Negative Binomial and Chi-square

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SUMMARY

The discussion centers on solving simultaneous equations for the parameters p and k in the context of the Negative Binomial distribution. The equations presented are: \(\bar{x} = \frac{k(1-p)}{p}\) and \(s^2 = \frac{k(1-p)}{p^2} = \frac{\bar{x}}{p}\). Participants express challenges in deriving values for p and k, indicating a need for clarity in the mathematical relationships between these variables. The conversation highlights the importance of understanding the statistical properties of the Negative Binomial distribution for accurate parameter estimation.

PREREQUISITES
  • Understanding of Negative Binomial distribution
  • Familiarity with simultaneous equations
  • Knowledge of statistical parameters such as mean (\(\bar{x}\)) and variance (\(s^2\))
  • Basic proficiency in algebraic manipulation
NEXT STEPS
  • Study the derivation of parameters in the Negative Binomial distribution
  • Learn about statistical estimation techniques for p and k
  • Explore the application of Chi-square tests in parameter fitting
  • Investigate software tools for statistical analysis, such as R or Python's SciPy library
USEFUL FOR

Statisticians, data analysts, and researchers working with Negative Binomial distributions and those interested in parameter estimation techniques in statistical modeling.

sam_0017
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can anyone help me with this question :


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

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

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