# EDOIF: Empirical Distribution Ordering Inference Framework (EDOIF) In EDOIF: Empirical Distribution Ordering Inference Framework (EDOIF)

## Description

EDOIF is a non-parametric framework based on Estimation Statistics principle. Its main purpose is to infer orders of empirical distributions from different categories base on a probability of finding a value in one distribution that greater than the expectation of another distribution.

Given a set of ordered-pair of real-category values the framework is capable of 1) inferring orders of domination of categories and representing orders in the form of a graph; 2) estimating magnitude of difference between a pair of categories in forms of confidence intervals; and 3) visualizing domination orders and magnitudes of difference of categories.

## Usage

 `1` ```EDOIF(Values, Group, bootT, alpha, methodType) ```

## Arguments

 `Values` is a vector of real-number values `Group` is a vector of categories of each real number in Values `bootT` is a number of times of sample with replacement for bootstrapping. The default is 1000. It must be above zero `alpha` is a significance level using in both confidence intervals and ordering inference it has the range [0,1]. The default is 0.05. `methodType` is an option for bootstrapping methods:either "perc" or "bca". The "perc" is the default option.

## Value

This class constructor returns an object of EDOIF class.

`obj` an object of EDOIF class that contains the results of ordering inference that can be print in text mode (print(obj)) or graphic mode (plot(obj)).

The `obj` consists of the following variables

 `Values, Group` The main inputs of the framework. They are the double and character vectors respectively. `bootT, alpha, methodType` The number of bootstrapping, significance level, and bootstrapping method parameters. `sortedGroupList` A list of names of categories ascendingly ordered by their means. `sortedmeanList` A list of means of categories that are ascendingly ordered. `MegDiffList[[i]]` Mean difference confidence intervals and related information of all categories that have higher means than sortedGroupList[i] category. `confInvsList[i,]` A mean confidence interval of sortedGroupList[i] category. confInvsList[i,1] is a lower bound and confInvsList[i,2] is an upper bound. `adjMat[i,j]` An element of adjacency matrix: one if sortedGroupList[j] category dominates sortedGroupList[i] using Mann-Whitney test, otherwise zero. `pValMat[i,j]` A p-value of Mann-Whitney test for adjMat[i,j]. `adjDiffMat[i,j]` A lower bound of confidence interval of mean difference for sortedGroupList[j] minus sortedGroupList[i] using methodType bootstrap. `adjBootMat[i,j]` One if adjDiffMat[i,j] is positive, otherwise, zero. `netDen` A network density of dominant-distribution network derived from `adjMat`. `gObj` An object of iGraph of a dominant-distribution network.

## Author(s)

Chainarong Amornbunchornvej, chai@ieee.org

Run `vignette("EDOIF_demo", package = "EDOIF")` in a terminal to learn more details about how to use our package.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28``` ```# Generate simulation data nInv<-100 initMean=10 stepMean=20 std=8 simData1<-c() simData1\$Values<-rnorm(nInv,mean=initMean,sd=std) simData1\$Group<-rep(c("C1"),times=nInv) simData1\$Values<-c(simData1\$Values,rnorm(nInv,mean=initMean,sd=std) ) simData1\$Group<-c(simData1\$Group,rep(c("C2"),times=nInv)) simData1\$Values<-c(simData1\$Values,rnorm(nInv,mean=initMean+2*stepMean,sd=std) ) simData1\$Group<-c(simData1\$Group,rep(c("C3"),times=nInv) ) simData1\$Values<-c(simData1\$Values,rnorm(nInv,mean=initMean+3*stepMean,sd=std) ) simData1\$Group<-c(simData1\$Group, rep(c("C4"),times=nInv) ) simData1\$Values<-c(simData1\$Values,rnorm(nInv,mean=initMean+4*stepMean,sd=std) ) simData1\$Group<-c(simData1\$Group, rep(c("C5"),times=nInv) ) # Performing ordering infernce from simData1 resultObj<-EDOIF(simData1\$Values,simData1\$Group) # Print results in text mode print(resultObj) # Plot results in graphic mode plot(resultObj) ```