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STATISTICS 1403

CASE STUDY: Q-Q PLOT GALLERY

Abstract. The Q-Q plot is a graphical test of normality. Here you will

provide some examples of how other, non-normal distributions meet the test.

1. Background and Problems

The quantile-quantile plot is a graphical test of normality, which plots the z- scores of observed data against the z-scores of the empirical CDF. If the data follows a Gaussian distribution, the points lie on or near a straight line, like this:

The Q-Q plot is easier to read if you are familiar with the different ways that non-Gaussian data appears when it (possibly) deviates from the line. So generate some examples!

2. Data

All data for this case study will be simulated in the MATLAB script.

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2 Q-Q PLOT GALLERY

3. Proposed Analysis and Methods

Create a “gallery” of Q-Q plots for a variety of different distributions. Plot at least 5 from this list:

• lognormal (µ = 0,σ = 1) • uniform (range = (0, 1) • exponential (mean = 1) • Weibull IFR (b > 1) • Weibull DFR (0 < b < 1) • beta (a = b = 0.8) • chi-square (df = 10) • T (df = 10) • F (df = 5, 20)

3.1. Recommended MATLAB Functions. The following MATLAB functions may be useful; read about these in the online MATLAB reference1

Statistics: random(), histfit(), qqplot(), ksdensity()

Graphics: subplot(), title()

This set of plots shows how these functions may be used in your analysis.

4. Presentation

Use the MATLAB publish tool to produce your complete analysis. Your write-up should include

• a title • your name • a brief abstract, describing what the analysis is about, and a general

summary of results • source code from your script • formatted output, numeric or graphic • comments on individual displays or tests • a detailed summary of results • a digital signature using this code disp([’signature ’, num2str(geomean(random(’Lognormal’, 3, 2, [50 1])))]);

Submit your completed write-up in Adobe PDF or Word DOC format2 via Blackboard.

1Follow the link, or type a function name in the MATLAB Command or Editor windows and

hit F1. 2We don’t do IKEA, so no .ZIP, .HTML, or .M files, please.