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Description

Admissible Exact Intervals for One-Dimensional Discrete Distributions.

Construct the admissible exact intervals for the binomial proportion, the Poisson mean and the total number of subjects with a certain attribute or the total number of the subjects for the hypergeometric distribution. Both one-sided and two-sided intervals are of interest. This package can be used to calculate the intervals constructed methods developed by Wang (2014) <doi:10.5705/ss.2012.257> and Wang (2015) <doi:10.1111/biom.12360>.

ExactCIone

An R package to construct the admissible exact intervals for the binomial proportion, the poisson mean and the total number of subjects with a certain attribute or the total number of the subjects for the hypergeometric distribution. Both one-sided and two-sided intervals are of interest. This package can be used to calculate the intervals constructed methods developed by Wang (2014) and Wang (2015).

Installation

You can install the development version of ExactCIone like so:

library("devtools")
install_github("befrthunder/ExactCIone",dependencies =TRUE, build_vignettes = TRUE)

Example

This is a basic example which shows you how to solve a common problem:

library(ExactCIone)
# For bin(n,p), construct 95% admissible CI for p on the observed sample x=2 when n=5.
WbinoCI(x=2,n=5,conf.level=0.95,details=TRUE)
#> $CI
#>      x     lower     upper
#> [1,] 2 0.0764403 0.8107447
#> 
#> $CIM
#>      x      lower     upper
#> [1,] 0 0.00000000 0.5000000
#> [2,] 1 0.01020614 0.6574084
#> [3,] 2 0.07644030 0.8107447
#> [4,] 3 0.18925530 0.9235597
#> [5,] 4 0.34259163 0.9897939
#> [6,] 5 0.49999997 1.0000000
#> 
#> $icp
#> [1] 0.95
WbinoCI(x=2,n=5,conf.level=0.95)
#> $CI
#>      x     lower     upper
#> [1,] 2 0.0764403 0.8107447
WbinoCI_lower(x=2,n=5,conf.level=0.95,details=TRUE)
#> $CI
#>      sample       lower upper
#> [1,]      0 0.000000000     1
#> [2,]      1 0.005050763     1
#> [3,]      2 0.052744951     1
#> [4,]      3 0.146632800     1
#> [5,]      4 0.283582064     1
#> [6,]      5 0.478176250     1
WbinoCI_lower(x=2,n=5,conf.level=0.95)
#> $CI
#>      sample      lower upper
#> [1,]      2 0.05274495     1
########################################################################
# For pois(lambda), construct 95% admissible CI for lambda on the observed sample x=3.
WpoisCI(x=3,details = TRUE)
#> $CI
#>      x     lower    upper
#> [1,] 3 0.8176914 8.395386
#> 
#> $CIM
#>      x      lower    upper
#> [1,] 0 0.00000000 3.453832
#> [2,] 1 0.05129329 5.491160
#> [3,] 2 0.35536150 6.921952
#> [4,] 3 0.81769144 8.395386
#> 
#> $icp
#> [1] 0.95
WpoisCI(x=1)
#> $CI
#>      x      lower   upper
#> [1,] 1 0.05129329 5.49116
WpoisCI_lower(x=1)
#> $CI
#>      sample               
#> [1,]      1 0.05129329 Inf
WpoisCI_lower(x=3,details = TRUE)
#> $CI
#>      x     lower upper
#> [1,] 3 0.8176914   Inf
#> 
#> $CIM
#>      sample      lower upper
#> [1,]      0 0.00000000   Inf
#> [2,]      1 0.05129329   Inf
#> [3,]      2 0.35536151   Inf
#> [4,]      3 0.81769145   Inf
WpoisCI_upper(x=1)
#> $CI
#>      sample           
#> [1,]      1 0 4.743865
WpoisCI_upper(x=3,details = TRUE)
#> $CI
#>      x lower    upper
#> [1,] 3     0 7.753657
#> 
#> $CIM
#>      sample lower    upper
#> [1,]      0     0 2.995732
#> [2,]      1     0 4.743865
#> [3,]      2     0 6.295794
#> [4,]      3     0 7.753657
#######################################################################
# For hyper(n,x,M,N-M), construct 95% admissible CI for N on the observed sample x=10 when n=50,M=800.
WhyperCI_N(10,50,800,0.95,details=TRUE)
#> $CI
#>       x lower upper
#> [1,] 10  2445  7955
#> 
#> $CIM
#>        x lower  upper
#>  [1,]  0 12572    Inf
#>  [2,]  1  7956 780253
#>  [3,]  2  6108 111784
#>  [4,]  3  4914  48296
#>  [5,]  4  4425  28760
#>  [6,]  5  3760  19857
#>  [7,]  6  3472  14911
#>  [8,]  7  3018  12571
#>  [9,]  8  2828  10875
#> [10,]  9  2657   8435
#> [11,] 10  2445   7955
#> [12,] 11  2243   6450
#> [13,] 12  2130   6107
#> [14,] 13  2026   5118
#> [15,] 14  1931   4913
#> [16,] 15  1844   4424
#> [17,] 16  1764   3938
#> [18,] 17  1689   3759
#> [19,] 18  1620   3471
#> [20,] 19  1555   3121
#> [21,] 20  1495   3017
#> [22,] 21  1439   2827
#> [23,] 22  1386   2656
#> [24,] 23  1336   2444
#> [25,] 24  1289   2321
#> [26,] 25  1255   2242
#> [27,] 26  1229   2129
#> [28,] 27  1200   2025
#> [29,] 28  1163   1930
#> [30,] 29  1125   1843
#> [31,] 30  1101   1763
#> [32,] 31  1082   1688
#> [33,] 32  1053   1619
#> [34,] 33  1020   1554
#> [35,] 34  1010   1494
#> [36,] 35   988   1438
#> [37,] 36   964   1385
#> [38,] 37   952   1335
#> [39,] 38   925   1288
#> [40,] 39   917   1231
#> [41,] 40   893   1199
#> [42,] 41   887   1162
#> [43,] 42   869   1124
#> [44,] 43   860   1081
#> [45,] 44   847   1052
#> [46,] 45   835   1019
#> [47,] 46   824    987
#> [48,] 47   815    951
#> [49,] 48   807    924
#> [50,] 49   801    892
#> [51,] 50   800    859
#> 
#> $icp
#> [1] 0.95
WhyperCI_N(50,50,800,0.95)
#> $CI
#>       x lower upper
#> [1,] 50   800   859
WhyperCI_N_lower(0,50,800,0.95,details=TRUE)
#> $CI
#>      sample lower upper
#> [1,]      0 13781   Inf
#> 
#> $CIM
#>       sample lower upper
#>  [1,]      0 13781   Inf
#>  [2,]      1  8772   Inf
#>  [3,]      2  6649   Inf
#>  [4,]      3  5426   Inf
#>  [5,]      4  4617   Inf
#>  [6,]      5  4036   Inf
#>  [7,]      6  3596   Inf
#>  [8,]      7  3251   Inf
#>  [9,]      8  2971   Inf
#> [10,]      9  2739   Inf
#> [11,]     10  2544   Inf
#> [12,]     11  2377   Inf
#> [13,]     12  2233   Inf
#> [14,]     13  2106   Inf
#> [15,]     14  1995   Inf
#> [16,]     15  1895   Inf
#> [17,]     16  1806   Inf
#> [18,]     17  1726   Inf
#> [19,]     18  1653   Inf
#> [20,]     19  1587   Inf
#> [21,]     20  1527   Inf
#> [22,]     21  1471   Inf
#> [23,]     22  1420   Inf
#> [24,]     23  1372   Inf
#> [25,]     24  1328   Inf
#> [26,]     25  1288   Inf
#> [27,]     26  1249   Inf
#> [28,]     27  1214   Inf
#> [29,]     28  1181   Inf
#> [30,]     29  1149   Inf
#> [31,]     30  1120   Inf
#> [32,]     31  1092   Inf
#> [33,]     32  1066   Inf
#> [34,]     33  1042   Inf
#> [35,]     34  1019   Inf
#> [36,]     35   997   Inf
#> [37,]     36   976   Inf
#> [38,]     37   957   Inf
#> [39,]     38   938   Inf
#> [40,]     39   921   Inf
#> [41,]     40   904   Inf
#> [42,]     41   889   Inf
#> [43,]     42   874   Inf
#> [44,]     43   860   Inf
#> [45,]     44   847   Inf
#> [46,]     45   835   Inf
#> [47,]     46   824   Inf
#> [48,]     47   815   Inf
#> [49,]     48   807   Inf
#> [50,]     49   801   Inf
#> [51,]     50   800   Inf
WhyperCI_N_lower(0,50,800,0.95)
#> $CI
#>      x          
#> [1,] 0 13781 Inf
WhyperCI_N_upper(0,50,800,0.95,details=TRUE)
#> $CI
#>      sample lower upper
#> [1,]      0     0   Inf
#> 
#> $CIM
#>       sample lower  upper
#>  [1,]      0     0    Inf
#>  [2,]      1     0 780253
#>  [3,]      2     0 111784
#>  [4,]      3     0  48296
#>  [5,]      4     0  28760
#>  [6,]      5     0  19857
#>  [7,]      6     0  14911
#>  [8,]      7     0  11814
#>  [9,]      8     0   9716
#> [10,]      9     0   8209
#> [11,]     10     0   7081
#> [12,]     11     0   6208
#> [13,]     12     0   5514
#> [14,]     13     0   4950
#> [15,]     14     0   4484
#> [16,]     15     0   4093
#> [17,]     16     0   3760
#> [18,]     17     0   3474
#> [19,]     18     0   3226
#> [20,]     19     0   3008
#> [21,]     20     0   2816
#> [22,]     21     0   2645
#> [23,]     22     0   2492
#> [24,]     23     0   2355
#> [25,]     24     0   2231
#> [26,]     25     0   2118
#> [27,]     26     0   2016
#> [28,]     27     0   1921
#> [29,]     28     0   1835
#> [30,]     29     0   1755
#> [31,]     30     0   1682
#> [32,]     31     0   1613
#> [33,]     32     0   1550
#> [34,]     33     0   1490
#> [35,]     34     0   1435
#> [36,]     35     0   1383
#> [37,]     36     0   1334
#> [38,]     37     0   1288
#> [39,]     38     0   1244
#> [40,]     39     0   1203
#> [41,]     40     0   1164
#> [42,]     41     0   1127
#> [43,]     42     0   1092
#> [44,]     43     0   1058
#> [45,]     44     0   1026
#> [46,]     45     0    995
#> [47,]     46     0    965
#> [48,]     47     0    936
#> [49,]     48     0    907
#> [50,]     49     0    878
#> [51,]     50     0    847
WhyperCI_N_upper(0,50,800,0.95)
#> $CI
#>      x      
#> [1,] 0 0 Inf
#######################################################################
# For hyper(n,x,M,N-M), construct 95% admissible CI for M on the observed sample x=0 when n=50, N=2000.
WhyperCI_M(0,50,2000,0.95,details = TRUE)
#> $CI
#>      X lower upper
#> [1,] 0     0   136
#> 
#> $CIM
#>        x lower upper
#>  [1,]  0     0   136
#>  [2,]  1     3   210
#>  [3,]  2    15   271
#>  [4,]  3    34   328
#>  [5,]  4    57   381
#>  [6,]  5    82   433
#>  [7,]  6   109   483
#>  [8,]  7   137   531
#>  [9,]  8   152   579
#> [10,]  9   192   625
#> [11,] 10   211   661
#> [12,] 11   251   715
#> [13,] 12   272   760
#> [14,] 13   315   803
#> [15,] 14   329   846
#> [16,] 15   382   888
#> [17,] 16   410   930
#> [18,] 17   434   971
#> [19,] 18   484  1000
#> [20,] 19   516  1028
#> [21,] 20   532  1069
#> [22,] 21   580  1111
#> [23,] 22   626  1153
#> [24,] 23   662  1196
#> [25,] 24   691  1239
#> [26,] 25   716  1284
#> [27,] 26   761  1309
#> [28,] 27   804  1338
#> [29,] 28   847  1374
#> [30,] 29   889  1420
#> [31,] 30   931  1468
#> [32,] 31   972  1484
#> [33,] 32  1000  1516
#> [34,] 33  1029  1566
#> [35,] 34  1070  1590
#> [36,] 35  1112  1618
#> [37,] 36  1154  1671
#> [38,] 37  1197  1685
#> [39,] 38  1240  1728
#> [40,] 39  1285  1749
#> [41,] 40  1339  1789
#> [42,] 41  1375  1808
#> [43,] 42  1421  1848
#> [44,] 43  1469  1863
#> [45,] 44  1517  1891
#> [46,] 45  1567  1918
#> [47,] 46  1619  1943
#> [48,] 47  1672  1966
#> [49,] 48  1729  1985
#> [50,] 49  1790  1997
#> [51,] 50  1864  2000
#> 
#> $CIM_p
#>          p lower_p upper_p
#>  [1,] 0.00  0.0000  0.0680
#>  [2,] 0.02  0.0015  0.1050
#>  [3,] 0.04  0.0075  0.1355
#>  [4,] 0.06  0.0170  0.1640
#>  [5,] 0.08  0.0285  0.1905
#>  [6,] 0.10  0.0410  0.2165
#>  [7,] 0.12  0.0545  0.2415
#>  [8,] 0.14  0.0685  0.2655
#>  [9,] 0.16  0.0760  0.2895
#> [10,] 0.18  0.0960  0.3125
#> [11,] 0.20  0.1055  0.3305
#> [12,] 0.22  0.1255  0.3575
#> [13,] 0.24  0.1360  0.3800
#> [14,] 0.26  0.1575  0.4015
#> [15,] 0.28  0.1645  0.4230
#> [16,] 0.30  0.1910  0.4440
#> [17,] 0.32  0.2050  0.4650
#> [18,] 0.34  0.2170  0.4855
#> [19,] 0.36  0.2420  0.5000
#> [20,] 0.38  0.2580  0.5140
#> [21,] 0.40  0.2660  0.5345
#> [22,] 0.42  0.2900  0.5555
#> [23,] 0.44  0.3130  0.5765
#> [24,] 0.46  0.3310  0.5980
#> [25,] 0.48  0.3455  0.6195
#> [26,] 0.50  0.3580  0.6420
#> [27,] 0.52  0.3805  0.6545
#> [28,] 0.54  0.4020  0.6690
#> [29,] 0.56  0.4235  0.6870
#> [30,] 0.58  0.4445  0.7100
#> [31,] 0.60  0.4655  0.7340
#> [32,] 0.62  0.4860  0.7420
#> [33,] 0.64  0.5000  0.7580
#> [34,] 0.66  0.5145  0.7830
#> [35,] 0.68  0.5350  0.7950
#> [36,] 0.70  0.5560  0.8090
#> [37,] 0.72  0.5770  0.8355
#> [38,] 0.74  0.5985  0.8425
#> [39,] 0.76  0.6200  0.8640
#> [40,] 0.78  0.6425  0.8745
#> [41,] 0.80  0.6695  0.8945
#> [42,] 0.82  0.6875  0.9040
#> [43,] 0.84  0.7105  0.9240
#> [44,] 0.86  0.7345  0.9315
#> [45,] 0.88  0.7585  0.9455
#> [46,] 0.90  0.7835  0.9590
#> [47,] 0.92  0.8095  0.9715
#> [48,] 0.94  0.8360  0.9830
#> [49,] 0.96  0.8645  0.9925
#> [50,] 0.98  0.8950  0.9985
#> [51,] 1.00  0.9320  1.0000
#> 
#> $icp
#> [1] 0.9500198
WhyperCI_M(0,50,2000,0.95)
#> $CI
#>      x lower upper
#> [1,] 0     0   136
#> 
#> $CI_p
#>      p lower upper
#> [1,] 0     0 0.068
WhyperCI_M_lower(0,50,2000,0.95,details = TRUE)
#> $CI
#>      X      N
#> [1,] 0 0 2000
#> 
#> $CIM
#>       sample lower upper
#>  [1,]      0     0  2000
#>  [2,]      1     3  2000
#>  [3,]      2    15  2000
#>  [4,]      3    34  2000
#>  [5,]      4    57  2000
#>  [6,]      5    82  2000
#>  [7,]      6   109  2000
#>  [8,]      7   137  2000
#>  [9,]      8   166  2000
#> [10,]      9   197  2000
#> [11,]     10   228  2000
#> [12,]     11   259  2000
#> [13,]     12   292  2000
#> [14,]     13   325  2000
#> [15,]     14   358  2000
#> [16,]     15   393  2000
#> [17,]     16   427  2000
#> [18,]     17   462  2000
#> [19,]     18   497  2000
#> [20,]     19   533  2000
#> [21,]     20   569  2000
#> [22,]     21   606  2000
#> [23,]     22   643  2000
#> [24,]     23   680  2000
#> [25,]     24   718  2000
#> [26,]     25   756  2000
#> [27,]     26   794  2000
#> [28,]     27   833  2000
#> [29,]     28   872  2000
#> [30,]     29   911  2000
#> [31,]     30   951  2000
#> [32,]     31   991  2000
#> [33,]     32  1032  2000
#> [34,]     33  1073  2000
#> [35,]     34  1114  2000
#> [36,]     35  1156  2000
#> [37,]     36  1198  2000
#> [38,]     37  1241  2000
#> [39,]     38  1284  2000
#> [40,]     39  1328  2000
#> [41,]     40  1372  2000
#> [42,]     41  1417  2000
#> [43,]     42  1463  2000
#> [44,]     43  1509  2000
#> [45,]     44  1557  2000
#> [46,]     45  1605  2000
#> [47,]     46  1655  2000
#> [48,]     47  1707  2000
#> [49,]     48  1761  2000
#> [50,]     49  1819  2000
#> [51,]     50  1886  2000
WhyperCI_M_lower(0,50,2000,0.95)
#> $CI
#>      X      N
#> [1,] 0 0 2000
WhyperCI_M_upper(0,50,2000,0.95,details = TRUE)
#> $CI
#>      X      
#> [1,] 0 0 114
#> 
#> $CIM
#>       sample lower upper
#>  [1,]      0     0   114
#>  [2,]      1     0   181
#>  [3,]      2     0   239
#>  [4,]      3     0   293
#>  [5,]      4     0   345
#>  [6,]      5     0   395
#>  [7,]      6     0   443
#>  [8,]      7     0   491
#>  [9,]      8     0   537
#> [10,]      9     0   583
#> [11,]     10     0   628
#> [12,]     11     0   672
#> [13,]     12     0   716
#> [14,]     13     0   759
#> [15,]     14     0   802
#> [16,]     15     0   844
#> [17,]     16     0   886
#> [18,]     17     0   927
#> [19,]     18     0   968
#> [20,]     19     0  1009
#> [21,]     20     0  1049
#> [22,]     21     0  1089
#> [23,]     22     0  1128
#> [24,]     23     0  1167
#> [25,]     24     0  1206
#> [26,]     25     0  1244
#> [27,]     26     0  1282
#> [28,]     27     0  1320
#> [29,]     28     0  1357
#> [30,]     29     0  1394
#> [31,]     30     0  1431
#> [32,]     31     0  1467
#> [33,]     32     0  1503
#> [34,]     33     0  1538
#> [35,]     34     0  1573
#> [36,]     35     0  1607
#> [37,]     36     0  1642
#> [38,]     37     0  1675
#> [39,]     38     0  1708
#> [40,]     39     0  1741
#> [41,]     40     0  1772
#> [42,]     41     0  1803
#> [43,]     42     0  1834
#> [44,]     43     0  1863
#> [45,]     44     0  1891
#> [46,]     45     0  1918
#> [47,]     46     0  1943
#> [48,]     47     0  1966
#> [49,]     48     0  1985
#> [50,]     49     0  1997
#> [51,]     50     0  2000
WhyperCI_M_upper(0,50,2000,0.95)
#> $CI
#>      X      
#> [1,] 0 0 114
## basic example code
Metadata

Version

1.0.5

License

Unknown

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  • i686-linux
  • i686-netbsd
  • i686-none
  • i686-openbsd
  • i686-windows
  • javascript-ghcjs
  • loongarch64-linux
  • m68k-linux
  • m68k-netbsd
  • m68k-none
  • microblaze-linux
  • microblaze-none
  • microblazeel-linux
  • microblazeel-none
  • mips-linux
  • mips-none
  • mips64-linux
  • mips64-none
  • mips64el-linux
  • mipsel-linux
  • mipsel-netbsd
  • mmix-mmixware
  • msp430-none
  • or1k-none
  • powerpc-netbsd
  • powerpc-none
  • powerpc64-linux
  • powerpc64le-linux
  • powerpcle-none
  • riscv32-linux
  • riscv32-netbsd
  • riscv32-none
  • riscv64-linux
  • riscv64-netbsd
  • riscv64-none
  • rx-none
  • s390-linux
  • s390-none
  • s390x-linux
  • s390x-none
  • vc4-none
  • wasm32-wasi
  • wasm64-wasi
  • x86_64-cygwin
  • x86_64-darwin
  • x86_64-freebsd
  • x86_64-genode
  • x86_64-linux
  • x86_64-netbsd
  • x86_64-none
  • x86_64-openbsd
  • x86_64-redox
  • x86_64-solaris
  • x86_64-windows