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Probability Mass Function | The Poisson distribution is used to model the number of events occurring within a given time interval.The formula for the Poisson probability mass function is is the shape parameter which indicates the average number of events in the given time interval. The following is the plot of the Poisson probability density function for four values of . | ||||||||||||||
Cumulative Distribution Function | The formula for the Poisson cumulative probability function is The following is the plot of the Poisson cumulative distribution function with the same values of as the pdf plots above. | ||||||||||||||
Percent Point Function | The Poisson percent point function does not exist in simple closed form. It is computed numerically. Note that because this is a discrete distribution that is only defined for integer values of x, the percent point function is not smooth in the way the percent point function typically is for a continuous distribution.The following is the plot of the Poisson percent point function with the same values of as the pdf plots above. | ||||||||||||||
Common Statistics |
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Parameter Estimation | The maximum likelihood estimator of is where is the sample mean. | ||||||||||||||
Software | Most general purpose statistical software programs support at least some of the probability functions for the Poisson distribution. |
Learning Objectives Create and interpret frequency polygons Create and interpret cumulative frequency polygons Create and interpret overlaid frequency polygons Frequency polygons are a graphical device for understanding the shapes of distributions. They serve the same purpose as histograms, but are especially helpful for comparing sets of data. Frequency polygons are also a good choice for displaying cumulative frequency distributions . To create a frequency polygon, start just as for histograms , by choosing a class interval. Then draw an X-axis representing the values of the scores in your data. Mark the middle of each class interval with a tick mark, and label it with the middle value represented by the class. Draw the Y-axis to indicate the frequency of each class. Place a point in the
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