# A test of uniformity of 1D data in a given interval based on Central Similarity Proximity Catch Digraph (CS-PCD) An object of class `"htest"` (i.e., hypothesis test) function which performs a hypothesis test of uniformity of 1D data in one interval based on the normal approximation of the arc density of the CS-PCD with expansion parameter $t>0$ and centrality parameter $c \in (0,1)$. The function yields the test statistic, $p$-value for the corresponding `alternative`, the confidence interval, estimate and null value for the parameter of interest (which is the arc density), and method and name of the data set used. The null hypothesis is that data is uniform in a finite interval (i.e., arc density of CS-PCD equals to its expected value under uniform distribution) and `alternative` could be two-sided, or left-sided (i.e., data is accumulated around the end points) or right-sided (i.e., data is accumulated around the mid point or center $M_c$). See also (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:revstat-2016;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r CSarc.dens.test.int( Xp, int, t, c = 0.5, alternative = c("two.sided", "less", "greater"), conf.level = 0.95 ) ``` ## Arguments - `Xp`: A set or `vector` of 1D points which constitute the vertices of CS-PCD. - `int`: A `vector` of two real numbers representing an interval. - `t`: A positive real number which serves as the expansion parameter in CS proximity region. - `c`: A positive real number in $(0,1)$ parameterizing the center inside `int`$=(a,b)$ with the default `c=.5`. For the interval, `int`$=(a,b)$, the parameterized center is $M_c=a+c(b-a)$. - `alternative`: Type of the alternative hypothesis in the test, one of `"two.sided"`, `"less"`, `"greater"`. - `conf.level`: Level of the confidence interval, default is `0.95`, for the arc density of CS-PCD based on the 1D data set `Xp`. ## Returns A `list` with the elements - **statistic**: Test statistic - **p.value**: The $p$-value for the hypothesis test for the corresponding `alternative` - **conf.int**: Confidence interval for the arc density at the given level `conf.level` and depends on the type of `alternative`. - **estimate**: Estimate of the parameter, i.e., arc density - **null.value**: Hypothesized value for the parameter, i.e., the null arc density, which is usually the mean arc density under uniform distribution. - **alternative**: Type of the alternative hypothesis in the test, one of `"two.sided"`, `"less"`, `"greater"` - **method**: Description of the hypothesis test - **data.name**: Name of the data set ## Examples ```r c<-.4 t<-2 a<-0; b<-10; int<-c(a,b) n<-10 Xp<-runif(n,a,b) num.arcsCSmid.int(Xp,int,t,c) CSarc.dens.test.int(Xp,int,t,c) num.arcsCSmid.int(Xp,int,t,c=.3) CSarc.dens.test.int(Xp,int,t,c=.3) num.arcsCSmid.int(Xp,int,t=1.5,c) CSarc.dens.test.int(Xp,int,t=1.5,c) Xp<-runif(n,a-1,b+1) num.arcsCSmid.int(Xp,int,t,c) CSarc.dens.test.int(Xp,int,t,c) c<-.4 t<-.5 a<-0; b<-10; int<-c(a,b) n<-10 #try also n<-20 Xp<-runif(n,a,b) CSarc.dens.test.int(Xp,int,t,c) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `PEarc.dens.test.int` ## Author(s) Elvan Ceyhan

CSarc.dens.test.int function