(Click On Image To See a Larger Version)

This is one of the following eleven articles on creating user-interactive graphs of statistical distributions in Excel

Overview of the Beta

Distribution

The beta distribution is a family of continuous probability distributions. This is evidenced by the smooth shape of the above graph of a beta distribution’s PDF (Probability Density Function) curve. The beta distribution is defined on the interval [0,1] and is defined by two positive shape parameters α and β. The Excel formulas that calculate the PDF and CDF of the beta distribution have optional inputs that enable the [0, 1] interval to be expanded to an arbitrary width.

The beta distribution is most often used to model events which are constrained to take place between a minimum and maximum time limit. In this case the beta distribution is used to calculate the probability that a project will be completed within a given period of time. For this reason, the beta distribution is often used for modeling project planning and control systems such as PERT (Project Evaluation and Review Technique) and CPM (Critical Path Method).

The beta distribution is used in general to model the variation of a variable across samples, such as the percentage of the day people spend watching television. The beta distribution can be applied to a wide variety of disciplines to model the behavior of a random variable limited to intervals of finite length. Examples include the modeling of the variability of soil properties and the proportions of the minerals in rocks in stratigraphy.

Graphing the Distribution’s PDF –

Probability Density Function

Step 1 – Create a Count

The Count becomes the basis for the X and Y values of each data point on the graph. This count will contain 100 points that count from 0 to 100 in increments 1. There are many ways to create a count. This count uses the method ROW() – ROW($B) to increment each cell value in the column by 1.

(Click On Image To See a Larger Version)

Step 2 – Create the X Values

One X value is created for each increment of the Count. The Min and Max Completion Times determine how wide the graph will be and therefore are part of the X value calculation.

(Click On Image To See a Larger Version)

Step 3 – Create the Y Values

One Y value is created for each increment of the Count. The Y value of each data point is its PDF value. The beta distribution’s PDF value requires the X value and its four parameters (α, β, and the Min and Max Completion Times) as follows:

(Click On Image To See a Larger Version)

The following Excel-generated graph shows the beta distribution’s PDF (Probability Density Function) for as the X value (the completion time) goes from 0 to 1 with α = 8 and β = 10.

The PDF value of a statistical distribution (the Y value) at a specific X value equals the probability that the value of a random sample will be equal to that X value if the population of data values from which the sample was taken is distributed according the stated distribution. The CDF value of a statistical distribution (the Y value) at a specific X value equals the probability that the value of a random sample will be up to that X value.

(Click On Image To See a Larger Version)

The process of creating an Excel area chart and connecting the user inputs to the chart is shown in detail in the section of this manual that provides instructions on how to create an interactive normal distribution PDF curve with outer tails.

The Effect of Changing Shape Parameter α

The following Excel-generated graph shows the Beta distribution’s PDF (Probability Density Function) for as the X value (the completion time) goes from 0 to 1 with α = 4 and β = 10.

(Click On Image To See a Larger Version)

The Effect of Changing Shape Parameter β

The following Excel-generated graph shows the Beta distribution’s PDF (Probability Density Function) for as the X value (the completion time) goes from 0 to 1 with α = 8 and β = 2.

(Click On Image To See a Larger Version)

The Effect of Changing Min and Max Completion Times

The following Excel-generated graph shows the Beta distribution’s PDF (Probability Density Function) as the X value (the completion time) goes from 1 to 2 with α = 8 and β = 10. Note the revised values of the X-axis units.

(Click On Image To See a Larger Version)

The Effect of Shifting and Expanding the X-Axis

The following Excel-generated graph shows effect of shifting and expanding the X-axis as the X value (the completion time) goes from 2 to 5 with α = 8 and β = 2. The X-axis was shifted and expanded in order to optimally present the entire PDF curve in a single graph.

(Click On Image To See a Larger Version)

Graphing the Beta Distribution’s

CDF – Cumulative Distribution

Function

The following Excel-generated graph shows the Beta distribution’s CDF (Cumulative Distribution Function) for 10 degrees of freedom as the X value (the completion time) goes from a completion time of 0 to 1.

The CDF value of a statistical distribution (the Y value) at a specific X value equals the probability that the value of a random sample will be up to that X value if the population of data values from which the sample was taken is distributed according the stated distribution. The PDF value of a statistical distribution (the Y value) at a specific X value equals the probability that the value of a random sample will be equal to that X value.

(Click On Image To See a Larger Version)

Excel Master Series Blog Directory

Statistical Topics and Articles In Each Topic

Technorati Tags: beta distribution,statistics,excel,excel 2010,excel 2013,excel chart,excel graph,distribution graph

Become an Excel Statistical Master

Excel Master Series - MBA-level statistics - Over 1,100+ Pages of Easy-To-Follow Instructions in Excel

It's a Full
Easy-To-Follow
MBA Course in Business Statistics

ALL IN EXCEL

&

MUCH Clearer

Than Your Text

Book

Download the
1,100+ Page Excel Statistical Master now

More Easy-To-

Follow eManuals

That You Will

Master Quickly

Step-By-Step Optimization With Excel Solver

What's In It?

For anyone who wants to be operating at a high level with the Excel Solver quickly, this is the book for you. Step-By-Step Optimization With Excel Solver is a 200+ page .pdf e-manual of simple yet thorough explanations on how to use the Excel Solver to solve today’s most widely known optimization problems. Loaded with screen shots that are coupled with easy-to-follow instructions, this book will simplify many difficult optimization problems and make you a master of the Excel Solver almost immediately.

Here are just some of the Solver optimization problems that are solved completely with simple-to-understand instructions and screen shots in this e-manual:

• The famous “Traveling Salesman” problem using Solver’s Alldifferent constraint and the Solver’s Evolutionary method to find the shortest path to reach all customers. This also provides an advanced use of the Excel INDEX function.

• The well-known “Knapsack Problem” which shows how optimize the use of limited space while satisfying numerous other criteria.

• How to perform nonlinear regression and curve-fitting on the Solver using the Solver’s GRG Nonlinear solving method.

• How to solve the “Cutting Stock Problem” faced by many manufacturing companies who are trying to determine the optimal way to cut sheets of material to minimize waste while satisfying customer orders.

• Portfolio optimization to maximize return or minimize risk.

• Venture capital investment selection using the Solver’s Binary constraint to maximize Net Present Value of selected cash flows at year 0. Clever use of the If-Then-Else statements makes this a simple problem.

• How use Solver to minimize the total cost of purchasing and shipping goods from multiple suppliers to multiple locations.

• How to optimize the selection of different production machine to minimize cost while fulfilling an order.

• How to optimally allocate a marketing budget to generate the greatest reach and frequency or number of inbound leads at the lowest cost.

Step-By-Step Optimization With Excel Solver has complete instructions and numerous tips on every aspect of operating the Excel Solver. You’ll fully understand the reports and know exactly how to tweek all of the Solver’s settings for total custom use. This e-manual also provides lots of inside advice and guidance on setting up the model in Excel so that it will be as simple and intuitive as possible to work with.

All of the optimization problems in this book are solved step-by-step using a 6-step process that works every time. In addition to detailed screen shots and easy-to-follow explanations on how to solve every optimization problem in the book, a link is provided to download an Excel workbook that has all problems completed exactly as they are in this e-manual.

Step-By-Step Optimization With Excel Solver is exactly the e-manual you need if you want to be optimizing at an advanced level with the Excel Solver quickly.

*******************

Become an Excel Statistical Master

It's a Full
Easy-To-Follow
MBA Course in Business Statistics

ALL IN EXCEL

&

MUCH Clearer

Than Your Text

Book

Download the
1,100+ Page Excel Statistical Master now

More Easy-To-

Follow eManuals

That You Will

Master Quickly

*******************

Become an Excel Statistical Master

It's a Full
Easy-To-Follow
MBA Course in Business Statistics

ALL IN EXCEL

&

MUCH Clearer

Than Your Text

Book

Download the
1,100+ Page Excel Statistical Master now

More Easy-To-

Follow eManuals

That You Will

Master Quickly

*******************

Become an Excel Statistical Master

It's a Full
Easy-To-Follow
MBA Course in Business Statistics

ALL IN EXCEL

&

MUCH Clearer

Than Your Text

Book

Download the
1,100+ Page Excel Statistical Master now

Immediate, Absolute, No-Questions-Asked, Money-Back Guarantee If Not TOTALLY, 100% Satisfied. In Other Words, If Any Excel Master Series eManual That You've Purchased Here Does Not Provide Instructions That Are CRYSTAL CLEAR and EASY TO UNDERSTAND, You Get All Of Your Money Back Immediately and Keep the eManual. Guaranteed!

Meet The Author