Calculate Gamma Distribution: 5% at $627, 95% at $1444

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    Distribution Gamma
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SUMMARY

The discussion focuses on calculating the Gamma distribution, specifically determining payout thresholds where 5% of payouts are approximately $627 and 95% are around $1444. The calculation involves using the cumulative distribution function (CDF) to find the percentage of payouts below a certain value. To reverse this process, the inverse CDF function is utilized, which takes a percentage input and returns the corresponding payout amount. This method is essential for understanding payout distributions in financial contexts.

PREREQUISITES
  • Understanding of Gamma distribution and its parameters (shape and scale)
  • Familiarity with cumulative distribution functions (CDF)
  • Knowledge of inverse CDF functions
  • Basic proficiency in statistical analysis tools or programming languages (e.g., Python, R)
NEXT STEPS
  • Research the properties and applications of the Gamma distribution in finance
  • Learn how to implement the cumulative distribution function (CDF) in Python using libraries like SciPy
  • Explore the use of inverse CDF functions for various probability distributions
  • Study statistical modeling techniques for payout distributions in risk management
USEFUL FOR

Statisticians, financial analysts, data scientists, and anyone involved in risk assessment and payout modeling will benefit from this discussion.

euler_fan
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On the included link, it is calculated that 5% of payouts are around $627 and 95% of payouts are at $1444. I would appreciate if someone can direct me as to how the came up with this answer.

http://www.brighton-webs.co.uk/distributions/gamma.asp"
 
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First off they use "less than" and "greater than", not "equal". Those are the limits of the payouts. In general, the F(x) or CDF or Cumulative Probability function takes as an input a number x (payout) along with the distribution parameters, shape, and scale. It returns a percentage as an answer such that y percent of things (payouts) will be less than x.

Now to go the other way you need the inverse CDF function. You feed it a percentage, y, and it returns x (payout amount). Usually this is done with a tabulated chart of values or a computer/calculator function.
 

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