## Tuesday, May 27, 2014

### Interactive Graph of Poisson Distribution in Excel 2010 and Excel 2013 (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

Interactive Statistical Distribution Graph in Excel 2010 and Excel 2013

Interactive Graph of the Normal Distribution in Excel 2010 and Excel 2013

Interactive Graph of the Chi-Square Distribution in Excel 2010 and Excel 2013

Interactive Graph of the t-Distribution in Excel 2010 and Excel 2013

Interactive Graph of the t-Distribution’s PDF in Excel 2010 and Excel 2013

Interactive Graph of the t-Distribution’s CDF in Excel 2010 and Excel 2013

Interactive Graph of the Binomial Distribution in Excel 2010 and Excel 2013

Interactive Graph of the Exponential Distribution in Excel 2010 and Excel 2013

Interactive Graph of the Beta Distribution in Excel 2010 and Excel 2013

Interactive Graph of the Gamma Distribution in Excel 2010 and Excel 2013

Interactive Graph of the Poisson Distribution in Excel 2010 and Excel 2013

# Poisson Distribution Overview

The Poisson distribution is a family of discrete probability distributions. This is evidenced by the stepwise shape of the above graph of a Poisson distribution’s PDF (Probability Density Function) curve. The stepwise shape of a discrete distribution indicates that the discrete distribution can only assume discrete values and is not continuous.

The Poisson distribution has one parameter, λ (Lamda). λ equals the average number of events occurring in a given unit of time. The Poisson Distribution is used to calculate the probability of a specific number of events occurring over a unit of time if the average number of events occurring over that unit of time equals λ and the occurrence of the event is distributed according to the Poisson distribution.

Previous measurement must have been taken to determine the following:

1) The events occur in frequency according to the Poisson distribution

2) The average rate, which is the expected number of occurrences of that event over the given time period.

The PDF (Probability Density Function) of the Poisson distribution predicts the degree of spread around a known average rate of occurrence.

Examples of events whose frequency of occurrence over a given period of time are often distributed according to the Poisson distribution are the following:

Number of telephone calls that come over a switchboard

Number of cars arriving at a traffic light

Number of accidents at an intersection

Number of customers arriving at a sales counter

Number of insurance losses/claims filed

Number of goals in sports involving two competing teams

Number of jumps in stock price

Number of times a web server is accessed

## Graphing the Poisson 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

The X values for each data point are created. The X-Axis expander and X-Axis shifter values are part of this calculation because the location and width of the normal distribution’s PDF graph varies significantly when its only parameter λ change. The X axis must be properly sized to enable the Poisson distribution’s PDF curve to be fully visible and fully expanded in the graph. (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 Poisson distribution’s PDF value requires its only parameter λ. (Click on Image To See a Larger Version)

The following Excel-generated graph shows the normal distribution’s PDF (Probability Density Function) for as the X value goes from 2 to 15 with λ = 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.

### Effect of Changing λ (Click on Image To See a Larger Version)

### Effect of Changing the X-Axis Shifter (Click on Image To See a Larger Version)

### Effect of Changing the X-Axis Expander (Click on Image To See a Larger Version)

## Graphing the Poisson Distribution’s CDF – Cumulative Distribution Function

The following Excel-generated graph shows the Poisson distribution’s CDF (Cumulative Distribution Function) for λ = 10 as the X value goes from 2 to 35.

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

• Histograms in Excel
• Bar Chart in Excel
• Combinations & Permutations in Excel
• Normal Distribution in Excel
• t-Distribution in Excel
• Binomial Distribution in Excel
• z-Tests in Excel
• t-Tests in Excel
• Hypothesis Tests of Proportion in Excel
• Chi-Square Independence Tests in Excel
• Chi-Square Goodness-Of-Fit Tests in Excel
• F Tests in Excel
• Correlation in Excel
• Pearson Correlation in Excel
• Spearman Correlation in Excel
• Confidence Intervals in Excel
• Simple Linear Regression in Excel
• Multiple Linear Regression in Excel
• Logistic Regression in Excel
• Single-Factor ANOVA in Excel
• Two-Factor ANOVA With Replication in Excel
• Two-Factor ANOVA Without Replication in Excel
• Randomized Block Design ANOVA in Excel
• Repeated-Measures ANOVA in Excel
• ANCOVA in Excel
• Normality Testing in Excel
• Nonparametric Testing in Excel
• Post Hoc Testing in Excel
• Creating Interactive Graphs of Statistical Distributions in Excel
• Solving Problems With Other Distributions in Excel
• Optimization With Excel Solver
• Chi-Square Population Variance Test in Excel
• Analyzing Data With Pivot Tables
• SEO Functions in Excel
• Time Series Analysis in Excel
• VLOOKUP

#### 1 comment:

1. i never know the use of adobe shadow until i saw this post. thank you for this! this is very helpful. 그래프게임