352346302, 2.12499999998454, 4.66666666666667, 2.66666666666667, 11.3333333333333, 3.7037037037037, NA, 2.87500000004184, 24.3999999997159, 1.88888888888889, 10.4444444444444, NA, 3.73333333333333, 7.08571428566715, 15.8333333333333, 11.2499999999181, 2.59999999996973, NA, 43.6, 3.24999999997635, 22.9213483149066, NA, 5.22935779808415, 1.85714285711197, 14.3333333333333, 15.4285714286997, 4.363636363544, 1.8571428571583, 7.36363636365585, 6.37499999995362, 51.3333333333333, 3.42857142854862, 1.043478260859, 4.94736842102232, 2.76923076920597, 5.09090909090909, 2.5, 7.49999999994543, 9.71428571436649, 7.25581395352766, 29.8823529407672, 6.62500000009641, NA, 6.12500000008913, 5.59322033900236, 5.12499999996271, 5.45454545460318, 7.00000000005821, 2.44444444444444, 3.05882352936987, 16.9999999998021, 7.71428571434986, 16.8571428568625, NA, 8.83333333333333, 6.77777777777778, 2.78787878787879, 5.06666666666667, 8.83333333333333, 9.17647058829813, 14.1666666666667, 5.5, 36.6666666666667, 4.23529411767606, 7.48387096779814, 5.33333333333333, 2.73244781783923, 2.13333333333333, 2.5, 11.5, 6.42857142862488, 3, 1.79310344827586, 8.00000000006652, 24.8571428567295, NA, 6.09523809523809, 68.5517241373807, 21.2500000003092, 6.21052631575142, 19.2857142858747, 15.1111111111111, 5.5714285714749, 42.6506024095189, 42.615384615003, 4.87499999996453, 13.3333333333333, 11.8709677420246, 8.83116883122224, 6.31578947364551, 9.83333333333333, 1.99999999996674, 7.69230769223881, 4.39999999994878, 17.3076923070723, 8.13333333333333, 16.461538461391, 1.65517241377981, 7.03999999986887, 10.2857142855432, 2.12500000003092, 1.14285714283814, 1.14285714286665, 13.1764705880548, 3.7826086956426, NA, 28.1333333333333, 3.75000000005457, 8.38709677406756, 6.83870967731663, 3.20610687022758, 6.49999999995271, 6.32432432430443, 13.8666666666667, 8.42857142843125, 2.83333333333333, 13.4210526314967, 3.33333333333333, 14.1538461537194, 0.933333333333333, 15.8333333333333, NA, 8.2962962962963, 5.31818181819589, 13.5714285715414, 10.1249999999263, 6.28571428576655, 39.260869565118, 26.6000000006193, 4.00000000005821, NA, 3.74193548389907, 5.35104364326849, 0.749999999994543, 12.0000000001118, 4.30769230765373, 6.57142857148322, 6.00000000002686, 13.3333333333333, 5.33333333333333, 16.1999999998114, 1.87499999998636, 13.1200000001222, 11.0588235294875, 2.0689655172746, 5.57142857140541, 17.1428571429997, 12.8571428572498, 10.4615384617258, 27.2727272730159, 25.5714285716412, 9.25000000013461, 12.3956043957313, 20.8235294114795, 4.54183266930586, 6.25000000009095, 14.000000000326, 1.33333333333333, 8.13333333333333, 7.15789473666668, NA, 62.6666666666667, 18.0000000003224, 0.117647058821918, 6.66666666666667, 43.8571428575075, 8.55172413806835, 5.40540540543942, 7.71428571434986, 11.0000000001601, 18.2857142858663, 52.6451612895318, 26.4, 5.6, 13.1612903226795, 5.93939393939394, 2.48366013073029, 1.53846153844776, 2.36363636363636, 4.14285714289159, 1.33333333333333, 9.23076923093455, NA, 2.83333333333333, 10.9230769229791, 2.19354838706382, 18.6666666666667, 3.57142857136918, 1.6, 8.50000000012369, 9.85714285722482, 11.2500000001637, 1.74999999994907, 6.367346938715, 33, 10.8749999999209, 23.9999999999393, 23.4838709679183, 3.73205741626378, 2.74999999997999, 20.6666666666667, 4.14814814814815, 13.2857142858248, 4.57142857142857, 15.2432432431953, 5.85714285719156, 10, 2.5882352940822, 20.5000000002983, 58.3749999995753, 1.875, 5.08108108101713, 13.5714285715414, 10.8235294116165, 2.66666666666667, 27.4782608692871, 30.9230769228, 17.6, 7.77272727274784, 15.7500000002292, 2.46753246754739, 2.77777777777778, 12.6428571428046, 3.6, 11.2222222222222, 6.79999999992084, 20.705882353083, 2.85714285716662, 14.1818181819683, 3.51515151515152, 11.7777777777778, 57.8888888888889, 3.9999999999709, 5.58620689660779, 15.4285714286997, 11.3548387097627, 1.00000000000832, 23.9999999999393, 25.3333333333333, 20.1250000002929, 4.88372093023256, 13.1111111111111, 2.57812500003752, 2.66666666666667, 12.0000000002794, 7.74999999994361, 23.2857142859079, 10.3333333333333, NA, 4.74999999996544, 12.545454545189, 1.74999999998727, 8, 55.999999999233, 2.12499999998454, 5.05882352944641, 24.5714285716329, 8.21052631573917, 1.99999999998545, 29.17322834643, 30.5060240963)
par(mfrow = c(2, 2))
hist(nph)
hist(dph)
qqnorm(nph)
qqline(nph)
qqnorm(dph)
qqline(dph)

Dies sind die Distributionen:

Da die Daten offensichtlich nicht normal verteilt sind, können viele statistische Tests nicht auf diese Daten angewendet werden. Aber vielleicht kann ich die Daten in eine Normalverteilung umwandeln?

Wie kann ich herausfinden, um welche Distribution es sich handelt?
Und wie kann ich die Daten auf eine Normalverteilung übertragen?

Ziel ist eine Varianzanalyse (MANOVA) oder eine solche (die hier dargestellten Daten sind die beiden abhängigen Variablen).

Die Daten scheinen eine Exponentialverteilung zu haben . Für die Transformation scheint ein einfaches Protokoll gut zu funktionieren.

hist(log(dph), freq=FALSE, ylim=c(0, .4))
lines(seq(-6, 6, by=0.01), dnorm(seq(-6, 6, by=0.01), 2, 1), col="red")
qqnorm(log(dph), ylim=c(0, 5))
qqline(log(dph), col="red")

$Y$$F_Y$$\Phi$

$X$

$Y$$\lambda$

das sieht ähnlich aus wie ein Logarithmus:

$\Phi^{-1}$

1. Wie kann ich herausfinden, um welche Distribution es sich handelt? Hier können Sie einige statistische Tests aus dem R-Paket fitdistrplus verwenden. Aus dem Paket finden Sie passende Kraterien, dh AIC, BIC usw. Die Anpassung der Verteilung Gamma oder Mor Verteilung wie "normal". Hier sind die Methoden.

   • MAXIMUM-LIKELIHOOD-SCHÄTZUNG
   • MOMENT PASSENDE SCHÄTZUNG
   • QUANTILE PASSENDE SCHÄTZUNG
   • MAXIMALE SCHÄTZUNG DER PASSGUTHEIT (Statistik der Anpassungsgüte und Kriterien für die Anpassungsgüte)

Schließlich finden Sie unter mehreren theoretischen Modellen das beste, das Ihren beobachteten Daten ähnelt.

2. Und wie kann ich die Daten auf eine Normalverteilung übertragen? Hier können Sie Box Cox Transfom verwenden

   Box_Cox_tran=function(x, lambda, jacobian.adjusted = FALSE) 
   {
     bc1 <- function(x, lambda) 
     {
       if (any(x[!is.na(x)] <= 0)) 
         stop("First argument must be strictly positive.")
       z <- if (abs(lambda) <= 1e-06) 
         log(x)
       else ((x^lambda) - 1)/lambda
       if (jacobian.adjusted == TRUE) {
         z * (exp(mean(log(x), na.rm = TRUE)))^(1 - lambda)
       }
       else z
     }
     out <- x
     out <- if (is.matrix(out) | is.data.frame(out)) {
       if (is.null(colnames(out))) 
         colnames(out) <- paste("Z", 1:dim(out)[2], sep = "")
       for (j in 1:ncol(out)) {
         out[, j] <- bc1(out[, j], lambda[j])
       }
       colnames(out) <- paste(colnames(out), round(lambda, 2), 
                              sep = "^")
       out
     }
     else bc1(out, lambda)
     out
   }
   

Hier ist mein Arbeitsbeispiel:

# ---------------------------------------------------------------------------------------------------------------------------
# Objective three starts Here
# (3)= Bivariate modelling of annual maxima using traditional approach 
# a)    First transform onbserved seasonal maxima into normal distribution using Box-Cox Transformations(x to z)
# b)    Finaly, Estimate Pearson coefficient using traditional bivariate normal distribution
# ---------------------------------------------------------------------------------------------------------------------------
rm(list=ls())
Sys.setenv(LANGUAGE="en")  # to set languege from Polish to English
setwd("C:/Users/sdebele/Desktop/From_oldcomp/Old_Computer/Seasonal_APP/Data/Data_Winter&Summer")
# Loading the required package here
library(MASS)
library(geoR)
require(scales)
require(plyr)
require(car)
library(ggplot2)
require(alr3)
library(ggplot2)
library(reshape2)
library(nortest)
require(AID)
require(distr)
require(fBasics)
# -----------------------------------------------------------------------------------------------------------------------------
# Here the Box-Cox Transformations equations
# x(lambda)=x^lamda-1/lambda, if lambda is not zero
# else log(x) if lambda=0
#--------------------------------------------------------------------------------------------------------------------------------
# Here is the data for six guaging stations of dependant ( 51.12% to 89.85%)
filenames=c("ZAPALOW.txt","GORLICZYNA.txt","SARZYNA.txt","OSUCHY.txt","HARASIUKI.txt","RUDJASTKOWSKA.txt")
# ---------------------------------------------------------------------------------------------------------------------------
# (1)= For ZAPALOW hydrological guaging stations starts here
# --------------------------------------------------------------------------------------------------------------------------------
ZAPALOW=read.table(file=filenames[1],head=T,sep="\t")
newZAPALOW <- na.omit(ZAPALOW) # to eliminte the missing value from the data sets 
Years=newZAPALOW$Year
    Winter=newZAPALOW$Winter
Summer=newZAPALOW$Sumer
    source("Box_Cox_Transfom.R") # R_script containing the tranformation equations 
    # estimation of lambda using AID R package 
    # boxcoxnc(Sumer, method="ac", lam=seq(-2,2,0.01), plotit=TRUE, rep=30, p.method="BY")
    # boxcoxnc(Winter, method="ac", lam=seq(-2,2,0.01), plotit=TRUE, rep=30, p.method="BY")
    Trans_Win=boxcoxnc(Winter)
    Trans_Sum=boxcoxnc(Summer)
    Winter_trans=Box_Cox_tran(Winter,Trans_Win$result[1,1],jacobian.adjusted=T)
Summer_trans=Box_Cox_tran(Summer,Trans_Sum$result[1,1],jacobian.adjusted=T)
    newZAPALOW[,4]=Winter_trans
    newZAPALOW[,5]=Summer_trans
    colnames(newZAPALOW)= c("Year","Winter " ,"Summer","Winter_Trans","Summer_Trans")
    par(mfrow=c(2,2))
    par("lwd"=2)
    ## Plot histogram with overlayed normal distribution.
    hist(newZAPALOW[,4],main="",xlab="Discharge",freq=FALSE,col="lightblue")
    curve(dnorm(x,mean=mean(newZAPALOW[,4]),sd=sd(newZAPALOW[,4])), add=TRUE, col="darkred",lwd=2)
    qq.plot(newZAPALOW[,4], dist= "norm", col=palette()[1], ylab="Sample Quantiles",
            main="Normal Probability Plot", pch=19)
    #b <- mydata[,c(2,3)] # select interesting columns
    result <- shapiro.test(newZAPALOW[,4]) # checking for normality test 
    result$p.value
ad.test(newZAPALOW[,4]) # checking for normality test 
## Plot histogram with overlayed normal distribution.
hist(newZAPALOW[,5],main="",xlab="Discharge",freq=FALSE,col="lightblue")
curve(dnorm(x,mean=mean(newZAPALOW[,5]),sd=sd(newZAPALOW[,5])), add=TRUE, col="darkred",lwd=2)
qq.plot(newZAPALOW[,5], dist= "norm", col=palette()[1], ylab="Sample Quantiles",
        main="Normal Probability Plot", pch=19)
result <- shapiro.test(newZAPALOW[,5]) # checking for normality test 
result$p.value
ad.test(newZAPALOW[,5]) # checking for normality test 
write.table(newZAPALOW, "newZAPALOW_trans.txt", sep="\t")
For sure this will be helpfull for you.