R/convertToPDFe.R

In PDFEstimator: Multivariate Nonparametric Probability Density Estimator

convertToPDFe <- function(sample, x, pdf) {
  
  if (!is.numeric(sample)) {
    stop("a numeric vector of sample data is required")
  }
  
  if (!is.numeric(x)) {
    stop("a numeric vector of x values is required")
  }
  
  if (!is.numeric(pdf)) {
    stop("a numeric vector of pdf values is required")
  }
  
  if (min(sample) < min(x)) {
    x = c(min(sample), x)
    pdf = c(0, pdf)
  }
  
  if (max(sample) > max(x)) {
    x = c(x, max(sample))
    pdf = c(pdf, 0)
  }
  
  cdf = cumsum(pdf) / sum(pdf)
  
  sample = sort(sample)
  sqrSize = length(sample)
  position = 1:sqrSize / (sqrSize + 1)
  
  r = approx(x, y = cdf, xout = sample);
  minNumber = -.Machine$double.xmax
  scores = c(minNumber, -6.474,-6.4649,-6.4557,-6.4466,-6.4375,-6.4283,-6.4192,-6.4101,-6.4009,-6.3918,-6.3827,-6.3735,-6.3644,-6.3553,-6.3462,-6.337,-6.3279,-6.3188,-6.3096,-6.3005,-6.2914,-6.2822,-6.2731,-6.264,-6.2548,-6.2457,-6.2366,-6.2274,-6.2183,-6.2092,-6.2,-6.1909,-6.1818,-6.1727,-6.1635,-6.1544,-6.1453,-6.1361,-6.127,-6.1179,-6.1087,-6.0996,-6.0905,-6.0813,-6.0722,-6.0631,-6.0539,-6.0448,-6.0357,-6.0265,-6.0174,-6.0083,-5.9991,-5.99,-5.9809,-5.9718,-5.9626,-5.9535,-5.9444,-5.9352,-5.9261,-5.917,-5.9078,-5.8987,-5.8896,-5.8804,-5.8713,-5.8622,-5.853,-5.8439,-5.8348,-5.8256,-5.8165,-5.8074,-5.7983,-5.7891,-5.78,-5.7709,-5.7617,-5.7526,-5.7435,-5.7343,-5.7252,-5.7161,-5.7069,-5.6978,-5.6887,-5.6795,-5.6704,-5.6613,-5.6521,-5.643,-5.6339,-5.6248,-5.6156,-5.6065,-5.5974,-5.5882,-5.5791,-5.57,-5.5608,-5.5517,-5.5426,-5.5334,-5.5243,-5.5152,-5.506,-5.4969,-5.4878,-5.4786,-5.4695,-5.4604,-5.4513,-5.4421,-5.433,-5.4239,-5.4147,-5.4056,-5.3965,-5.3873,-5.3782,-5.3691,-5.3599,-5.3508,-5.3417,-5.3325,-5.3234,-5.3143,-5.3051,-5.296,-5.2869,-5.2777,-5.2686,-5.2595,-5.2504,-5.2412,-5.2321,-5.223,-5.2138,-5.2047,-5.1956,-5.1864,-5.1773,-5.1682,-5.159,-5.1499,-5.1408,-5.1316,-5.1225,-5.1134,-5.1042,-5.0951,-5.086,-5.0769,-5.0677,-5.0586,-5.0495,-5.0403,-5.0312,-5.0221,-5.0129,-5.0038,-4.9947,-4.9855,-4.9764,-4.9673,-4.9581,-4.949,-4.9399,-4.9307,-4.9216,-4.9125,-4.9034,-4.8942,-4.8851,-4.876,-4.8668,-4.8577,-4.8486,-4.8394,-4.8303,-4.8212,-4.812,-4.8029,-4.7938,-4.7846,-4.7755,-4.7664,-4.7572,-4.7481,-4.739,-4.7299,-4.7207,-4.7116,-4.7025,-4.6933,-4.6842,-4.6751,-4.6659,-4.6568,-4.6477,-4.6385,-4.6294,-4.6203,-4.6111,-4.602,-4.5929,-4.5837,-4.5746,-4.5655,-4.5563,-4.5472,-4.5381,-4.529,-4.5198,-4.5107,-4.5016,-4.4924,-4.4833,-4.4742,-4.465,-4.4559,-4.4468,-4.4376,-4.4285,-4.4194,-4.4102,-4.4011,-4.392,-4.3828,-4.3737,-4.3646,-4.3555,-4.3463,-4.3372,-4.3281,-4.3189,-4.3098,-4.3007,-4.2915,-4.2824,-4.2733,-4.2641,-4.255,-4.2459,-4.2367,-4.2276,-4.2185,-4.2093,-4.2002,-4.1911,-4.182,-4.1728,-4.1637,-4.1546,-4.1454,-4.1363,-4.1272,-4.118,-4.1089,-4.0998,-4.0906,-4.0815,-4.0724,-4.0632,-4.0541,-4.045,-4.0358,-4.0267,-4.0176,-4.0085,-3.9993,-3.9902,-3.9811,-3.9719,-3.9628,-3.9537,-3.9445,-3.9354,-3.9263,-3.9171,-3.908,-3.8989,-3.8897,-3.8806,-3.8715,-3.8623,-3.8532,-3.8441,-3.835,-3.8258,-3.8167,-3.8076,-3.7984,-3.7893,-3.7802,-3.771,-3.7619,-3.7528,-3.7436,-3.7345,-3.7254,-3.7162,-3.7071,-3.698,-3.6888,-3.6797,-3.6706,-3.6614,-3.6523,-3.6432,-3.6341,-3.6249,-3.6158,-3.6067,-3.5975,-3.5884,-3.5793,-3.5701,-3.561,-3.5519,-3.5427,-3.5336,-3.5245,-3.5153,-3.5062,-3.4971,-3.4879,-3.4788,-3.4697,-3.4606,-3.4514,-3.4423,-3.4332,-3.424,-3.4149,-3.4058,-3.3966,-3.3875,-3.3784,-3.3692,-3.3601,-3.351,-3.3418,-3.3327,-3.3236,-3.3144,-3.3053,-3.2962,-3.2871,-3.2779,-3.2688,-3.2597,-3.2505,-3.2414,-3.2323,-3.2231,-3.214,-3.2049,-3.1957,-3.1866,-3.1775,-3.1683,-3.1592,-3.1501,-3.1409,-3.1318,-3.1227,-3.1136,-3.1044,-3.0953,-3.0862,-3.077,-3.0679,-3.0588,-3.0496,-3.0405,-3.0314,-3.0222,-3.0131,-3.004,-2.9948,-2.9857,-2.9766,-2.9674,-2.9583,-2.9492,-2.94,-2.9309,-2.9218,-2.9127,-2.9035,-2.8944,-2.8853,-2.8761,-2.867,-2.8579,-2.8487,-2.8396,-2.8305,-2.8213,-2.8122,-2.8031,-2.7939,-2.7848,-2.7757,-2.7665,-2.7574,-2.7483,-2.7392,-2.73,-2.7209,-2.7118,-2.7026,-2.6935,-2.6844,-2.6752,-2.6661,-2.657,-2.6478,-2.6387,-2.6296,-2.6204,-2.6113,-2.6022,-2.593,-2.5839,-2.5748,-2.5657,-2.5565,-2.5474,-2.5383,-2.5291,-2.52,-2.5109,-2.5017,-2.4926,-2.4835,-2.4743,-2.4652,-2.4561,-2.4469,-2.4378,-2.4287,-2.4195,-2.4104,-2.4013,-2.3922,-2.383,-2.3739,-2.3648,-2.3556,-2.3465,-2.3374,-2.3282,-2.3191,-2.31,-2.3008,-2.2917,-2.2826,-2.2734,-2.2643,-2.2552,-2.246,-2.2369,-2.2278,-2.2187,-2.2095,-2.2004,-2.1913,-2.1821,-2.173,-2.1639,-2.1547,-2.1456,-2.1365,-2.1273,-2.1182,-2.1091,-2.0999,-2.0908,-2.0817,-2.0725,-2.0634,-2.0543,-2.0451,-2.036,-2.0269,-2.0178,-2.0086,-1.9995,-1.9904,-1.9812,-1.9721,-1.963,-1.9538,-1.9447,-1.9356,-1.9264,-1.9173,-1.9082,-1.899,-1.8899,-1.8808,-1.8716,-1.8625,-1.8534,-1.8443,
             -1.8351,-1.826,-1.8169,-1.8077,-1.7986,-1.7895,-1.7803,-1.7712,-1.7621,            -1.7529,-1.7438,-1.7347,-1.7255,-1.7164,-1.7073,-1.6981,-1.689,-1.6799,-1.6708,-1.6616,-1.6525,-1.6434,-1.6342,-1.6251,-1.616,-1.6068,-1.5977,-1.5886,-1.5794,-1.5703,-1.5612,-1.552,-1.5429,-1.5338,-1.5246,-1.5155,-1.5064,-1.4973,-1.4881,-1.479,-1.4699,-1.4607,-1.4516,-1.4425,-1.4333,-1.4242,-1.4151,-1.4059,-1.3968,-1.3877,-1.3785,-1.3694,-1.3603,-1.3511,-1.342,-1.3329,-1.3237,-1.3146,-1.3055,-1.2964,-1.2872,-1.2781,-1.269,-1.2598,-1.2507,-1.2416,-1.2324,-1.2233,-1.2142,-1.205,-1.1959,-1.1868,-1.1776,-1.1685,-1.1594,-1.1502,-1.1411,-1.132,-1.1229,-1.1137,-1.1046,-1.0955,-1.0863,-1.0772,-1.0681,-1.0589,-1.0498,-1.0407,-1.0315,-1.0224,-1.0133,-1.0041,-0.99501,-0.98588,-0.97675,-0.96762,-0.95848,-0.94935,-0.94022,-0.93109,-0.92196,-0.91283,-0.90369,-0.89456,-0.88543,-0.8763,-0.86717,-0.85804,-0.8489,-0.83977,-0.83064,-0.82151,-0.81238,-0.80325,-0.79411,-0.78498,-0.77585,-0.76672,-0.75759,-0.74846,-0.73932,-0.73019,-0.72106,-0.71193,-0.7028,-0.69367,-0.68454,-0.6754,-0.66627,-0.65714,-0.64801,-0.63888,-0.62975,-0.62061,-0.61148,-0.60235,-0.59322,-0.58409,-0.57496,-0.56582,-0.55669,-0.54756,-0.53843,-0.5293,-0.52017,-0.51103,-0.5019,-0.49277,-0.48364,-0.47451,-0.46538,-0.45624,-0.44711,-0.43798,-0.42885,-0.41972,-0.41059,-0.40145,-0.39232,-0.38319,-0.37406,-0.36493,-0.3558,-0.34666,-0.33753,-0.3284,-0.31927,-0.31014,-0.30101,-0.29187,-0.28274,-0.27361,-0.26448,-0.25535,-0.24622,-0.23708,-0.22795,-0.21882,-0.20969,-0.20056,-0.19143,-0.18229,-0.17316,-0.16403,-0.1549,-0.14577,-0.13664,-0.12751,-0.11837,-0.10924,-0.10011,-0.090979,-0.081847,0,5.0)
  surds = c(0, 1.7764e-15,1.761e-06,3.7079e-06,5.8413e-06,8.1782e-06,1.0748e-05,1.3589e-05,1.6745e-05,2.0266e-05,2.4202e-05,2.8601e-05,3.3513e-05,3.8979e-05,4.5038e-05,5.1718e-05,5.9042e-05,6.7022e-05,7.5664e-05,8.4965e-05,9.4915e-05,0.0001055,0.0001167,0.0001285,0.00014087,0.00015379,0.00016722,0.00018116,0.00019556,0.00021042,0.0002257,0.00024139,0.00025746,0.00027389,0.00029066,0.00030775,0.00032514,0.00034281,0.00036074,0.00037891,0.00039729,0.00041586,0.00043462,0.00045352,0.00047256,0.00049171,0.00051095,0.00053026,0.00054963,0.00056903,0.00058845,0.00060788,0.00062728,0.00064667,0.00066601,0.00068529,0.00070452,0.00072367,0.00074275,0.00076173,0.00078063,0.00079942,0.00081812,0.00083671,0.0008552,0.00087359,0.00089188,0.00091006,0.00092814,0.00094613,0.00096403,0.00098184,0.00099957,0.0010172,0.0010348,0.0010523,0.0010698,0.0010872,0.0011046,0.0011219,0.0011392,0.0011565,0.0011738,0.001191,0.0012083,0.0012255,0.0012428,0.00126,0.0012773,0.0012946,0.001312,0.0013293,0.0013467,0.0013641,0.0013816,0.0013991,0.0014166,0.0014341,0.0014517,0.0014692,0.0014868,0.0015044,0.0015221,0.0015397,0.0015573,0.001575,0.0015926,0.0016102,0.0016278,0.0016453,0.0016628,0.0016803,0.0016977,0.0017151,0.0017325,0.0017497,0.0017669,0.0017841,0.0018011,0.0018181,0.001835,0.0018519,0.0018686,0.0018853,0.0019019,0.0019184,0.0019349,0.0019513,0.0019676,0.0019838,0.002,0.0020161,0.0020321,0.0020481,0.002064,0.0020799,0.0020957,0.0021116,0.0021273,0.0021431,0.0021588,0.0021745,0.0021902,0.0022059,0.0022216,0.0022373,0.0022531,0.0022688,0.0022845,0.0023003,0.0023161,0.0023319,0.0023478,0.0023637,0.0023797,0.0023957,0.0024117,0.0024278,0.0024439,0.0024602,0.0024764,0.0024927,0.0025091,0.0025256,0.0025421,0.0025586,0.0025753,0.002592,0.0026088,0.0026256,0.0026426,0.0026596,0.0026766,0.0026938,0.002711,0.0027283,0.0027457,0.0027632,0.0027808,0.0027984,0.0028162,0.0028341,0.002852,0.0028701,0.0028882,0.0029065,0.0029249,0.0029435,0.0029621,0.0029809,0.0029998,0.0030189,0.0030381,0.0030575,0.003077,0.0030967,0.0031166,0.0031367,0.003157,0.0031774,0.0031981,0.003219,0.0032401,0.0032615,0.0032831,0.003305,0.0033271,0.0033495,0.0033722,0.0033951,0.0034184,0.003442,0.0034659,0.0034901,0.0035146,0.0035396,0.0035648,0.0035905,0.0036165,0.0036429,0.0036697,0.0036969,0.0037246,0.0037526,0.0037812,0.0038101,0.0038396,0.0038695,0.0038999,0.0039309,0.0039623,0.0039943,0.0040268,0.0040599,0.0040935,0.0041278,0.0041626,0.0041981,0.0042341,0.0042709,0.0043083,0.0043464,0.0043852,0.0044248,0.0044651,0.0045061,0.004548,0.0045907,0.0046342,0.0046785,0.0047238,0.0047699,0.004817,0.0048651,0.0049142,0.0049642,0.0050154,0.0050676,0.0051209,0.0051753,0.005231,0.0052878,0.0053459,0.0054052,0.0054659,0.0055278,0.0055912,0.005656,0.0057222,0.0057898,0.005859,0.0059298,0.0060021,0.006076,0.0061516,0.0062288,0.0063078,0.0063885,0.006471,0.0065553,0.0066414,0.0067294,0.0068193,0.0069111,0.0070048,0.0071006,0.0071983,0.007298,0.0073998,0.0075037,0.0076097,0.0077177,0.0078279,0.0079402,0.0080547,0.0081713,0.0082901,0.0084111,0.0085343,0.0086597,0.0087874,0.0089173,0.0090494,0.0091837,0.0093204,0.0094592,0.0096004,0.0097438,0.0098895,0.010037,0.010188,0.01034,0.010495,0.010652,0.010811,0.010973,0.011137,0.011303,0.011472,0.011643,0.011816,0.011991,0.012169,0.012349,0.012531,0.012716,0.012902,0.013092,0.013283,0.013477,0.013673,0.013871,0.014072,0.014274,0.01448,0.014687,0.014896,0.015108,0.015322,0.015539,0.015757,0.015978,0.016201,0.016426,0.016654,0.016883,0.017115,0.017349,0.017585,0.017823,0.018064,0.018306,0.018551,0.018797,0.019046,0.019297,0.01955,0.019805,0.020062,0.020321,0.020582,0.020845,0.02111,0.021378,0.021647,0.021918,0.022192,0.022467,0.022745,0.023025,0.023306,0.02359,0.023876,0.024165,0.024455,0.024748,0.025043,0.02534,0.025639,0.025941,0.026245,0.026552,0.026861,0.027173,0.027487,0.027804,0.028124,0.028446,0.028771,0.029099,0.02943,0.029764,0.030101,0.030441,0.030784,0.031131,0.031481,0.031834,0.032191,0.032551,0.032915,0.033282,0.033654,0.034029,0.034408,0.034791,0.035178,0.035569,0.035964,
            0.036364,0.036768,0.037176,0.037589,0.038006,0.038428,0.038855,0.039286,0.039722,0.040163,0.040609,0.041059,0.041515,0.041976,0.042442,0.042914,0.04339,0.043872,0.04436,0.044853,0.045351,0.045855,0.046364,0.04688,0.047401,0.047927,0.04846,0.048999,0.049543,0.050094,0.050651,0.051214,0.051783,0.052359,0.052941,0.05353,0.054125,0.054727,0.055336,0.055951,0.056574,0.057203,0.05784,0.058484,0.059135,0.059794,0.060461,0.061135,0.061817,0.062507,0.063205,0.063911,0.064626,0.065349,0.066081,0.066821,0.067571,0.068329,0.069097,0.069874,0.070661,0.071458,0.072265,0.073081,0.073908,0.074746,0.075594,0.076453,0.077323,0.078204,0.079097,0.080001,0.080918,0.081846,0.082786,0.083739,0.084705,0.085683,0.086674,0.087679,0.088697,0.089729,0.090774,0.091834,0.092907,0.093995,0.095098,0.096215,0.097348,0.098495,0.099658,0.10084,0.10203,0.10324,0.10447,0.10571,0.10697,0.10824,0.10953,0.11084,0.11216,0.1135,0.11486,0.11624,0.11763,0.11904,0.12047,0.12192,0.12338,0.12486,0.12636,0.12788,0.12942,0.13098,0.13255,0.13415,0.13576,0.1374,0.13905,0.14073,0.14243,0.14414,0.14588,0.14765,0.14943,0.15124,0.15307,0.15493,0.15681,0.15872,0.16065,0.16261,0.1646,0.16661,0.16866,0.17073,0.17284,0.17498,0.17715,0.17935,0.18159,0.18386,0.18617,0.18852,0.1909,0.19333,0.19579,0.19829,0.20084,0.20342,0.20605,0.20873,0.21144,0.21421,0.21702,0.21987,0.22277,0.22572,0.22871,0.23175,0.23484,0.23798,0.24116,0.2444,0.24768,0.251,0.25438,0.2578,0.26127,0.26479,0.26836,0.27197,0.27563,0.27934,0.28309,0.28689,0.29074,0.29464,0.29859,0.30258,0.30663,0.31073,0.31487,0.31908,0.32333,0.32764,0.33201,0.33644,0.34093,0.34548,0.35009,0.35478,0.35953,0.36435,0.36925,0.37423,0.37928,0.38442,0.38964,0.39494,0.40034,0.40582,0.4114,0.41707,0.42283,0.42869,0.43465,0.44071,0.44686,0.45311,0.45945,0.46589,0.47243,0.47906,0.48579,0.4926,0.49951,0.5065,0.51357,0.52073,0.52798,0.5353,0.5427,0.55018,0.55774,0.56537,0.57309,0.58087,0.58874,0.59669,0.60471,0.61282,0.62101,0.62929,0.63765,0.6461,0.65464,0.66328,0.672,0.68082,0.68972,0.69872,0.70779,0.71695,0.72617,0.73546,0.7448,0.75419,0.7636,0.77303,0.78245,0.79186,0.80124,0.81056,0.81982,0.829,0.83809,0.84706,0.8559,0.86462,0.87319,0.8816,0.88986,0.89795,0.90585,0.91357,0.92109,0.9284,0.93547,0.94229,0.94882,0.95505,0.96093,0.96642,0.97149,0.97611,0.98025,0.9839,0.98704,0.98971,0.99192,0.99371,0.99513,0.99625,0.99711,0.99777,0.99828,0.99867,0.99898,0.99923,0.99945,0.99964,0.99982,0.99999,1.0)

  u = seq(from = 1 / (sqrSize + 1), 
          by = 1 / (sqrSize + 1), to = sqrSize / (sqrSize + 1))
  sigma = sqrt((u * (1 - u)) / (sqrSize + 1))
  test = (u - r$y) / sigma;
  score = -sum(test ^ 2) / sqrSize;
  surd = approx(scores, surds, score)
  threshold = (surd$y) * 100
  failedSolution = FALSE
  if (threshold < 5) {
    failedSolution = TRUE
  }
  
  
  residual = r$y - position;
  sqr = residual * sqrt(sqrSize + 2);
  
  estimatePDFe = list(x = x, pdf = pdf, sample = sample, 
                      sqrSize = sqrSize, sqr = sqr, cdf = cdf, 
                      threshold = threshold, failedSolution = failedSolution,
                      isSpecifyPoints = FALSE, outputLength = length(x))
  class(estimatePDFe) <- "PDFe"
  return(estimatePDFe)
}