Goodness of Fit Tests for Poisson Distribution

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In summary, the conversation discusses the use of goodness of fit tests, specifically the Shapiro-Wilk test, for testing exponential and Poisson distributions. It is mentioned that Shapiro-Wilk tests normality and therefore cannot be used for these distributions. The use of Pearson's Chi-Square test for these distributions is suggested.
  • #1
Mark J.
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Hi.
For testing exponential distribution we can use several goodness of fit tests like Shapiro-Wilk etc.Can we use this tests for poisson distribution as well or for poisson discrete distribution different tests are generally used?
Can you mention some of them pls?
Regards
 
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  • #2
Mark J. said:
Hi.
For testing exponential distribution we can use several goodness of fit tests like Shapiro-Wilk etc.Can we use this tests for poisson distribution as well or for poisson discrete distribution different tests are generally used?
Can you mention some of them pls?
Regards

Hi Mark,

Shapiro-Wilk tests normality, so you can't use it either for Poisson or Exponential distributions. A general and simple method is the Pearson's Chi-Square goodness of fit test.
 
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  • #3
Think u can still measure Weibull, exponential, lognormal with S_W test. In Minitab they use chi-square as well.
 

1. What is a "goodness of fit" test for Poisson distribution?

A "goodness of fit" test for Poisson distribution is a statistical method used to determine whether a given set of data follows a Poisson distribution or not. This test compares the observed data with the expected values from a Poisson distribution, and if the deviation is too large, it suggests that the data does not fit the Poisson distribution.

2. How do you perform a goodness of fit test for Poisson distribution?

To perform a goodness of fit test for Poisson distribution, you need to first calculate the expected values for the given data using the Poisson distribution formula. Then, you need to calculate the chi-square test statistic by comparing the observed and expected values. Finally, you can compare the calculated chi-square value with the critical value from the chi-square distribution to determine the level of significance and whether the data fits the Poisson distribution.

3. What are the assumptions of a goodness of fit test for Poisson distribution?

The assumptions of a goodness of fit test for Poisson distribution include the following:

  • The data must be random and independent.
  • The data must be counts or frequencies.
  • The data must be discrete and cannot be negative.
  • The expected values from the Poisson distribution must be at least 5.
If these assumptions are not met, the results of the test may not be accurate.

4. What is the significance level in a goodness of fit test for Poisson distribution?

The significance level in a goodness of fit test for Poisson distribution is the probability of rejecting the null hypothesis when it is actually true. This is typically set at 5% or 0.05, meaning that if the calculated p-value is less than 0.05, we can reject the null hypothesis and conclude that the data does not fit the Poisson distribution.

5. What are the limitations of a goodness of fit test for Poisson distribution?

One of the limitations of a goodness of fit test for Poisson distribution is that it assumes the data is independent and random. This may not always be the case in real-world scenarios. Additionally, the test may not be accurate if the expected values from the Poisson distribution are less than 5 or if the sample size is small. It is also important to note that a significant result from the test does not necessarily mean that the data does not fit the Poisson distribution, but rather that there may be other factors at play.

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