[R] Empirical density estimation

[Jim Lemon]

Hi Christofer,
You may be looking for ecdf (stats) for a start, then working out a
way to translate the cumulative density values into probability
values.

Jim


On Mon, Mar 12, 2018 at 5:45 AM, Christofer Bogaso
<bogaso.christofer at gmail.com> wrote:
> Hi,
>
> Let say I have below vector of data-points :
>
> Dat = c(-0.444444444444444, -0.25, -0.237449799196787, -0.227467046669042,
>
> -0.227454464682363, -0.22, -0.214876033057851, -0.211781206171108,
>
> -0.199891067538126, -0.192920353982301, -0.192307692307692, -0.186046511627907,
>
> -0.184418145956608, -0.181818181818182, -0.181818181818182, -0.181266261925412,
>
> -0.181003118503119, -0.179064587973274, -0.178217821782178, -0.17809021675454,
>
> -0.177685950413223, -0.177570093457944, -0.176470588235294, -0.176470588235294,
>
> -0.174825741611282, -0.168021680216802, -0.166666666666667, -0.166666666666667,
>
> -0.166380789022298, -0.164209115281501, -0.164011246485473, -0.162689804772234,
>
> -0.162361623616236, -0.160161507402423, -0.16, -0.155038759689922,
>
> -0.154172560113154, -0.15311004784689, -0.151515151515152, -0.151462994836489,
>
> -0.151098901098901, -0.150537634408602, -0.150442477876106, -0.150406504065041,
>
> -0.149904214559387, -0.149882903981265, -0.149797570850202, -0.148496240601504,
>
> -0.148325358851675, -0.147540983606557, -0.147239263803681, -0.146989966555184,
>
> -0.14622641509434, -0.146095717884131, -0.145994832041344, -0.14572864321608,
>
> -0.145161290322581, -0.144292237442922, -0.144144144144144, -0.144021739130435,
>
> -0.14375, -0.142212189616253, -0.141122913505311, -0.140324963072378,
>
> -0.139344262295082, -0.13884007029877, -0.138356164383562, -0.137626262626263,
>
> -0.137142857142857, -0.136690647482014, -0.136577708006279, -0.136363636363636,
>
> -0.136094674556213, -0.135879774577332, -0.135586319218241, -0.135135135135135,
>
> -0.132780082987552, -0.132209405501331, -0.132023755139333, -0.131233595800525,
>
> -0.130434782608696, -0.130434782608696, -0.130268199233717, -0.128813559322034,
>
> -0.1284046692607, -0.128205128205128, -0.128182616330114, -0.127937336814621,
>
> -0.126283367556468, -0.125853658536585, -0.125448028673835, -0.125425564840607,
>
> -0.125311203319502, -0.125, -0.124401913875598, -0.124248496993988,
>
> -0.124031007751938, -0.123572170301142, -0.123188405797102, -0.122905027932961,
>
> -0.121666666666667, -0.121573685907772, -0.120658135283364, -0.120540019286403,
>
> -0.119858156028369, -0.11965811965812, -0.11965811965812, -0.119565217391304,
>
> -0.118942731277533, -0.117820324005891, -0.116257947320618, -0.115789473684211,
>
> -0.115683584819387, -0.115384615384615, -0.115281501340483, -0.114492753623188,
>
> -0.114357262103506, -0.114285714285714, -0.114035087719298, -0.113181972212809,
>
> -0.112790697674419, -0.112781954887218, -0.112195121951219, -0.112191473448018,
>
> -0.111111111111111, -0.111111111111111, -0.110813226094727, -0.110384300899428,
>
> -0.110147441457069, -0.110137672090113, -0.109913793103448, -0.109792284866469,
>
> -0.109375, -0.10919540229885, -0.109112709832134, -0.10844250363901,
>
> -0.107776617954071, -0.10752688172043, -0.107317073170732, -0.106674272675414,
>
> -0.106382978723404, -0.106100795755968, -0.106060606060606, -0.10595160235448,
>
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>
> -0.103916449086162, -0.103723404255319, -0.103448275862069, -0.102737680438029,
>
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>
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>
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>
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>
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>
> -0.097345132743363, -0.0971472629144179, -0.0971438645980254,
>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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> -0.0360915492957746, -0.0357142857142857, -0.0356663184599313,
>
> -0.0356413696552528, -0.035513103110458, -0.0353194103194103,
>
> -0.0352112676056338, -0.0350119904076739, -0.0349794238683129,
>
> -0.0349373764007909, -0.0349091600875106, -0.0347826086956522,
>
> -0.0347728547392037, -0.0347682119205298, -0.0346083788706739,
>
> -0.0344706296166022, -0.0344421548425081, -0.0341176470588236,
>
> -0.0338983050847458, -0.033457249070632, -0.0334208223972004,
>
> -0.0333333333333334, -0.0333333333333333, -0.0329670329670331,
>
> -0.0329144225014961, -0.0326797385620915, -0.0323033707865168,
>
> -0.0322118826055834, -0.0321750321750322, -0.0320890635232481,
>
> -0.0318302387267905, -0.0316666666666666, -0.0315586914688903,
>
> -0.0312606184165817, -0.030881017257039, -0.0308764940239045,
>
> -0.0305419952434597, -0.030406198638178, -0.0299651567944252,
>
> -0.029945999018164, -0.0298786181139121, -0.0295741147960329,
>
> -0.0293917033546227, -0.029171528588098, -0.0291327913279132,
>
> -0.0290497291974397, -0.0288721376760064, -0.0287704170466792,
>
> -0.0286236297198539, -0.0285714285714286, -0.0277575837684224,
>
> -0.0277085471338513, -0.0275897304892068, -0.0275526742301458,
>
> -0.027027027027027, -0.0270270270270269, -0.0269087523277468,
>
> -0.0268918695148203, -0.02676704307821, -0.026454253142356, -0.0263157894736842,
>
> -0.0263157894736842, -0.0261660978384529, -0.025974025974026,
>
> -0.0257503107796129, -0.0255319148936171, -0.0254237288135594,
>
> -0.025297619047619, -0.0249174422095467, -0.0248888888888889,
>
> -0.024767619719967, -0.0246053853296194, -0.0245269796776454,
>
> -0.024390243902439, -0.0241935483870968, -0.0238907849829351,
>
> -0.0238153295944078, -0.0234413496961306, -0.0232558139534884,
>
> -0.0232558139534883, -0.0230392156862745, -0.0230360307147077,
>
> -0.0228847365106026, -0.0225806451612903, -0.0224519940915805,
>
> -0.0214786344110332, -0.0212360867018161, -0.0205245153933865,
>
> -0.0204170602339606, -0.0200986321764215, -0.0200729927007299,
>
> -0.0199828473413379, -0.0194174757281553, -0.0193536931818183,
>
> -0.0192885771543086, -0.019222732971166, -0.0191414840759143,
>
> -0.0189573459715641, -0.0188902007083826, -0.0186903321231681,
>
> -0.0184456468273487, -0.0183066361556064, -0.0182166826462128,
>
> -0.0181149908112366, -0.0179372197309418, -0.0179172441100772,
>
> -0.0178571428571429, -0.0174672489082969, -0.0174216027874564,
>
> -0.0171428571428572, -0.017017253604349, -0.0169252468265163,
>
> -0.0165094339622642, -0.0158730158730158, -0.0158415841584159,
>
> -0.0157247037374659, -0.0157089706490286, -0.0156250000000001,
>
> -0.0153846153846153, -0.0151668351870576, -0.0151589242053789,
>
> -0.0150489089541008, -0.0150262202501008, -0.0150081124932396,
>
> -0.0148196281468128, -0.0144251166737377, -0.0142857142857142,
>
> -0.0140638734251392, -0.0136986301369863, -0.0133333333333333,
>
> -0.0129464285714286, -0.0129449838187702, -0.0127813811522321,
>
> -0.0126030053320408, -0.0125721665147373, -0.0125, -0.0122160435399906,
>
> -0.0122116689280869, -0.0121019108280255, -0.0118747750989563,
>
> -0.0118277953189996, -0.0117107942973524, -0.0115172759138707,
>
> -0.0114087997381585, -0.0113924050632912, -0.0111524163568772,
>
> -0.0111248454882571, -0.0111111111111111, -0.0102570933795125,
>
> -0.0102040816326532, -0.00963463463463469, -0.00958657878969439,
>
> -0.00941028858218319, -0.00874453466583389, -0.00779588944011335,
>
> -0.00713620850139625, -0.00710720027075056, -0.00709219858156026,
>
> -0.00624999999999998, -0.00551977920883173, -0.00521499557217353,
>
> -0.00453998797354176, -0.00444444444444444, -0.00166389351081533,
>
> -0.00118483412322285, -0.00100704934541787, -0.000937500000000036,
>
> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
>
> 0.000218031178458569, 0.000796495420151402, 0.00167130919220062,
>
> 0.00190476190476193, 0.00350058343057173, 0.00363914958820145,
>
> 0.00432900432900424, 0.00456037942356804, 0.00477446915441642,
>
> 0.0050825509873745, 0.00525691029336935, 0.00603318250377083,
>
> 0.00652173913043472, 0.00733192494097176, 0.00747663551401869,
>
> 0.00760456273764256, 0.00812529439472442, 0.00991231414410967,
>
> 0.0101685066821615, 0.0106182565507793, 0.0109070034443169, 0.0115183246073298,
>
> 0.0115442244823827, 0.0127659574468085, 0.0128076846107665, 0.0135135135135135,
>
> 0.0140845070422535, 0.0150730098916627, 0.0159362549800796, 0.0172413793103449,
>
> 0.0176899063475547, 0.0186954715413378, 0.0187765706188003, 0.0195757403189066,
>
> 0.019607843137255, 0.0199999999999999, 0.0210526315789473, 0.0221979621542939,
>
> 0.0239410681399632, 0.0239999999999999, 0.025149051490515, 0.0260869565217392,
>
> 0.0262475696694749, 0.028180542563143, 0.0285714285714286, 0.0303030303030302,
>
> 0.0315904139433552, 0.0341864716636198, 0.0375782881002089, 0.038479809976247,
>
> 0.0387596899224806, 0.0416666666666667, 0.0428100987925357, 0.0428134556574923,
>
> 0.0437201907790144, 0.0451127819548872, 0.0460251046025105, 0.0487779511180447,
>
> 0.048975188781014, 0.0529872938632063, 0.0562390158172233, 0.0589335827876521,
>
> 0.0617551462621885, 0.0628115653040877, 0.0671812464265294, 0.0721784776902887,
>
> 0.0736842105263157, 0.0833333333333334, 0.083862394802894, 0.0970464135021097,
>
> 0.0971168437025795, 0.102272727272727, 0.111111111111111, 0.117117117117117,
>
> 0.123532699832309, 0.141304347826087, 0.179487179487179, 0.191268191268191,
>
> 0.205128205128205, 0.219020172910663, 0.271590909090909, 0.333333333333333
>
> )
>
>
> Now I want to estimate empirical PDF for interval of (-1, 1) including
> all points of Dat
>
> I have looked into the density() function, however it appears that,
> empirical density is estimated for equally distant points, which not
> necessarily contains actual supplied points (in my case, Dat)
>
> Is there any option to achieve the same?
>
> Thanks for your pointer.
>
> ______________________________________________
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