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+--------+-------------------------+-------------------------+--------+--------+
|00000000| 00 0a 42 69 6e 6f 6d 69 | 61 6c 2e 63 00 00 00 00 |..Binomi|al.c....|
|00000010| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000020| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000030| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000040| 00 54 45 58 54 4d 4d 43 | 43 00 00 00 00 00 00 00 |.TEXTMMC|C.......|
|00000050| 00 00 00 00 00 1f f8 00 | 00 02 ca aa ac 1b bb aa |........|........|
|00000060| ac 1b bb 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000070| 00 00 00 00 00 00 00 00 | 00 00 81 81 91 43 00 00 |........|.....C..|
|00000080| 2f 2a 0d 42 69 6e 6f 6d | 69 61 6c 2e 63 0d 43 6f |/*.Binom|ial.c.Co|
|00000090| 70 79 72 69 67 68 74 20 | 28 63 29 20 31 39 39 30 |pyright |(c) 1990|
|000000a0| 2c 31 39 39 31 2c 31 39 | 39 32 2c 31 39 39 34 20 |,1991,19|92,1994 |
|000000b0| 44 65 6e 69 73 20 47 2e | 20 50 65 6c 6c 69 0d 0d |Denis G.| Pelli..|
|000000c0| 56 61 72 69 6f 75 73 20 | 72 6f 75 74 69 6e 65 73 |Various |routines|
|000000d0| 20 74 68 61 74 20 64 65 | 61 6c 20 77 69 74 68 20 | that de|al with |
|000000e0| 42 69 6e 6f 6d 69 61 6c | 20 73 74 61 74 69 73 74 |Binomial| statist|
|000000f0| 69 63 73 2c 20 69 6e 63 | 6c 75 64 69 6e 67 20 67 |ics, inc|luding g|
|00000100| 65 6e 65 72 61 74 69 6e | 67 20 72 61 6e 64 6f 6d |eneratin|g random|
|00000110| 0d 73 61 6d 70 6c 65 73 | 20 61 6e 64 20 63 6f 6d |.samples| and com|
|00000120| 70 75 74 69 6e 67 20 63 | 6f 6e 66 69 64 65 6e 63 |puting c|onfidenc|
|00000130| 65 20 69 6e 74 65 72 76 | 61 6c 73 2e 0d 0d 54 68 |e interv|als...Th|
|00000140| 69 73 20 66 69 6c 65 20 | 63 6f 6e 74 61 69 6e 73 |is file |contains|
|00000150| 20 74 77 6f 20 67 65 6e | 65 72 61 74 69 6f 6e 73 | two gen|erations|
|00000160| 20 6f 66 20 72 6f 75 74 | 69 6e 65 73 20 74 68 61 | of rout|ines tha|
|00000170| 74 20 67 65 6e 65 72 61 | 74 65 20 63 6f 6e 66 69 |t genera|te confi|
|00000180| 64 65 6e 63 65 0d 69 6e | 74 65 72 76 61 6c 73 2e |dence.in|tervals.|
|00000190| 20 54 68 65 20 6f 72 69 | 67 69 6e 61 6c 20 72 6f | The ori|ginal ro|
|000001a0| 75 74 69 6e 65 73 20 42 | 69 6e 6f 6d 69 61 6c 55 |utines B|inomialU|
|000001b0| 70 70 65 72 42 6f 75 6e | 64 20 61 6e 64 20 42 69 |pperBoun|d and Bi|
|000001c0| 6e 6f 6d 69 61 6c 4c 6f | 77 65 72 42 6f 75 6e 64 |nomialLo|werBound|
|000001d0| 20 61 72 65 0d 6f 6c 64 | 2c 20 62 75 74 20 61 72 | are.old|, but ar|
|000001e0| 65 20 6d 6f 72 65 20 72 | 6f 62 75 73 74 2e 20 54 |e more r|obust. T|
|000001f0| 68 65 20 6e 65 77 20 72 | 6f 75 74 69 6e 65 73 20 |he new r|outines |
|00000200| 61 72 65 20 62 61 73 65 | 64 20 6f 6e 20 61 20 4e |are base|d on a N|
|00000210| 75 6d 65 72 69 63 61 6c | 20 52 65 63 69 70 65 73 |umerical| Recipes|
|00000220| 20 69 6e 20 43 0d 72 6f | 75 74 69 6e 65 20 74 6f | in C.ro|utine to|
|00000230| 20 63 6f 6d 70 75 74 65 | 20 74 68 65 20 69 6e 63 | compute| the inc|
|00000240| 6f 6d 70 6c 65 74 65 20 | 62 65 74 61 20 66 75 6e |omplete |beta fun|
|00000250| 63 74 69 6f 6e 2e 20 54 | 68 65 20 6e 65 77 20 72 |ction. T|he new r|
|00000260| 6f 75 74 69 6e 65 73 20 | 61 64 64 20 6c 69 74 74 |outines |add litt|
|00000270| 6c 65 20 74 6f 0d 74 68 | 65 20 6f 6c 64 20 72 6f |le to.th|e old ro|
|00000280| 75 74 69 6e 65 73 2c 20 | 61 6e 64 20 72 65 71 75 |utines, |and requ|
|00000290| 69 72 65 20 74 68 65 20 | 4e 75 6d 65 72 69 63 61 |ire the |Numerica|
|000002a0| 6c 20 52 65 63 69 70 65 | 73 20 69 6e 20 43 2c 20 |l Recipe|s in C, |
|000002b0| 73 6f 20 49 20 63 6f 6d | 6d 65 6e 74 65 64 20 74 |so I com|mented t|
|000002c0| 68 65 6d 0d 6f 75 74 2e | 20 0d 0d 41 6c 73 6f 20 |hem.out.| ..Also |
|000002d0| 73 65 65 3a 20 43 68 69 | 53 71 75 61 72 65 2e 63 |see: Chi|Square.c|
|000002e0| 2c 20 45 78 70 6f 6e 65 | 6e 74 69 61 6c 2e 63 2c |, Expone|ntial.c,|
|000002f0| 20 4e 6f 72 6d 61 6c 2e | 63 2c 20 55 6e 69 66 6f | Normal.|c, Unifo|
|00000300| 72 6d 2e 63 0d 0d 48 49 | 53 54 4f 52 59 3a 0d 31 |rm.c..HI|STORY:.1|
|00000310| 2f 35 2f 39 31 20 41 64 | 64 65 64 20 6e 65 77 20 |/5/91 Ad|ded new |
|00000320| 62 69 6e 6f 6d 69 61 6c | 20 72 6f 75 74 69 6e 65 |binomial| routine|
|00000330| 73 2e 20 54 68 65 73 65 | 20 72 6f 75 74 69 6e 65 |s. These| routine|
|00000340| 73 20 6d 61 79 20 62 65 | 20 0d 09 09 63 6f 6d 6d |s may be| ...comm|
|00000350| 65 6e 74 65 64 20 6f 75 | 74 20 62 79 20 73 65 74 |ented ou|t by set|
|00000360| 74 69 6e 67 20 4e 45 57 | 5f 42 49 4e 4f 4d 49 41 |ting NEW|_BINOMIA|
|00000370| 4c 20 74 6f 20 7a 65 72 | 6f 2e 0d 31 2f 37 2f 39 |L to zer|o..1/7/9|
|00000380| 31 20 52 65 77 72 6f 74 | 65 20 42 69 6e 6f 6d 69 |1 Rewrot|e Binomi|
|00000390| 61 6c 55 70 70 65 72 42 | 6f 75 6e 64 20 26 20 42 |alUpperB|ound & B|
|000003a0| 69 6e 6f 6d 69 61 6c 4c | 6f 77 65 72 42 6f 75 6e |inomialL|owerBoun|
|000003b0| 64 20 74 6f 20 61 6c 6c | 6f 77 20 73 70 65 63 69 |d to all|ow speci|
|000003c0| 66 69 63 61 74 69 6f 6e | 20 6f 66 20 74 68 65 0d |fication| of the.|
|000003d0| 09 09 64 65 73 69 72 65 | 64 20 63 6f 6e 66 69 64 |..desire|d confid|
|000003e0| 65 6e 63 65 20 6f 66 20 | 74 68 65 20 69 6e 74 65 |ence of |the inte|
|000003f0| 72 76 61 6c 2e 0d 34 2f | 32 34 2f 39 32 09 64 67 |rval..4/|24/92.dg|
|00000400| 70 09 41 64 64 65 64 20 | 42 69 6e 6f 6d 69 61 6c |p.Added |Binomial|
|00000410| 53 61 6d 70 6c 65 51 75 | 69 63 6b 6c 79 28 29 2e |SampleQu|ickly().|
|00000420| 0d 34 2f 32 37 2f 39 32 | 09 64 67 70 09 4f 6f 70 |.4/27/92|.dgp.Oop|
|00000430| 73 2e 20 49 20 6a 75 73 | 74 20 6e 6f 74 69 63 65 |s. I jus|t notice|
|00000440| 64 20 74 68 61 74 20 74 | 68 69 73 20 66 69 6c 65 |d that t|his file|
|00000450| 20 77 61 73 20 61 6c 77 | 61 79 73 20 69 6e 63 6c | was alw|ays incl|
|00000460| 75 64 69 6e 67 20 6e 72 | 2e 68 2c 20 77 68 69 63 |uding nr|.h, whic|
|00000470| 68 20 79 6f 75 27 64 0d | 09 09 09 6f 6e 6c 79 20 |h you'd.|...only |
|00000480| 68 61 76 65 20 69 66 20 | 79 6f 75 20 6f 77 6e 20 |have if |you own |
|00000490| 74 68 65 20 4e 75 6d 65 | 72 69 63 61 6c 20 52 65 |the Nume|rical Re|
|000004a0| 63 69 70 65 73 2e 20 49 | 20 6d 6f 76 65 64 20 74 |cipes. I| moved t|
|000004b0| 68 65 20 69 6e 63 6c 75 | 64 65 20 73 74 61 74 65 |he inclu|de state|
|000004c0| 6d 65 6e 74 0d 09 09 09 | 64 6f 77 6e 20 69 6e 73 |ment....|down ins|
|000004d0| 69 64 65 20 74 68 65 20 | 63 6f 6e 64 69 74 69 6f |ide the |conditio|
|000004e0| 6e 61 6c 20 62 65 6c 6f | 77 2c 20 77 68 65 72 65 |nal belo|w, where|
|000004f0| 20 69 74 20 62 65 6c 6f | 6e 67 73 2e 20 0d 2a 2f | it belo|ngs. .*/|
|00000500| 0d 23 69 6e 63 6c 75 64 | 65 20 22 56 69 64 65 6f |.#includ|e "Video|
|00000510| 54 6f 6f 6c 62 6f 78 2e | 68 22 0d 23 69 6e 63 6c |Toolbox.|h".#incl|
|00000520| 75 64 65 20 3c 6d 61 74 | 68 2e 68 3e 0d 0d 23 64 |ude <mat|h.h>..#d|
|00000530| 65 66 69 6e 65 20 4e 45 | 57 5f 42 49 4e 4f 4d 49 |efine NE|W_BINOMI|
|00000540| 41 4c 20 30 0d 0d 6c 6f | 6e 67 20 42 69 6e 6f 6d |AL 0..lo|ng Binom|
|00000550| 69 61 6c 53 61 6d 70 6c | 65 28 64 6f 75 62 6c 65 |ialSampl|e(double|
|00000560| 20 70 2c 6c 6f 6e 67 20 | 6e 29 0d 2f 2a 0d 52 65 | p,long |n)./*.Re|
|00000570| 74 75 72 6e 73 20 61 20 | 61 20 73 61 6d 70 6c 65 |turns a |a sample|
|00000580| 20 66 72 6f 6d 20 61 20 | 62 69 6e 6f 6d 69 61 6c | from a |binomial|
|00000590| 20 64 69 73 74 72 69 62 | 75 74 69 6f 6e 3a 20 6e | distrib|ution: n|
|000005a0| 75 6d 62 65 72 20 6f 66 | 20 68 65 61 64 73 20 69 |umber of| heads i|
|000005b0| 6e 20 6e 20 66 6c 69 70 | 73 20 6f 66 0d 61 20 77 |n n flip|s of.a w|
|000005c0| 65 69 67 68 74 65 64 20 | 63 6f 69 6e 20 77 69 74 |eighted |coin wit|
|000005d0| 68 20 61 20 70 72 6f 62 | 61 62 69 6c 69 74 79 20 |h a prob|ability |
|000005e0| 70 20 6f 66 20 61 20 68 | 65 61 64 20 6f 6e 20 65 |p of a h|ead on e|
|000005f0| 61 63 68 20 66 6c 69 70 | 2e 20 54 68 69 73 20 69 |ach flip|. This i|
|00000600| 73 20 66 69 6e 65 20 69 | 66 20 6e 20 69 73 20 73 |s fine i|f n is s|
|00000610| 6d 61 6c 6c 2e 20 48 6f | 77 65 76 65 72 2c 0d 69 |mall. Ho|wever,.i|
|00000620| 66 20 6e 20 69 73 20 6c | 61 72 67 65 2c 20 65 2e |f n is l|arge, e.|
|00000630| 67 2e 20 6e 3e 31 30 30 | 2c 20 74 68 65 6e 20 74 |g. n>100|, then t|
|00000640| 68 69 73 20 72 6f 75 74 | 69 6e 65 20 77 69 6c 6c |his rout|ine will|
|00000650| 20 62 65 20 72 61 74 68 | 65 72 20 73 6c 6f 77 2c | be rath|er slow,|
|00000660| 20 61 6e 64 20 79 6f 75 | 20 6d 61 79 20 70 72 65 | and you| may pre|
|00000670| 66 65 72 0d 74 6f 20 75 | 73 65 20 74 68 65 20 6d |fer.to u|se the m|
|00000680| 6f 72 65 20 65 6c 61 62 | 6f 72 61 74 65 20 4e 75 |ore elab|orate Nu|
|00000690| 6d 65 72 69 63 61 6c 20 | 52 65 63 69 70 65 73 20 |merical |Recipes |
|000006a0| 62 6e 6c 64 65 76 28 29 | 20 72 6f 75 74 69 6e 65 |bnldev()| routine|
|000006b0| 2e 0d 2a 2f 0d 7b 0d 09 | 6c 6f 6e 67 20 6b 2c 69 |..*/.{..|long k,i|
|000006c0| 3b 0d 0d 09 6b 3d 30 3b | 0d 09 66 6f 72 28 69 3d |;...k=0;|..for(i=|
|000006d0| 30 3b 69 3c 6e 3b 69 2b | 2b 29 20 69 66 28 70 3e |0;i<n;i+|+) if(p>|
|000006e0| 55 6e 69 66 6f 72 6d 53 | 61 6d 70 6c 65 28 29 29 |UniformS|ample())|
|000006f0| 6b 2b 2b 3b 0d 09 72 65 | 74 75 72 6e 20 6b 3b 0d |k++;..re|turn k;.|
|00000700| 7d 0d 0d 69 6e 74 20 42 | 69 6e 6f 6d 69 61 6c 53 |}..int B|inomialS|
|00000710| 61 6d 70 6c 65 51 75 69 | 63 6b 6c 79 28 69 6e 74 |ampleQui|ckly(int|
|00000720| 20 6e 29 0d 2f 2f 20 44 | 6f 65 73 20 6e 20 66 6c | n).// D|oes n fl|
|00000730| 69 70 73 20 6f 66 20 61 | 6e 20 75 6e 77 65 69 67 |ips of a|n unweig|
|00000740| 68 74 65 64 20 63 6f 69 | 6e 20 61 6e 64 20 72 65 |hted coi|n and re|
|00000750| 74 75 72 6e 73 20 74 68 | 65 20 6e 75 6d 62 65 72 |turns th|e number|
|00000760| 20 6f 66 20 68 65 61 64 | 73 2e 20 56 65 72 79 20 | of head|s. Very |
|00000770| 66 61 73 74 20 69 66 20 | 6e 3c 31 30 30 30 2e 20 |fast if |n<1000. |
|00000780| 0d 2f 2f 20 46 6f 72 20 | 6c 61 72 67 65 72 20 6e |.// For |larger n|
|00000790| 20 69 74 20 77 6f 75 6c | 64 20 62 65 20 66 61 73 | it woul|d be fas|
|000007a0| 74 65 72 20 74 6f 20 75 | 73 65 20 62 6e 6c 64 65 |ter to u|se bnlde|
|000007b0| 76 28 29 2e 0d 7b 0d 09 | 72 65 67 69 73 74 65 72 |v()..{..|register|
|000007c0| 20 69 6e 74 20 69 2c 6b | 3d 30 3b 0d 09 72 65 67 | int i,k|=0;..reg|
|000007d0| 69 73 74 65 72 20 73 68 | 6f 72 74 20 72 3b 0d 09 |ister sh|ort r;..|
|000007e0| 0d 09 66 6f 72 28 69 3d | 6e 3b 69 3e 3d 38 3b 69 |..for(i=|n;i>=8;i|
|000007f0| 2d 3d 38 29 7b 0d 09 09 | 72 3d 72 61 6e 64 55 28 |-=8){...|r=randU(|
|00000800| 29 3b 09 2f 2f 20 55 73 | 65 20 6f 6e 6c 79 20 74 |);.// Us|e only t|
|00000810| 68 65 20 75 70 70 65 72 | 20 38 20 62 69 74 73 2c |he upper| 8 bits,|
|00000820| 20 77 68 69 63 68 20 61 | 72 65 20 72 65 70 75 74 | which a|re reput|
|00000830| 65 64 20 74 6f 20 62 65 | 20 6d 6f 72 65 20 72 61 |ed to be| more ra|
|00000840| 6e 64 6f 6d 2e 0d 09 09 | 69 66 28 72 3c 30 29 6b |ndom....|if(r<0)k|
|00000850| 2b 2b 3b 0d 09 09 72 3c | 3c 3d 31 3b 0d 09 09 69 |++;...r<|<=1;...i|
|00000860| 66 28 72 3c 30 29 6b 2b | 2b 3b 0d 09 09 72 3c 3c |f(r<0)k+|+;...r<<|
|00000870| 3d 31 3b 0d 09 09 69 66 | 28 72 3c 30 29 6b 2b 2b |=1;...if|(r<0)k++|
|00000880| 3b 0d 09 09 72 3c 3c 3d | 31 3b 0d 09 09 69 66 28 |;...r<<=|1;...if(|
|00000890| 72 3c 30 29 6b 2b 2b 3b | 0d 09 09 72 3c 3c 3d 31 |r<0)k++;|...r<<=1|
|000008a0| 3b 0d 09 09 69 66 28 72 | 3c 30 29 6b 2b 2b 3b 0d |;...if(r|<0)k++;.|
|000008b0| 09 09 72 3c 3c 3d 31 3b | 0d 09 09 69 66 28 72 3c |..r<<=1;|...if(r<|
|000008c0| 30 29 6b 2b 2b 3b 0d 09 | 09 72 3c 3c 3d 31 3b 0d |0)k++;..|.r<<=1;.|
|000008d0| 09 09 69 66 28 72 3c 30 | 29 6b 2b 2b 3b 0d 09 09 |..if(r<0|)k++;...|
|000008e0| 72 3c 3c 3d 31 3b 0d 09 | 09 69 66 28 72 3c 30 29 |r<<=1;..|.if(r<0)|
|000008f0| 6b 2b 2b 3b 0d 09 09 72 | 3c 3c 3d 31 3b 0d 09 7d |k++;...r|<<=1;..}|
|00000900| 0d 09 69 66 28 69 3e 30 | 29 7b 0d 09 09 72 3d 72 |..if(i>0|){...r=r|
|00000910| 61 6e 64 55 28 29 3b 0d | 09 09 66 6f 72 28 3b 69 |andU();.|..for(;i|
|00000920| 3e 30 3b 69 2d 2d 29 7b | 0d 09 09 09 69 66 28 72 |>0;i--){|....if(r|
|00000930| 3c 30 29 6b 2b 2b 3b 0d | 09 09 09 72 3c 3c 3d 31 |<0)k++;.|...r<<=1|
|00000940| 3b 0d 09 09 7d 0d 09 7d | 0d 09 72 65 74 75 72 6e |;...}..}|..return|
|00000950| 20 6b 3b 0d 7d 0d 0d 2f | 2a 0d 42 69 6e 6f 6d 69 | k;.}../|*.Binomi|
|00000960| 61 6c 55 70 70 65 72 42 | 6f 75 6e 64 20 61 6e 64 |alUpperB|ound and|
|00000970| 20 42 69 6e 6f 6d 69 61 | 6c 4c 6f 77 65 72 42 6f | Binomia|lLowerBo|
|00000980| 75 6e 64 20 72 65 74 75 | 72 6e 20 61 20 50 20 63 |und retu|rn a P c|
|00000990| 6f 6e 66 69 64 65 6e 63 | 65 20 69 6e 74 65 72 76 |onfidenc|e interv|
|000009a0| 61 6c 20 66 6f 72 20 74 | 68 65 0d 75 6e 64 65 72 |al for t|he.under|
|000009b0| 6c 79 69 6e 67 20 62 69 | 6e 6f 6d 69 61 6c 20 70 |lying bi|nomial p|
|000009c0| 72 6f 62 61 62 69 6c 69 | 74 79 20 61 73 73 75 6d |robabili|ty assum|
|000009d0| 65 64 20 74 6f 20 68 61 | 76 65 20 67 65 6e 65 72 |ed to ha|ve gener|
|000009e0| 61 74 65 64 20 74 68 65 | 20 64 61 74 61 2e 0d 0d |ated the| data...|
|000009f0| 54 68 65 20 66 6f 72 6d | 75 6c 61 20 69 73 20 62 |The form|ula is b|
|00000a00| 61 73 65 64 20 6f 6e 20 | 61 20 47 61 75 73 73 69 |ased on |a Gaussi|
|00000a10| 61 6e 20 61 70 70 72 6f | 78 69 6d 61 74 69 6f 6e |an appro|ximation|
|00000a20| 2c 20 73 6f 6c 76 69 6e | 67 20 66 6f 72 20 74 68 |, solvin|g for th|
|00000a30| 65 20 70 20 74 68 61 74 | 20 77 69 6c 6c 0d 70 75 |e p that| will.pu|
|00000a40| 74 20 74 68 65 20 6f 62 | 73 65 72 76 65 64 20 72 |t the ob|served r|
|00000a50| 65 73 75 6c 74 20 74 68 | 65 20 72 69 67 68 74 20 |esult th|e right |
|00000a60| 6e 75 6d 62 65 72 20 6f | 66 20 73 74 61 6e 64 61 |number o|f standa|
|00000a70| 72 64 20 64 65 76 69 61 | 74 69 6f 6e 73 20 61 77 |rd devia|tions aw|
|00000a80| 61 79 20 66 72 6f 6d 20 | 74 68 65 0d 6d 65 61 6e |ay from |the.mean|
|00000a90| 2c 20 70 6c 75 73 20 6f | 72 20 6d 69 6e 75 73 20 |, plus o|r minus |
|00000aa0| 30 2e 35 2c 20 61 73 20 | 61 20 22 63 6f 6e 74 69 |0.5, as |a "conti|
|00000ab0| 6e 75 69 74 79 20 63 6f | 72 72 65 63 74 69 6f 6e |nuity co|rrection|
|00000ac0| 22 2e 0d 0d 54 68 69 73 | 20 69 73 20 74 68 65 20 |"...This| is the |
|00000ad0| 62 65 73 74 20 66 6f 72 | 6d 75 6c 61 20 49 20 63 |best for|mula I c|
|00000ae0| 6f 75 6c 64 20 66 69 6e | 64 20 69 6e 20 6c 6f 6f |ould fin|d in loo|
|00000af0| 6b 69 6e 67 20 74 68 72 | 6f 75 67 68 20 73 65 76 |king thr|ough sev|
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|00000b20| 74 68 65 20 72 65 73 75 | 6c 74 20 68 61 73 20 74 |the resu|lt has t|
|00000b30| 6f 20 62 65 20 74 61 6b | 65 6e 20 77 69 74 68 20 |o be tak|en with |
|00000b40| 61 20 67 72 61 69 6e 20 | 6f 66 20 73 61 6c 74 20 |a grain |of salt |
|00000b50| 62 65 63 61 75 73 65 20 | 69 74 20 69 73 0d 6e 6f |because |it is.no|
|00000b60| 74 20 70 6f 73 73 69 62 | 6c 65 20 74 6f 20 70 72 |t possib|le to pr|
|00000b70| 6f 64 75 63 65 20 61 20 | 62 69 6e 6f 6d 69 61 6c |oduce a |binomial|
|00000b80| 20 63 6f 6e 66 69 64 65 | 6e 63 65 20 69 6e 74 65 | confide|nce inte|
|00000b90| 72 76 61 6c 20 74 68 61 | 74 20 77 69 6c 6c 20 73 |rval tha|t will s|
|00000ba0| 61 74 69 73 66 79 20 74 | 68 65 0d 73 74 72 69 63 |atisfy t|he.stric|
|00000bb0| 74 20 64 65 66 69 6e 69 | 74 69 6f 6e 20 6f 66 20 |t defini|tion of |
|00000bc0| 61 20 63 6f 6e 66 69 64 | 65 6e 63 65 20 69 6e 74 |a confid|ence int|
|00000bd0| 65 72 76 61 6c 2c 20 6e | 61 6d 65 6c 79 20 6f 6e |erval, n|amely on|
|00000be0| 65 20 74 68 61 74 20 77 | 69 6c 6c 20 68 61 76 65 |e that w|ill have|
|00000bf0| 20 74 68 65 0d 73 70 65 | 63 69 66 69 65 64 20 70 | the.spe|cified p|
|00000c00| 72 6f 62 61 62 69 6c 69 | 74 79 20 50 20 6f 66 20 |robabili|ty P of |
|00000c10| 63 6f 6e 74 61 69 6e 69 | 6e 67 20 74 68 65 20 75 |containi|ng the u|
|00000c20| 6e 6b 6e 6f 77 6e 20 62 | 75 74 20 66 69 78 65 64 |nknown b|ut fixed|
|00000c30| 20 70 61 72 61 6d 65 74 | 65 72 20 70 2e 20 54 68 | paramet|er p. Th|
|00000c40| 61 74 27 73 0d 62 65 63 | 61 75 73 65 2c 20 75 6e |at's.bec|ause, un|
|00000c50| 6c 69 6b 65 20 74 68 65 | 20 4e 6f 72 6d 61 6c 20 |like the| Normal |
|00000c60| 64 69 73 74 72 69 62 75 | 74 69 6f 6e 2c 20 74 68 |distribu|tion, th|
|00000c70| 65 20 42 69 6e 6f 6d 69 | 61 6c 20 64 69 73 74 72 |e Binomi|al distr|
|00000c80| 69 62 75 74 69 6f 6e 20 | 69 73 20 6e 6f 74 0d 74 |ibution |is not.t|
|00000c90| 72 61 6e 73 6c 61 74 69 | 6f 6e 20 69 6e 76 61 72 |ranslati|on invar|
|00000ca0| 69 61 6e 74 2e 20 0d 0d | 49 20 67 61 76 65 20 73 |iant. ..|I gave s|
|00000cb0| 6f 6d 65 20 74 68 6f 75 | 67 68 74 20 74 6f 20 74 |ome thou|ght to t|
|00000cc0| 61 6b 69 6e 67 20 61 20 | 42 61 79 65 73 69 61 6e |aking a |Bayesian|
|00000cd0| 20 61 70 70 72 6f 61 63 | 68 2c 20 61 73 73 75 6d | approac|h, assum|
|00000ce0| 69 6e 67 20 61 20 75 6e | 69 66 6f 72 6d 20 70 72 |ing a un|iform pr|
|00000cf0| 69 6f 72 20 70 64 66 0d | 66 6f 72 20 70 20 61 6e |ior pdf.|for p an|
|00000d00| 64 20 74 68 65 6e 20 63 | 6f 6d 70 75 74 69 6e 67 |d then c|omputing|
|00000d10| 20 61 6e 20 61 20 70 6f | 73 74 65 72 69 6f 72 69 | an a po|steriori|
|00000d20| 20 63 6f 6e 66 69 64 65 | 6e 63 65 20 69 6e 74 65 | confide|nce inte|
|00000d30| 72 76 61 6c 2e 20 54 68 | 69 73 20 63 61 6e 20 62 |rval. Th|is can b|
|00000d40| 65 20 64 6f 6e 65 2c 0d | 62 75 74 20 69 74 27 73 |e done,.|but it's|
|00000d50| 20 68 61 72 64 2e 20 49 | 20 63 6f 6e 63 6c 75 64 | hard. I| conclud|
|00000d60| 65 64 20 74 68 61 74 20 | 69 74 27 73 20 70 6f 69 |ed that |it's poi|
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|00001f40| 64 6f 75 62 6c 65 20 62 | 29 0d 09 2f 2a 0d 09 54 |double b|)../*..T|
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|00002060| 2b 68 69 67 68 29 2a 30 | 2e 35 3b 0d 09 7d 0d 09 |+high)*0|.5;..}..|
|00002070| 0d 23 65 6e 64 69 66 0d | 00 00 00 00 00 00 00 00 |.#endif.|........|
|00002080| 00 00 01 00 00 00 02 6c | 00 00 01 6c 00 00 00 5e |.......l|...l...^|
|00002090| 70 79 72 69 67 68 74 20 | 28 63 29 20 31 39 39 30 |pyright |(c) 1990|
|000020a0| 20 44 65 6e 69 73 20 47 | 2e 20 50 65 6c 6c 69 0d | Denis G|. Pelli.|
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|000020c0| 50 61 72 74 53 49 54 21 | 00 00 00 00 00 00 00 00 |PartSIT!|........|
|000020d0| 00 00 50 61 72 74 53 49 | 54 21 00 00 00 00 00 00 |..PartSI|T!......|
|000020e0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000020f0| 00 00 ab bf ee 57 00 00 | 00 00 00 00 02 ca 0d 74 |.....W..|.......t|
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|00002180| 00 00 00 1e 00 50 00 20 | 01 dd 02 3d 00 50 00 20 |.....P. |...=.P. |
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|000021b0| 09 42 69 6e 6f 6d 69 61 | 6c 00 00 00 0e 0e 00 00 |.Binomia|l.......|
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|000021d0| 42 6f 75 6e 64 00 00 00 | 18 18 00 00 18 23 0b 42 |Bound...|.....#.B|
|000021e0| 69 6e 6f 6d 69 61 6c 50 | 64 66 00 00 04 cb 00 00 |inomialP|df......|
|000021f0| 04 d9 0f 42 69 6e 6f 6d | 69 61 6c 53 61 6d 70 6c |...Binom|ialSampl|
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|00002220| 00 00 10 2c 00 00 10 3e | 13 42 69 6e 6f 6d 69 61 |...,...>|.Binomia|
|00002230| 6c 55 70 70 65 72 42 6f | 75 6e 64 00 00 00 1d 0c |lUpperBo|und.....|
|00002240| 00 00 1d 1a 0f 49 6e 63 | 6f 6d 70 6c 65 74 65 42 |.....Inc|ompleteB|
|00002250| 65 74 61 00 00 00 1a 1d | 00 00 1a 2c 0f 49 6e 76 |eta.....|...,.Inv|
|00002260| 65 72 73 65 42 69 6e 6f | 6d 69 61 6c 00 00 1e 98 |erseBino|mial....|
|00002270| 00 00 1e ad 15 49 6e 76 | 65 72 73 65 49 6e 63 6f |.....Inv|erseInco|
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|00002290| 12 d1 05 6d 61 69 6e 00 | 00 00 00 48 00 09 4d 6f |...main.|...H..Mo|
|000022a0| 6e 61 63 6f 00 00 00 00 | 00 00 00 00 00 00 00 00 |naco....|........|
|000022b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 03 |........|........|
|000022c0| 00 04 00 3d 00 03 01 a0 | 02 7d 00 3d 00 03 01 a0 |...=....|.}.=....|
|000022d0| 02 7d ab 31 05 f1 00 00 | 00 00 00 00 00 02 00 00 |.}.1....|........|
|000022e0| 00 00 00 00 00 00 00 04 | 00 01 00 01 00 00 01 00 |........|........|
|000022f0| 00 00 02 6c 00 00 01 6c | 00 00 00 5e 00 b8 5c 88 |...l...l|...^..\.|
|00002300| 3a 06 00 00 00 1c 00 5e | 00 01 4d 50 53 52 00 02 |:......^|..MPSR..|
|00002310| 00 12 4d 57 42 42 00 00 | 00 36 03 f0 ff ff 00 00 |..MWBB..|.6......|
|00002320| 00 00 00 00 00 00 03 ef | ff ff 00 00 00 22 00 00 |........|....."..|
|00002330| 00 00 03 ed ff ff 00 00 | 01 18 00 00 00 00 03 f0 |........|........|
|00002340| ff ff 00 00 01 64 00 00 | 00 00 00 00 00 00 00 00 |.....d..|........|
|00002350| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002360| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002370| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
+--------+-------------------------+-------------------------+--------+--------+