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S S E R P Number of LVs Continuum Parameter PLS_Toolbox 4.2 Reference Manualf for use with MATLAB™ Barry M. Wise Neal B. Gallagher Rasmus Bro Jeremy M. Shaver Willem Windig R. Scott Koch

Eigenvector Research, Inc., Software License Agreement READ THE TERMS AND CONDITIONS OF THIS LICENSE AGREEMENT CAREFULLY BEFORE USING THIS SOFTWARE. THIS LICENSE AGREEMENT REPRESENTS THE ENTIRE AGREEMENT BETWEEN YOU (THE “LICENSEE” - EITHER AN INDIVIDUAL OR AN ENTITY) AND EIGENVECTOR RESEARCH, INC., (“EVRI”) CONCERNING THE PLS_TOOLBOX COMPUTER SOFTWARE CONTAINED HEREIN (“PROGRAM”), AND THE ACCOMPANYING USER DOCUMENTATION. BY USING THE SOFTWARE, YOU ACCEPT THE TERMS OF THIS AGREEMENT. IF YOU ARE NOT WILLING TO DO SO, RETURN THE UNOPENED SOFTWARE IMMEDIATELY FOR A FULL REFUND. LICENSE GRANT: This license permits licensee to install and use one copy of the Program on a single computer. If licensee has multiple licenses for the Program, then Licensee may at any time have as many copies of the Program and its Electronic Documentation in use as it has licenses. “Use” means that a copy is loaded into temporary memory or installed into the permanent memory of a computer, except that a copy installed on a network server for the sole purpose of distribution to other computers is not in “use”. Licensee is responsible for limiting the number of possible concurrent users to the number licensed. Each copy of the Program may be used on a backup computer (when the original is disabled) or a replacement computer. Replacements may be either permanent or temporary, at the same or different site as the original computer. The Hardcopy documentation provided with the Program may not be copied. Licensee shall use the Program only for its internal operations. “Internal operations” shall include use of the Program in the performance of consulting or research for third parties who engage Licensee as an employee or independent contractor. Licensee may allow use of the Program by employees, consultants, students and/or (in the case of individual licensees) colleagues, but Licensee may not make the Program available for use by third parties generally on a “time sharing” basis. Licensee may make copies of the Program only for backup or archival purposes. All copies of Program, Electronic Documentation and Hardcopy Documentation shall contain all copyright and proprietary notices in the originals. Licensee shall not re-compile, translate or convert “M-files” contained in the Program for use with any software other than MATLAB®, which is a product of The MathWorks, Inc. 3 Apple Hill Drive, Natick, MA 01760-2098, without express written consent of EVRI. Licensee shall not re-distribute “M-files” contained in the Program, or any derivative thereof, without express written consent of EVRI. Licensee shall take appropriate action by instruction, agreement, or otherwise with any persons permitted access to the Program, so as to enable Licensee to satisfy the obligations under this agreement. TERM OF AGREEMENT. This Agreement shall continue until terminated by EVRI or Licensee as provided below. TERMINATION. EVRI may terminate this license by written notice to Licensee if Licensee (a) breaches any material term of this Agreement, (b) fails to pay the amount charged for this license within Thirty (30) days after the date due, or (c) ceases conducting business in the normal course, becomes insolvent or bankrupt, or avails itself of or becomes subject to any proceedings pertaining to insolvency or protection of creditors. Licensee may terminate this Agreement at any time by written notice to EVRI. Licensee shall not be entitled to any refund if this Agreement is terminated, except of license fees paid for any Licensed Product for which the testing period has not expired at the time of termination. Upon termination, Licensee shall promptly return all copies of the Programs and Documentation in Licensee’s possession or control, or promptly provide written certification of their destruction. LIMITED WARRANTY; LIMITATION OF REMEDIES. For a period of ninety (90) days from delivery, EVRI warrants that (a) the media shall be free of defects, or replaced at no cost to Licensee, and (b) the Program will conform in all material respects to the description of such Program’s operation in the Documentation. In the event that the Program does not materially operate as warranted, licensees exclusive remedy and EVRI’s sole liability under this warranty shall be (a) the correction or workaround by EVRI of major defects within a reasonable time or (b) should such correction or workaround prove neither satisfactory nor practical, termination of the License and refund of the license fee paid to EVRI for the Program. THE FOREGOING WARRANTY IS IN LIEU OF ALL OTHER WARRANTIES, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. EVRI SHALL NOT BE LIABLE FOR ANY SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES, INCLUDING WITHOUT LIMITATION LOST PROFITS. Licensee accepts responsibility for its use of the Program and the results obtained therefrom. 1

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Table of Contents EIGENVECTOR RESEARCH, INC., SOFTWARE LICENSE AGREEMENT ..........................................1 TABLE OF CONTENTS.....................................................................................................................................3 FORMATS AND CONVENTIONS....................................................................................................................4 PLS_TOOLBOX FUNCTIONS..........................................................................................................................5 DISTRIBUTION FITTING TOOL SET - GENERAL FUNCTIONS ........................................................368 DISTRIBUTION FITTING TOOL SET - DISTRIBUTION FUNCTIONS ..............................................403 3

Formats and Conventions The manual for the PLS_Toolbox uses a format consistent with that used for MATLAB. For additional information on usage see the main PLS_Toolbox manual. The following format is used in the Reference section: Purpose Provides short concise descriptions of a PLS_Toolbox command or function. Synopsis Shows the input/output format of the command or function. Description Describes what the command or function does and any rules or restrictions that apply. Examples Provides examples of how the command or function can be used. Options Describes advanced options of the command or function. Algorithm Describes algorithms and routines used within the command or function. See Also Refers to other related commands or functions in the PLS_Toolbox. and the following conventions: Monospace Commands, function names, and screen displays; for example, pca. Italics Book titles, names of sections in this book, MATLAB toolbox names, and for introduction of new terms; for example, Chemometrics. Monospace Optional input variables from PLS_Toolbox functions. Routines in the PLS_Toolbox follow the convention of having samples in rows and variables in columns. 4

PLS_Toolbox Functions 5

abline Purpose Adds a line on the current axes with a given slope and intercept. Synopsis h = abline(slope,intercept) h = abline(slope,intercept,...) %additional linestyle information Description ABLINE draws a line on on an existing axes with a given slope, slope, and intercept, intercept, using the existing x-axis range for values. If a 3D plot is shown, slope and intercept can be 2-element vectors describing the slope and intercept of the line in the y and z dimensions. Optional line style information can also be included. For more information on linestyle information, see the manual page on the line command. The handle of the new line object is returned. Examples abline( 3, -1, 'color', 'r', 'linestyle', '--') plots a dashed red line with a slope of 3 and an intercept of -1 on the axes. See Also dp, hline, line, vline 6

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