# Gamma Distribution Homework: Estimating % Days > 10

• EvLer
In summary, the conversation discusses how to model electricity consumption data using a Gamma distribution and estimate the percentage of days with consumption over 10. The speaker mentions finding moment estimates for the two parameters, but is unsure how to apply them to the question. They request for someone to explain and provide relevant formulas for assistance.
EvLer

## Homework Statement

so, I'm given some sample data: electricity consumption on randomly selected n days, and asked to model the problem using Gamma distribution, then the question is to estimate percentage of days on which consumption was > 10 by using moment estimates.

So, I can find the moment estimates for the two parameters: alpha number of exponentially distributed RVs each with mean lambda.
But I do not know how to relate the estimates of the parameters to the question I am asked!

Really, you have to give the relevant formulas here to get more people (such as me) to try to help.

## 1. What is the Gamma distribution?

The Gamma distribution is a type of probability distribution that is commonly used to model continuous data. It is characterized by two parameters, shape and scale, and is often used to model data that is skewed to the right.

## 2. How is the Gamma distribution used to estimate % days > 10?

The Gamma distribution can be used to estimate the percentage of days that are greater than 10 by fitting the data to the distribution and calculating the area under the curve for values greater than 10. This area represents the estimated percentage of days that are greater than 10.

## 3. What are the assumptions made when using the Gamma distribution for this type of homework?

Some assumptions that are typically made when using the Gamma distribution for estimating % days > 10 include: the data is continuous, the data is positively skewed, and the data follows a specific pattern of variability. Additionally, the data should be independent and identically distributed.

## 4. Can the Gamma distribution be used for any type of data?

No, the Gamma distribution is most commonly used for continuous data that is positively skewed. If the data does not meet these criteria, other types of distributions may be more appropriate for estimating % days > 10.

## 5. How can one validate the results of using the Gamma distribution for estimating % days > 10?

One way to validate the results is to compare them to other methods of estimation, such as using a different distribution or using a different statistical approach. Additionally, one can perform sensitivity analyses by varying the assumptions and parameters used in the estimation process to see how it affects the results.

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