procunivariate				package:procunivariate			R Documentation

A procedure to assist in carrying out univariate data analysis.
Includes functions that can be used independantly of the overall procedure.

Description:

	Takes a vector and returns 5 different graphs and also outputs 3 different types of numerical summaries

Usage:
	
	procunivariate(x,name="data",type=1)


	
	
Outline:
		5 graphs consists of
			RawQuantile plot with super imposed box plot
			QiQ plot against a uniform
			Quantile based Histogram
			Quantile plot of mean assuming Normality
			Quantile plot of standard deviation assuming Normality
		3 numerical outputs

	Graph functions:

		rqplot(x) Raw Quantile Plot consist of the sample quantiles graphed against the uniform quantiles. 
			A box plot (without the whiskers) is super-imposed for ease in examining a 5 number 
			summary.

		qiqp(x) QiQ plot is a graph of the quantiles of the sample data standardized according to the 
			mid-distribution and 2 times the interquartile range against the uniform quantiles.  When 
			using the mid-distribution function to define the quantile function as described by 
			Parzen (2004), the qiq-values of any 1st and 3rd quartile, regardless of the distribution will
			be -.25 and .25 respectively.  Because of this unique property the qiq-plots are ideally 
			suited both for identifying possible bi-modality and for examining the type of skewness or 
			kurtosis that is exhibited by a sample.  Any points that lie above a qiq of .5 indicates the
			presence of a right tail, and likewise any value below -.5 indicates the presence of a left tail.  
			A good way to compare two distributions that a sample might come from is to plot the 
			theoretical samples onto the same graph and by visual inspection determine which 
			distribution a sample may have more likely come from.  In demonstration of this method 
			this particular qiq plot superimposes both the standard normal and exponential(1) onto the 
			plot.  One may notice that rarely will a sample from an exponential distribution ever have 
			any data points below a qiq of -.5, and such a sample will almost always have at least a few 
			data points above a qiq of .5.

		qhist(x) A histogram such that the bin cut points are determined by starting at the midquartile point 
			and expanding in both directions in increments of .5 times the IQR.  Sample points that 
			happen to land on the cut points are distributed to the bins by the mid-distribution function
			(defined by Parzen 2004).  The usefulness of this method lies in the fact 
			that all histograms done by such method are universally equivalent.

		qmean(x) The quantile function of the sample mean assuming the parent distribution is approximately 
			Normal.  The 95% Confidence Interval for the mean is supperimposed for a graphical 
			interpretation of the interval.   

 		qsig(x) The quantile function of the sample standard deviation assuming the parent distribution is 
			approximately Normal.  The 95% Confidence Interval for the standard deviation is 
			supperimposed for a graphical interpretation of the interval.   

	Numerical Summaries:
	
		EQA Summary: The 5-number summary along with the minimum and maximum qiq-values, the 
			qiq-value of the median, the mid-quartile value and the twice the interquartile range (the 
			scale parameter for qiq-values).  As a matter of notation the qiq of the median (or any 
			other specified qiq-value) is listed as QI(.5).
	
		Normal comparison chart:  7 prespecified quantiles that are useful for comparison of sample 
			quantiles to standard normal quantiles
	
		Exponential comparison chart: 5 prespecifed quantile that are useful for comparison of sample 
			quantiles to standard exponential quantiles

Arguments:

	x: the data 
	
	name: explicitly write the name of the data on the output plots
	
	type: Takes either 1 or 2.  Type 2  includes an extra plot with 95% confidence intervals for the 
		quantiles on the raw quantile plot, and all numerical summaries are exclued.


References:
Proceedings of the 2004 Winter Simulation Conference
R. G. Ingalls, M. D. Rossetti, J. S. Smith, and B. A. Peters, eds.
INPUT MODELING USING QUANTILE STATISTICAL METHODS
Abhishek Gupta
Department of Industrial Engineering
Texas A & M University
College Station, TX 77843, U.S.A.
Emanuel Parzen
Department of Statistics
Texas A & M University
College Station, TX 77843, U.S.A.

http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.ss/1113832730
Source: Statist. Sci.  19, no. 4 (2004), 652–662

Example:

#(Make sure procunivariate is loaded first)

#analyzing random samples from a N(1,0) distribution

	x<-rnorm(40)
	procunivariate(x,name="40 random normals")

#analyzing random samples from an exponential(1) distribution

	x<-rexp(40)
	procunivariate(x,name="40 random exponentials")