Percentile example for Stats.SE

percentile.r

# Get data
x <- c(93150, 93116, 93096, 93085, 92923, 92823, 92745, 92150, 91785, 91775,
91775, 91735, 91727, 91633, 91616, 91604, 91587, 91579, 91488, 91427, 91398,
91339, 91338, 91290, 91268, 91084, 91072, 90909, 86164, 85372, 83835, 83428,
81372, 81281, 81238, 81195, 81131, 81030, 81011, 80730, 80721, 80682, 80666,
80585, 80565, 80534, 80497, 80464, 80374, 80226, 80223, 80178, 80178, 80147,
80137, 80111, 80048, 80027, 79948, 79902, 79818, 79785, 79752, 79675, 79651,
79620, 79586, 79535, 79491, 79388, 79277, 79269, 79254, 79194, 79191, 79180,
79170, 79162, 79154, 79142, 79129, 79090, 79062, 79039, 79011, 78981, 78979,
78936, 78923, 78913, 78829, 78809, 78742, 78735, 78725, 78618, 78606, 78577,
78527, 78509, 78491, 78448, 78289, 78284, 78277, 78238, 78171, 78156, 77998,
77998, 77978, 77956, 77925, 77848, 77846, 77759, 77729, 77695, 77677, 77382,
70473, 70449, 69886, 69767, 69704, 69573, 69479, 69398, 69328, 69311, 69265,
69178, 69162, 69104, 69100, 69072, 69062, 68971, 68944, 68929, 68924, 68904,
68879, 68877, 68799, 68755, 68726, 68666, 68623, 68588, 68547, 68458, 68457,
68453, 68438, 68438, 68429, 68426, 68394, 68374, 68363, 68357, 68337, 68300,
68256, 68250, 68228, 68216, 68180, 68149, 68124, 68114, 68060, 68029, 68029,
68025, 68004, 67996, 67981, 67964, 67938, 67925, 67914, 67901, 67853, 67819,
67818, 67788, 67770, 67767, 67688, 67670, 67669, 67629, 67618, 67609, 67602,
67583, 67540, 67479, 67475, 67470, 67433, 67420, 67387, 67343, 67339, 67337,
67315, 67273, 67224, 67208, 67160, 67137, 67102, 67045, 66449, 66408, 66338,
66211, 63784, 63557, 63091, 63021, 62895, 62663, 62182, 62079, 62044, 61907,
61888, 61856, 61847, 61792, 61764, 61683, 61641, 61612, 61514, 61511, 61503,
61411, 61263, 61248, 60965, 60941, 60907, 60876, 60773, 60669, 60537, 60525,
60387, 60194, 59673, 59576, 59561, 59556, 57652, 57458, 57308, 57264, 57158,
57106, 56288, 56245, 56054, 56031, 55930, 55841, 55533, 55532, 55316, 55281,
55230, 55196, 55111, 55101, 50957, 50870, 49580, 48353, 21349, 21319, 21288,
21274, 21270, 21255, 21232, 21208, 21196, 21184, 21164, 21150, 21149, 21143,
21129, 21108, 21100, 21072, 21043, 20934, 20912, 20908, 20882, 20871, 20858,
20843, 20839, 20834, 20800, 20790, 20788, 20757, 20752, 20748, 20744, 20739,
20721, 20712, 20710, 20671, 20620, 20575, 20572, 20567, 20551, 20536, 20522,
20510, 20484, 20430, 20415, 20398, 20368, 20362, 20357, 20349, 20347, 20341,
20338, 20335, 20335, 20334, 20332, 20332, 20332, 20330, 20326, 20324, 20323,
20307, 20304, 20299, 20297, 20292, 20282, 20280, 20275, 20270, 20270, 20258,
20257, 20257, 20256, 20254, 20252, 20251, 20247, 20243, 20231, 20229, 20223,
20223, 20221, 20219, 20217, 20215, 20212, 20211, 20210, 20208, 20202, 20202,
20202, 20197, 20192, 20190, 20190, 20187, 20186, 20184, 20179, 20175, 20175,
20170, 20170, 20170, 20166, 20162, 20158, 20157, 20157, 20156, 20153, 20152,
20151, 20151, 20148, 20146, 20141, 20141, 20139, 20137, 20133, 20132, 20130,
20129, 20124, 20124, 20123, 20114, 20109, 20104, 20104, 20094, 20092, 20091,
20088, 20086, 20085, 20084, 20083, 20078, 20076, 20076, 20070, 20068, 20065,
20060, 20052, 20049, 20045, 20041, 20040, 20039, 20037, 20036, 20036, 20032,
20032, 20021, 20020, 20017, 20009, 20007, 20007, 20004, 20004, 20002, 19989,
19985, 19974, 19973, 19973, 19967, 19961, 19960, 19959, 19957, 19953, 19952,
19950, 19943, 19942, 19940, 19940, 19939, 19937, 19936, 19935, 19935, 19925,
19921, 19920, 19914, 19908, 19907, 19900, 19900, 19900, 19899, 19899, 19898,
19898, 19894, 19893, 19891, 19891, 19888, 19888, 19888, 19883, 19883, 19882,
19882, 19880, 19878, 19875, 19875, 19874, 19873, 19871, 19867, 19864, 19862,
19861, 19860, 19857, 19856, 19854, 19854, 19848, 19848, 19844, 19842, 19840,
19840, 19835, 19833, 19831, 19830, 19828, 19826, 19820, 19817, 19812, 19812,
19811, 19809, 19805, 19799, 19792, 19789, 19788, 19785, 19780, 19770, 19765,
19763, 19762, 19754, 19743, 19742, 19738, 19737, 19735, 19731, 19724, 19722,
19721, 19711, 19710, 19699, 19698, 19697, 19695, 19692, 19687, 19683, 19672,
19670, 19665, 19664, 19660, 19654, 19651, 19644, 19643, 19643, 19641, 19640,
19620, 19619, 19618, 19617, 19614, 19613, 19608, 19607, 19607, 19605, 19579,
19575, 19568, 19556, 19553, 19553, 19551, 19550, 19548, 19536, 19535, 19500,
19500, 19473, 19462, 19461, 19455, 19451, 19391, 19388, 19386, 19384, 19375,
19371, 19353, 19338, 19318, 19273, 19271, 19269, 19265, 19258, 19230, 19228,
19222, 19221, 19221, 19215, 19196, 19180, 19177, 19166, 19161, 19154, 19148,
19138, 19134, 19129, 19116, 19113, 19107, 19105, 19102, 19096, 19092, 19088,
19085, 19085, 19083, 19072, 19067, 19066, 19061, 19058, 19050, 19049, 19045,
19044, 19043, 19043, 19032, 19005, 18996, 18968, 18957, 18948, 18938, 18936,
18920, 18920, 18913, 18897, 18897, 18892, 18884, 18878, 18878, 18878, 18871,
18870, 18869, 18866, 18864, 18864, 18864, 18862, 18862, 18862, 18860, 18859,
18858, 18858, 18853, 18852, 18852, 18851, 18851, 18848, 18847, 18846, 18846,
18846, 18845, 18845, 18844, 18842, 18841, 18841, 18840, 18840, 18837, 18837,
18836, 18836, 18835, 18834, 18833, 18831, 18830, 18830, 18829, 18829, 18829,
18828, 18826, 18825, 18823, 18822, 18822, 18822, 18821, 18821, 18821, 18819,
18819, 18818, 18816, 18813, 18812, 18812, 18812, 18812, 18810, 18809, 18809,
18809, 18809, 18808, 18808, 18806, 18805, 18805, 18804, 18803, 18802, 18802,
18801, 18801, 18801, 18801, 18800, 18799, 18799, 18798, 18797, 18796, 18796,
18796, 18795, 18795, 18793, 18792, 18792, 18792, 18791, 18791, 18791, 18789,
18789, 18789, 18788, 18787, 18783, 18782, 18782, 18782, 18781, 18781, 18780,
18780, 18779, 18779, 18779, 18779, 18778, 18777, 18777, 18776, 18775, 18773,
18773, 18772, 18772, 18771, 18770, 18770, 18770, 18769, 18769, 18767, 18767,
18766, 18762, 18762, 18761, 18761, 18761, 18758, 18757, 18757, 18756, 18756,
18755, 18751, 18750, 18749, 18749, 18749, 18746, 18746, 18746, 18746, 18746,
18745, 18745, 18744, 18744, 18743, 18742, 18739, 18739, 18738, 18737, 18736,
18734, 18729, 18729, 18727, 18727, 18723, 18723, 18723, 18723, 18721, 18721,
18721, 18719, 18719, 18719, 18719, 18718, 18717, 18716, 18714, 18710, 18710,
18710, 18708, 18707, 18704, 18702, 18701, 18701, 18699, 18695, 18694, 18692,
18691, 18690, 18689, 18689, 18686, 18684, 18683, 18681, 18679, 18675, 18675,
18672, 18665, 18665, 18665, 18658, 18656, 18655, 18654, 18654, 18654, 18652,
18650, 18649, 18646, 18645, 18642, 18640, 18638, 18638, 18636, 18633, 18633,
18631, 18630, 18629, 18625, 18625, 18623, 18622, 18619, 18617, 18617, 18616,
18616, 18614, 18614, 18614, 18614, 18611, 18611, 18609, 18609, 18600, 18597,
18596, 18594, 18593, 18591, 18589, 18585, 18580, 18578, 18578, 18578, 18572,
18569, 18567, 18566, 18565, 18563, 18559, 18559, 18557, 18557, 18554, 18551,
18548, 18547, 18545, 18544, 18544, 18541, 18539, 18539, 18536, 18535, 18531,
18529, 18526, 18524, 18524, 18522, 18517, 18515, 18503, 18502, 18497, 18496,
18496, 18496, 18495, 18493, 18492, 18487, 18487, 18486, 18486, 18485, 18482,
18479, 18473, 18471, 18470, 18464, 18463, 18460, 18459, 18454, 18454, 18452,
18450, 18447, 18446, 18442, 18442, 18442, 18440, 18439, 18434, 18432, 18427,
18426, 18425, 18421, 18416, 18414, 18408, 18407, 18407, 18407, 18403, 18402,
18398, 18397, 18396, 18394, 18393, 18392, 18391, 18390, 18383, 18378, 18357,
18356, 18354, 18349, 18342, 18341, 18338, 18337, 18336, 18333, 18328, 18319,
18314, 18313, 18302, 18295, 18295, 18291, 18291, 18288, 18284, 18281, 18278,
18276, 18272, 18269, 18268, 18263, 18262, 18261, 18259, 18257, 18251, 18247,
18240, 18240, 18238, 18235, 18235, 18234, 18232, 18225, 18222, 18221, 18214,
18214, 18213, 18213, 18210, 18210, 18206, 18205, 18204, 18203, 18194, 18192,
18191, 18190, 18187, 18184, 18179, 18179, 18179, 18175, 18171, 18170, 18156,
18152, 18151, 18151, 18149, 18149, 18148, 18148, 18147, 18146, 18140, 18139,
18137, 18137, 18136, 18135, 18135, 18134, 18133, 18133, 18128, 18128, 18127,
18127, 18125, 18122, 18121, 18120, 18120, 18119, 18117, 18110, 18108, 18108,
18099, 18097, 18096, 18096, 18095, 18087, 18085, 18084, 18083, 18067, 18060,
18056, 18056, 18054, 18053, 18050, 18049, 18048, 18038, 18036, 18033, 18033,
18028, 18027, 18025, 18023, 18022, 18010, 18010, 18010, 18000, 17995, 17983,
17980, 17978, 17975, 17974, 17974, 17968, 17968, 17967, 17965, 17964, 17962,
17961, 17956, 17955, 17943, 17938, 17935, 17934, 17933, 17932, 17930, 17925,
17923, 17919, 17912, 17912, 17904, 17897, 17896, 17894, 17884, 17880, 17874,
17872, 17870, 17865, 17857, 17856, 17854, 17854, 17845, 17843, 17841, 17836,
17834, 17831, 17831, 17828, 17822, 17821, 17821, 17816, 17804, 17803, 17799,
17798, 17794, 17794, 17793, 17790, 17787, 17786, 17783, 17782, 17781, 17777,
17777, 17777, 17772, 17772, 17771, 17766, 17766, 17758, 17750, 17747, 17743,
17715, 17699, 17694, 17683, 17682, 17681, 17668, 17668, 17630, 17619, 17617,
17610, 17609, 17609, 17607, 17607, 17599, 17587, 17565, 17551, 17542, 17532,
17531, 17514, 17514, 17512, 17509, 17503, 17483, 17481, 17475, 17465, 17463,
17449, 17433, 17404, 17397, 17356, 17356, 17214, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)

# R Quantile functions
help(quantile) # Note the 9 quantile algorithms
rquantileest <- sapply(1:9, function(TYPE) quantile(x, .95, type=TYPE)) 
rquantileest
sapply(rquantileest, function(X) mean(x <= X))


# Estimate of the 95th percentile if the data was normally distributed
qnormest <- qnorm(.95, mean(x), sd(x))
qnormest
mean(x <= qnormest)

# Is the data normally distributed?
plot(density(x))