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R : Copyright 2000, The R Development Core Team
 2 
R : Copyright 2001, The R Development Core Team
3 
Version 1.2.0 Under development (unstable) (2000-11-09)
 3 
Version 1.2.0 Patched (2001-01-06)
4 
 
 4 
 
5 
R is free software and comes with ABSOLUTELY NO WARRANTY.
 5 
R is free software and comes with ABSOLUTELY NO WARRANTY.
6 
You are welcome to redistribute it under certain conditions.
 6 
You are welcome to redistribute it under certain conditions.
7 
Type	"?license" or "?licence" for distribution details.
 7 
Type `license()' or `licence()' for distribution details.
8 
 
 8 
 
9 
R is a collaborative project with many contributors.
 9 
R is a collaborative project with many contributors.
10 
Type	"?contributors" for a list.
 10 
Type `contributors()' for more information.
11 
 
 11 
 
12 
Type	"demo()" for some demos, "help()" for on-line help, or
 12 
Type `demo()' for some demos, `help()' for on-line help, or
13 
    	"help.start()" for a HTML browser interface to help.
 13 
`help.start()' for a HTML browser interface to help.
14 
Type	"q()" to quit R.
 14 
Type `q()' to quit R.
15 
 
 15 
 
16 
> ##
 16 
> ##
17 
> ## RNG tests using DKW inequality for rate of convergence
 17 
> ## RNG tests using DKW inequality for rate of convergence
18 
> ##
 18 
> ##
19 
> ## P(sup F_n-F >t)<2exp(-2nt^2)
 19 
> ## P(sup | F_n - F | > t) < 2 exp(-2nt^2)
20 
> ##
 20 
> ##
21 
> ## The 2 in front of exp() was derived by Massart. It is the best possible
 21 
> ## The 2 in front of exp() was derived by Massart. It is the best possible
22 
> ## constant valid uniformly in t,n,F. For large nt^2 this agrees with the
 22 
> ## constant valid uniformly in t,n,F. For large n*t^2 this agrees with the
23 
> ## large-sample approximation to the Kolmogorov-Smirnov statistic.
 23 
> ## large-sample approximation to the Kolmogorov-Smirnov statistic.
24 
> ##
24 
> ##
25 
>
25 
>
26 
>
26 
>
27 
> superror<-function(rfoo,pfoo,sample.size,...){
 27 
> superror <- function(rfoo,pfoo,sample.size,...) {
28 
+     x<-rfoo(sample.size,...)
 28 
+     x <- rfoo(sample.size,...)
29 
+     tx<-table(x)
 29 
+     tx <- table(x)
30 
+     xi<-as.numeric(names(tx))
 30 
+     xi <- as.numeric(names(tx))
31 
+     f<-pfoo(xi,...)
 31 
+     f <- pfoo(xi,...)
32 
+     fhat<-cumsum(tx)/sample.size
 32 
+     fhat <- cumsum(tx)/sample.size
33 
+     max(abs(fhat-f))
 33 
+     max(abs(fhat-f))
34 
+ }
 34 
+ }
35 
>
35 
>
36 
> pdkwbound<-function(n,t) 2*exp(-2*n*t*t)
 36 
> pdkwbound <- function(n,t) 2*exp(-2*n*t*t)
37 
>
37 
>
38 
> qdkwbound<-function(n,p) sqrt(log(p/2)/(-2*n))
 38 
> qdkwbound <- function(n,p) sqrt(log(p/2)/(-2*n))
39 
>
39 
>
- 
 
 40 
> dkwtest <- function(stub = "norm", ...,
- 
 
 41 
+                     sample.size = 10000, pthreshold = 0.001,
40 
> dkwtest<-function(stub="norm",sample.size=10000,...,pthreshold=0.001,print.result=TRUE,print.detail=FALSE,stop.on.failure=TRUE){
 42 
+                     print.result = TRUE, print.detail = FALSE,
- 
 
 43 
+                     stop.on.failure = TRUE)
- 
 
 44 
+ {
41 
+     rfoo<-eval(as.name(paste("r",stub,sep="")))
 45 
+     rfoo <- eval(as.name(paste("r", stub, sep="")))
42 
+     pfoo<-eval(as.name(paste("p",stub,sep="")))
 46 
+     pfoo <- eval(as.name(paste("p", stub, sep="")))
43 
+     s<-superror(rfoo,pfoo,sample.size,...)
 47 
+     s <- superror(rfoo, pfoo, sample.size, ...)
44 
+     if (print.result | print.detail){
 48 
+     if (print.result || print.detail) {
45 
+         printargs<-substitute(list(...))
 49 
+         printargs <- substitute(list(...))
46 
+         printargs[[1]]<-as.name(stub)
 50 
+         printargs[[1]] <- as.name(stub)
47 
+         cat(deparse(printargs))
 51 
+         cat(deparse(printargs))
48 
+         if (print.detail)
 52 
+         if (print.detail)
- 
 
 53 
+             cat("\nsupremum error = ",signif(s,2),
49 
+             cat("\nsupremum error = ",signif(s,2)," with p-value=",min(1,round(pdkwbound(sample.size,s),4)),"\n")
 54 
+                 " with p-value=",min(1,round(pdkwbound(sample.size,s),4)),"\n")
50 
+     }
 55 
+     }
51 
+     rval<-(s<qdkwbound(sample.size,pthreshold))
 56 
+     rval <- (s < qdkwbound(sample.size,pthreshold))
52 
+     if (print.result)
 57 
+     if (print.result)
53 
+         cat(c(" FAILED\n"," PASSED\n",)[rval+1])
 58 
+         cat(c(" FAILED\n"," PASSED\n",)[rval+1])
54 
+     if (stop.on.failure & !rval)
 59 
+     if (stop.on.failure && !rval)
55 
+         stop("dkwtest failed")
 60 
+         stop("dkwtest failed")
56 
+     rval
 61 
+     rval
57 
+   }
 62 
+ }
- 
 
 63 
>
- 
 
 64 
> .proctime00 <- proc.time() # start timing
58 
>
65 
>
59 
>
66 
>
60 
> dkwtest("binom",size=1,prob=0.2)
 67 
> dkwtest("binom",size =   1,prob = 0.2)
61 
binom(size = 1, prob = 0.2) PASSED
 68 
binom(size = 1, prob = 0.2) PASSED
62 
[1] TRUE
 69 
[1] TRUE
- 
 
 70 
> dkwtest("binom",size =   2,prob = 0.2)
- 
 
 71 
binom(size = 2, prob = 0.2) PASSED
- 
 
 72 
[1] TRUE
63 
> dkwtest("binom",size=100,prob=0.2)
 73 
> dkwtest("binom",size = 100,prob = 0.2)
64 
binom(size = 100, prob = 0.2) PASSED
 74 
binom(size = 100, prob = 0.2) PASSED
65 
[1] TRUE
 75 
[1] TRUE
66 
> dkwtest("binom",size=1,prob=0.2)
 76 
> dkwtest("binom",size = 1e4,prob = 0.2)
67 
binom(size = 1, prob = 0.2) PASSED
 77 
binom(size = 10000, prob = 0.2) PASSED
68 
[1] TRUE
 78 
[1] TRUE
69 
> dkwtest("binom",size=1,prob=0.8)
 79 
> dkwtest("binom",size =   1,prob = 0.8)
70 
binom(size = 1, prob = 0.8) PASSED
 80 
binom(size = 1, prob = 0.8) PASSED
71 
[1] TRUE
 81 
[1] TRUE
72 
> dkwtest("binom",size=100,prob=0.8)
 82 
> dkwtest("binom",size = 100,prob = 0.8)
73 
binom(size = 100, prob = 0.8) PASSED
 83 
binom(size = 100, prob = 0.8) PASSED
74 
[1] TRUE
 84 
[1] TRUE
75 
> dkwtest("binom",size=100,prob=0.2)
 85 
> dkwtest("binom",size = 100,prob = 0.999)
76 
binom(size = 100, prob = 0.2) PASSED
 86 
binom(size = 100, prob = 0.999) PASSED
77 
[1] TRUE
 - 
 
78 
> dkwtest("binom",size=1,prob=0.2)
 - 
 
79 
binom(size = 1, prob = 0.2) PASSED
 - 
 
80 
[1] TRUE
 87 
[1] TRUE
81 
>
88 
>
82 
> dkwtest("pois",lambda=9.5)
 89 
> dkwtest("pois",lambda =  0.095)
83 
pois(lambda = 9.5) PASSED
 90 
pois(lambda = 0.095) PASSED
84 
[1] TRUE
 91 
[1] TRUE
85 
> dkwtest("pois",lambda=0.95)
 92 
> dkwtest("pois",lambda =  0.95)
86 
pois(lambda = 0.95) PASSED
 93 
pois(lambda = 0.95) PASSED
87 
[1] TRUE
 94 
[1] TRUE
88 
> dkwtest("pois",lambda=95)
 95 
> dkwtest("pois",lambda =  9.5)
89 
pois(lambda = 95) PASSED
 96 
pois(lambda = 9.5) PASSED
90 
[1] TRUE
 97 
[1] TRUE
91 
> dkwtest("pois",lambda=0.95)
 98 
> dkwtest("pois",lambda = 95)
92 
pois(lambda = 0.95) PASSED
 99 
pois(lambda = 95) PASSED
93 
[1] TRUE
 100 
[1] TRUE
94 
>
101 
>
95 
> dkwtest("nbinom",size=1,prob=0.2)
 102 
> dkwtest("nbinom",size =   1,prob = 0.2)
96 
nbinom(size = 1, prob = 0.2) PASSED
 103 
nbinom(size = 1, prob = 0.2) PASSED
97 
[1] TRUE
 104 
[1] TRUE
- 
 
 105 
> dkwtest("nbinom",size =   2,prob = 0.2)
- 
 
 106 
nbinom(size = 2, prob = 0.2) PASSED
- 
 
 107 
[1] TRUE
98 
> dkwtest("nbinom",size=100,prob=0.2)
 108 
> dkwtest("nbinom",size = 100,prob = 0.2)
99 
nbinom(size = 100, prob = 0.2) PASSED
 109 
nbinom(size = 100, prob = 0.2) PASSED
100 
[1] TRUE
 110 
[1] TRUE
101 
> dkwtest("nbinom",size=1,prob=0.2)
 111 
> dkwtest("nbinom",size = 1e4,prob = 0.2)
102 
nbinom(size = 1, prob = 0.2) PASSED
 112 
nbinom(size = 10000, prob = 0.2) PASSED
103 
[1] TRUE
 113 
[1] TRUE
104 
> dkwtest("nbinom",size=1,prob=0.8)
 114 
> dkwtest("nbinom",size =   1,prob = 0.8)
105 
nbinom(size = 1, prob = 0.8) PASSED
 115 
nbinom(size = 1, prob = 0.8) PASSED
106 
[1] TRUE
 116 
[1] TRUE
107 
> dkwtest("nbinom",size=100,prob=0.8)
 117 
> dkwtest("nbinom",size = 100,prob = 0.8)
108 
nbinom(size = 100, prob = 0.8) PASSED
 118 
nbinom(size = 100, prob = 0.8) PASSED
109 
[1] TRUE
 119 
[1] TRUE
110 
> dkwtest("nbinom",size=100,prob=0.2)
 120 
> dkwtest("nbinom",size = 100,prob = 0.999)
111 
nbinom(size = 100, prob = 0.2) PASSED
 121 
nbinom(size = 100, prob = 0.999) PASSED
112 
[1] TRUE
 - 
 
113 
> dkwtest("nbinom",size=1,prob=0.2)
 - 
 
114 
nbinom(size = 1, prob = 0.2) PASSED
 - 
 
115 
[1] TRUE
 122 
[1] TRUE
116 
>
123 
>
117 
> dkwtest("norm")
 124 
> dkwtest("norm")
118 
norm() PASSED
 125 
norm() PASSED
119 
[1] TRUE
 126 
[1] TRUE
120 
> dkwtest("norm",mean=5,sd=3)
 127 
> dkwtest("norm",mean = 5,sd = 3)
121 
norm(mean = 5, sd = 3) PASSED
 128 
norm(mean = 5, sd = 3) PASSED
122 
[1] TRUE
 129 
[1] TRUE
123 
>
130 
>
124 
> dkwtest("gamma",shape=0.1)
 131 
> dkwtest("gamma",shape =  0.1)
125 
gamma(shape = 0.1) PASSED
 132 
gamma(shape = 0.1) PASSED
126 
[1] TRUE
 133 
[1] TRUE
127 
> dkwtest("gamma",shape=10)
 134 
> dkwtest("gamma",shape =  0.2)
128 
gamma(shape = 10) PASSED
 135 
gamma(shape = 0.2) PASSED
129 
[1] TRUE
 136 
[1] TRUE
130 
> dkwtest("gamma",shape=0.1)
 - 
 
131 
gamma(shape = 0.1) PASSED
 - 
 
132 
[1] TRUE
 - 
 
133 
> dkwtest("gamma",shape=10)
 137 
> dkwtest("gamma",shape = 10)
134 
gamma(shape = 10) PASSED
 138 
gamma(shape = 10) PASSED
135 
[1] TRUE
 139 
[1] TRUE
- 
 
 140 
> dkwtest("gamma",shape = 20)
- 
 
 141 
gamma(shape = 20) PASSED
- 
 
 142 
[1] TRUE
136 
>
143 
>
137 
> dkwtest("hyper",m=40,n=30,k=20)
 144 
> dkwtest("hyper",m = 40,n = 30,k = 20)
138 
hyper(m = 40, n = 30, k = 20) PASSED
 145 
hyper(m = 40, n = 30, k = 20) PASSED
139 
[1] TRUE
 146 
[1] TRUE
140 
> dkwtest("hyper",m=4,n=3,k=2)
 147 
> dkwtest("hyper",m = 40,n =  3,k = 20)
141 
hyper(m = 4, n = 3, k = 2) PASSED
 148 
hyper(m = 40, n = 3, k = 20) PASSED
142 
[1] TRUE
 149 
[1] TRUE
143 
> dkwtest("hyper",m=40,n=30,k=20)
 150 
> dkwtest("hyper",m =  6,n =  3,k =  2)
144 
hyper(m = 40, n = 30, k = 20) PASSED
 151 
hyper(m = 6, n = 3, k = 2) PASSED
145 
[1] TRUE
 152 
[1] TRUE
146 
> dkwtest("hyper",m=4,n=3,k=2)
 - 
 
147 
hyper(m = 4, n = 3, k = 2) PASSED
 - 
 
148 
[1] TRUE
 - 
 
149 
> dkwtest("hyper",m=5,n=3,k=2)
 153 
> dkwtest("hyper",m =  5,n =  3,k =  2)
150 
hyper(m = 5, n = 3, k = 2) PASSED
 154 
hyper(m = 5, n = 3, k = 2) PASSED
151 
[1] TRUE
 155 
[1] TRUE
- 
 
 156 
> dkwtest("hyper",m =  4,n =  3,k =  2)
- 
 
 157 
hyper(m = 4, n = 3, k = 2) PASSED
- 
 
 158 
[1] TRUE
- 
 
 159 
>
152 
>
160 
>
153 
> dkwtest("signrank",n=1)
 161 
> dkwtest("signrank",n =  1)
154 
signrank(n = 1) PASSED
 162 
signrank(n = 1) PASSED
155 
[1] TRUE
 163 
[1] TRUE
156 
> dkwtest("signrank",n=10)
 164 
> dkwtest("signrank",n =  2)
157 
signrank(n = 10) PASSED
 165 
signrank(n = 2) PASSED
158 
[1] TRUE
 166 
[1] TRUE
159 
> dkwtest("signrank",n=1)
 167 
> dkwtest("signrank",n = 10)
160 
signrank(n = 1) PASSED
 168 
signrank(n = 10) PASSED
161 
[1] TRUE
 169 
[1] TRUE
162 
> dkwtest("signrank",n=30)
 170 
> dkwtest("signrank",n = 30)
163 
signrank(n = 30) PASSED
 171 
signrank(n = 30) PASSED
164 
[1] TRUE
 172 
[1] TRUE
165 
>
173 
>
166 
> dkwtest("wilcox",m=40,n=30)
 174 
> dkwtest("wilcox",m = 40,n = 30)
167 
wilcox(m = 40, n = 30) PASSED
 175 
wilcox(m = 40, n = 30) PASSED
168 
[1] TRUE
 176 
[1] TRUE
169 
> dkwtest("wilcox",m=4,n=3)
 177 
> dkwtest("wilcox",m = 40,n = 10)
170 
wilcox(m = 4, n = 3) PASSED
 178 
wilcox(m = 40, n = 10) PASSED
171 
[1] TRUE
 179 
[1] TRUE
172 
> dkwtest("wilcox",m=40,n=30)
 180 
> dkwtest("wilcox",m =  6,n =  3)
173 
wilcox(m = 40, n = 30) PASSED
 181 
wilcox(m = 6, n = 3) PASSED
174 
[1] TRUE
 182 
[1] TRUE
175 
> dkwtest("wilcox",m=4,n=3)
 - 
 
176 
wilcox(m = 4, n = 3) PASSED
 - 
 
177 
[1] TRUE
 - 
 
178 
> dkwtest("wilcox",m=5,n=3)
 183 
> dkwtest("wilcox",m =  5,n =  3)
179 
wilcox(m = 5, n = 3) PASSED
 184 
wilcox(m = 5, n = 3) PASSED
180 
[1] TRUE
 185 
[1] TRUE
- 
 
 186 
> dkwtest("wilcox",m =  4,n =  3)
- 
 
 187 
wilcox(m = 4, n = 3) PASSED
- 
 
 188 
[1] TRUE
181 
>
189 
>
182 
> dkwtest("chisq",df=1)
 190 
> dkwtest("chisq",df =  1)
183 
chisq(df = 1) PASSED
 191 
chisq(df = 1) PASSED
184 
[1] TRUE
 192 
[1] TRUE
185 
> dkwtest("chisq",df=10)
 193 
> dkwtest("chisq",df = 10)
186 
chisq(df = 10) PASSED
 194 
chisq(df = 10) PASSED
187 
[1] TRUE
 195 
[1] TRUE
188 
>
196 
>
189 
> dkwtest("logis")
 197 
> dkwtest("logis")
190 
logis() PASSED
 198 
logis() PASSED
191 
[1] TRUE
 199 
[1] TRUE
192 
> dkwtest("logis",location=4,scale=2)
 200 
> dkwtest("logis",location = 4,scale = 2)
193 
logis(location = 4, scale = 2) PASSED
 201 
logis(location = 4, scale = 2) PASSED
194 
[1] TRUE
 202 
[1] TRUE
195 
>
203 
>
196 
> dkwtest("t",df=1)
 204 
> dkwtest("t",df =  1)
197 
t(df = 1) PASSED
 205 
t(df = 1) PASSED
198 
[1] TRUE
 206 
[1] TRUE
199 
> dkwtest("t",df=10)
 207 
> dkwtest("t",df = 10)
200 
t(df = 10) PASSED
 208 
t(df = 10) PASSED
201 
[1] TRUE
 209 
[1] TRUE
202 
> dkwtest("t",df=40)
 210 
> dkwtest("t",df = 40)
203 
t(df = 40) PASSED
 211 
t(df = 40) PASSED
204 
[1] TRUE
 212 
[1] TRUE
205 
>
213 
>
206 
> dkwtest("beta",shape1=1,shape2=1)
 214 
> dkwtest("beta",shape1 = 1, shape2 = 1)
207 
beta(shape1 = 1, shape2 = 1) PASSED
 215 
beta(shape1 = 1, shape2 = 1) PASSED
208 
[1] TRUE
 216 
[1] TRUE
209 
> dkwtest("beta",shape1=2,shape2=1)
 217 
> dkwtest("beta",shape1 = 2, shape2 = 1)
210 
beta(shape1 = 2, shape2 = 1) PASSED
 218 
beta(shape1 = 2, shape2 = 1) PASSED
211 
[1] TRUE
 219 
[1] TRUE
212 
> dkwtest("beta",shape1=2,shape2=2)
 220 
> dkwtest("beta",shape1 = 1, shape2 = 2)
213 
beta(shape1 = 2, shape2 = 2) PASSED
 221 
beta(shape1 = 1, shape2 = 2) PASSED
214 
[1] TRUE
 222 
[1] TRUE
215 
> dkwtest("beta",shape1=2,shape2=2)
 223 
> dkwtest("beta",shape1 = 2, shape2 = 2)
216 
beta(shape1 = 2, shape2 = 2) PASSED
 224 
beta(shape1 = 2, shape2 = 2) PASSED
217 
[1] TRUE
 225 
[1] TRUE
218 
> dkwtest("beta",shape1=.2,shape2=.2)
 226 
> dkwtest("beta",shape1 = .2,shape2 = .2)
219 
beta(shape1 = 0.2, shape2 = 0.2) PASSED
 227 
beta(shape1 = 0.2, shape2 = 0.2) PASSED
220 
[1] TRUE
 228 
[1] TRUE
221 
>
229 
>
222 
> dkwtest("cauchy")
 230 
> dkwtest("cauchy")
223 
cauchy() PASSED
 231 
cauchy() PASSED
224 
[1] TRUE
 232 
[1] TRUE
225 
> dkwtest("cauchy",location=4,scale=2)
 233 
> dkwtest("cauchy",location = 4,scale = 2)
226 
cauchy(location = 4, scale = 2) PASSED
 234 
cauchy(location = 4, scale = 2) PASSED
227 
[1] TRUE
 235 
[1] TRUE
228 
>
236 
>
229 
> dkwtest("f",df1=1,df2=1)
 237 
> dkwtest("f",df1 =  1,df2 =  1)
230 
f(df1 = 1, df2 = 1) PASSED
 238 
f(df1 = 1, df2 = 1) PASSED
231 
[1] TRUE
 239 
[1] TRUE
232 
> dkwtest("f",df1=1,df2=10)
 240 
> dkwtest("f",df1 =  1,df2 = 10)
233 
f(df1 = 1, df2 = 10) PASSED
 241 
f(df1 = 1, df2 = 10) PASSED
234 
[1] TRUE
 242 
[1] TRUE
235 
> dkwtest("f",df1=10,df2=10)
 243 
> dkwtest("f",df1 = 10,df2 = 10)
236 
f(df1 = 10, df2 = 10) PASSED
 244 
f(df1 = 10, df2 = 10) PASSED
237 
[1] TRUE
 245 
[1] TRUE
238 
> dkwtest("f",df1=30,df2=3)
 246 
> dkwtest("f",df1 = 30,df2 =  3)
239 
f(df1 = 30, df2 = 3) PASSED
 247 
f(df1 = 30, df2 = 3) PASSED
240 
[1] TRUE
 248 
[1] TRUE
241 
>
249 
>
242 
> dkwtest("weibull",shape=1)
 250 
> dkwtest("weibull",shape = 1)
243 
weibull(shape = 1) PASSED
 251 
weibull(shape = 1) PASSED
244 
[1] TRUE
 252 
[1] TRUE
245 
> dkwtest("weibull",shape=4,scale=4)
 253 
> dkwtest("weibull",shape = 4,scale = 4)
246 
weibull(shape = 4, scale = 4) PASSED
 254 
weibull(shape = 4, scale = 4) PASSED
247 
[1] TRUE
 255 
[1] TRUE
248 
>
256 
>
- 
 
 257 
>
- 
 
 258 
> cat('Time elapsed: ', proc.time() - .proctime00,'\n')
- 
 
 259 
Time elapsed:  22.67 0.15 22.82 0 0
- 
 
 260 
>
- 
 
 261 
>