How Do You Calculate Estimators and Analyze Complication Rates in Statistics?

In summary, the conversation is about two questions. The first question involves finding the method of moments estimator and the maximum likelihood estimator for λ for a continuous random variable with a given density function. The second question is about comparing complication rates between two surgical procedures and determining if there is a significant difference. The person asking for help has been working on the questions for some time but has not made much progress. They are asked to provide any progress they have made so far to help the helpers understand where they are stuck.
  • #1
NYCStats22
2
0
Really need help with these two questions. I have been working on them for some time and just can't seem to make any significant progress1) X is a continuous random variable with density function

f(x) = (θ + 1)x^θ , 0 < x < 1 and 0 elsewhere

Derive both the method of moments estimator and the maximum likelihood estimator for λ.

*For the MOM estimator you will need to find the mean*2) Two surgical procedures are compares and what is of interest are the complication rates. 150 patients had procedure A and there were 35 complications while procedure B tested 138 patients and there were 34 complications. Does this indicate a difference at a 1% level. What is the P-value?
 
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  • #2
Hello and welcome to MHB, NYCStats11! (Wave)

Even though you say you have not made significant progress, can you post what progress you have made? This will give our helpers some idea where you are stuck and how to best help you, even if all you can state is what theorems you think may apply.
 

FAQ: How Do You Calculate Estimators and Analyze Complication Rates in Statistics?

What is the Method of Moments Estimator?

The Method of Moments Estimator is a statistical technique used to estimate the parameters of a probability distribution based on a set of observed data. It works by equating the theoretical moments of the distribution to the corresponding sample moments, and solving for the unknown parameters.

How does the Method of Moments Estimator work?

The Method of Moments Estimator works by using the moments (such as mean, variance, etc.) of a probability distribution to estimate the parameters of that distribution. It assumes that the theoretical moments of the distribution are equal to the sample moments, and uses this information to solve for the unknown parameters.

What are the advantages of using the Method of Moments Estimator?

The Method of Moments Estimator is a simple and intuitive method for estimating parameters of a probability distribution. It does not require any assumptions about the underlying distribution, and can be easily applied to a wide range of distributions. Additionally, it is a consistent estimator, which means that as the sample size increases, the estimated parameters will converge to the true values.

What are the limitations of the Method of Moments Estimator?

The Method of Moments Estimator may not always provide the most accurate estimates, especially when the sample size is small. It also relies on the assumption that the theoretical moments are equal to the sample moments, which may not always be true in practice. Additionally, it may not be suitable for complex distributions with many parameters.

How is the Method of Moments Estimator different from other estimation methods?

The Method of Moments Estimator differs from other methods such as Maximum Likelihood Estimation and Bayes Estimation in its approach to estimating parameters. While the Method of Moments uses moments to estimate parameters, Maximum Likelihood Estimation uses the likelihood function, and Bayes Estimation incorporates prior beliefs about the parameters. Each method has its own strengths and limitations, and the choice of which to use depends on the specific situation and goals of the analysis.

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