R Under development (unstable) (2024-10-15 r87238 ucrt) -- "Unsuffered Consequences"
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> library(RTDE)
Loading required package: parallel
> 
> # ?EPD
> 
> #####
> # (1) density function
> x <- seq(0, 5, length=24)
> 
> cbind(x, dEPD(x, 1/2, 1/4, -1))
              x              
 [1,] 0.0000000  0.000000e+00
 [2,] 0.2173913 -1.930799e+01
 [3,] 0.4347826 -1.642687e+05
 [4,] 0.6521739  4.562695e+01
 [5,] 0.8695652  6.186917e+00
 [6,] 1.0869565  2.032956e+00
 [7,] 1.3043478  9.380732e-01
 [8,] 1.5217391  5.174295e-01
 [9,] 1.7391304  3.185337e-01
[10,] 1.9565217  2.112457e-01
[11,] 2.1739130  1.478507e-01
[12,] 2.3913043  1.078003e-01
[13,] 2.6086957  8.116773e-02
[14,] 2.8260870  6.272437e-02
[15,] 3.0434783  4.952410e-02
[16,] 3.2608696  3.981453e-02
[17,] 3.4782609  3.250593e-02
[18,] 3.6956522  2.689492e-02
[19,] 3.9130435  2.251292e-02
[20,] 4.1304348  1.903918e-02
[21,] 4.3478261  1.624883e-02
[22,] 4.5652174  1.398095e-02
[23,] 4.7826087  1.211821e-02
[24,] 5.0000000  1.057366e-02
> 
> #####
> # (2) distribution function
> 
> cbind(x, pEPD(x, 1/2, 1/4, -1, lower=FALSE))
              x           
 [1,] 0.0000000 1.00000000
 [2,] 0.2173913 1.00000000
 [3,] 0.4347826 1.00000000
 [4,] 0.6521739 1.00000000
 [5,] 0.8695652 1.00000000
 [6,] 1.0869565 0.78495778
 [7,] 1.3043478 0.48307926
 [8,] 1.5217391 0.33109783
 [9,] 1.7391304 0.24262646
[10,] 1.9565217 0.18613164
[11,] 2.1739130 0.14765726
[12,] 2.3913043 0.12018031
[13,] 2.6086957 0.09982576
[14,] 2.8260870 0.08430175
[15,] 3.0434783 0.07217710
[16,] 3.2608696 0.06251812
[17,] 3.4782609 0.05469335
[18,] 3.6956522 0.04826264
[19,] 3.9130435 0.04291120
[20,] 4.1304348 0.03840883
[21,] 4.3478261 0.03458392
[22,] 4.5652174 0.03130636
[23,] 4.7826087 0.02847596
[24,] 5.0000000 0.02601457
> cbind(x, pEPD(x, 1/2, 1/4, -1))
              x          
 [1,] 0.0000000 0.0000000
 [2,] 0.2173913 0.0000000
 [3,] 0.4347826 0.0000000
 [4,] 0.6521739 0.0000000
 [5,] 0.8695652 0.0000000
 [6,] 1.0869565 0.2150422
 [7,] 1.3043478 0.5169207
 [8,] 1.5217391 0.6689022
 [9,] 1.7391304 0.7573735
[10,] 1.9565217 0.8138684
[11,] 2.1739130 0.8523427
[12,] 2.3913043 0.8798197
[13,] 2.6086957 0.9001742
[14,] 2.8260870 0.9156982
[15,] 3.0434783 0.9278229
[16,] 3.2608696 0.9374819
[17,] 3.4782609 0.9453066
[18,] 3.6956522 0.9517374
[19,] 3.9130435 0.9570888
[20,] 4.1304348 0.9615912
[21,] 4.3478261 0.9654161
[22,] 4.5652174 0.9686936
[23,] 4.7826087 0.9715240
[24,] 5.0000000 0.9739854
> 
> #####
> # (3) quantile function
> 
> qEPD(1/2, 1/2, 1/4, -1)
[1] 1.286796
> qEPD(1:10/11, 1/2, 1/4, -1)
 [1] 1.032712 1.071149 1.117116 1.173311 1.243979 1.336263 1.463325 1.652884
 [9] 1.977314 2.726650
> cbind(x, qEPD(pEPD(x, 1/2, 1/4, -1), 1/2, 1/4, -1)) #first five lines should be different
              x         
 [1,] 0.0000000 1.000000
 [2,] 0.2173913 1.000000
 [3,] 0.4347826 1.000000
 [4,] 0.6521739 1.000000
 [5,] 0.8695652 1.000000
 [6,] 1.0869565 1.086957
 [7,] 1.3043478 1.304348
 [8,] 1.5217391 1.521739
 [9,] 1.7391304 1.739130
[10,] 1.9565217 1.956522
[11,] 2.1739130 2.173913
[12,] 2.3913043 2.391304
[13,] 2.6086957 2.608696
[14,] 2.8260870 2.826087
[15,] 3.0434783 3.043478
[16,] 3.2608696 3.260870
[17,] 3.4782609 3.478261
[18,] 3.6956522 3.695652
[19,] 3.9130435 3.913043
[20,] 4.1304348 4.130435
[21,] 4.3478261 4.347826
[22,] 4.5652174 4.565217
[23,] 4.7826087 4.782609
[24,] 5.0000000 5.000000
> 
> 
> x <- seq(1, 10, length=21)
> cbind(x, qEPD(pEPD(x, 1/2, 1/4, -1), 1/2, 1/4, -1))
          x      
 [1,]  1.00  1.00
 [2,]  1.45  1.45
 [3,]  1.90  1.90
 [4,]  2.35  2.35
 [5,]  2.80  2.80
 [6,]  3.25  3.25
 [7,]  3.70  3.70
 [8,]  4.15  4.15
 [9,]  4.60  4.60
[10,]  5.05  5.05
[11,]  5.50  5.50
[12,]  5.95  5.95
[13,]  6.40  6.40
[14,]  6.85  6.85
[15,]  7.30  7.30
[16,]  7.75  7.75
[17,]  8.20  8.20
[18,]  8.65  8.65
[19,]  9.10  9.10
[20,]  9.55  9.55
[21,] 10.00 10.00
> 
> system.time(x <- qEPD(1:10000/10001, 1/2, 1/4, -1))
   user  system elapsed 
   0.88    0.00    0.87 
> head(x)
[1] 1.000033 1.000067 1.000100 1.000133 1.000167 1.000200
> tail(x)
[1] 32.66762 35.78447 40.00700 46.19466 56.57491 80.00650
> 
> 
> proc.time()
   user  system elapsed 
   1.14    0.06    1.18