Negative Binomial and Chi-square

Thread starter sam_0017
Start date Sep 30, 2011
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Binomial Negative

In summary, Negative Binomial and Chi-square distributions are two different probability distributions used in statistics. Negative Binomial distribution models the number of trials needed to achieve a certain number of successes, while Chi-square distribution is used to test the goodness of fit of a sample. The mean and variance of Negative Binomial distribution can be calculated by multiplying the number of trials and the probability of success, and n(1-p)/p^2, respectively. The Negative Binomial distribution is closely related to the Poisson distribution, and the Chi-square test is commonly used in hypothesis testing to assess the association between two categorical variables. However, both distributions cannot be used for continuous data and are only applicable to discrete data.

Sep 30, 2011

sam_0017

can anyone help me with this question :

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Sep 30, 2011

Stephen Tashi

Science Advisor

I haven't looked at the problem closely. Is there some difficulty in solving the simultaneous equations for p and k ?

[tex] \bar{x} = \frac{ k(1-p)}{p} [/tex]
[tex] s^2 = \frac{k(1-p)}{p^2} = \frac{\bar{x}}{p}[/tex]

1. What is the difference between Negative Binomial and Chi-square distributions?

Negative Binomial and Chi-square distributions are both probability distributions used in statistics, but they serve different purposes. Negative Binomial distribution is used to model the number of trials needed to achieve a certain number of successes in a series of independent trials, while Chi-square distribution is used to test the goodness of fit of a sample to a theoretical distribution.

2. How do you calculate the mean and variance of a Negative Binomial distribution?

The mean of a Negative Binomial distribution is equal to the product of the number of trials (n) and the probability of success (p). The variance is equal to n(1-p)/p^2.

3. What is the relationship between the Negative Binomial and Poisson distributions?

The Negative Binomial distribution is closely related to the Poisson distribution, as it can be seen as a generalization of the Poisson distribution. While the Poisson distribution models the number of events occurring in a fixed time or space interval, the Negative Binomial distribution models the number of trials needed to achieve a certain number of successes.

4. How is the Chi-square test used in hypothesis testing?

The Chi-square test is used to determine if there is a significant difference between the observed and expected frequencies in a categorical data set. It is commonly used in hypothesis testing to assess the association between two categorical variables and to determine if any observed differences are due to chance or if they are statistically significant.

5. Can the Negative Binomial and Chi-square distributions be used for continuous data?

No, both the Negative Binomial and Chi-square distributions are discrete distributions and therefore cannot be used for continuous data. They are only applicable to discrete data, such as counts or categories.