RMarkdown案例 In this project you will demonstrate how to use Method of Moments and Maximum Likelihood Estimation to find parameters of a distribution for which you believe were used in the data generating process.

R  HW- estimation (20pts)
Name______________

Introduction
In this project you will demonstrate how to use Method of Moments and Maximum Likelihood Estimation to find parameters of a distribution for which you believe were used in the data generating process. Consider the data set on Norwegian fire losses provided for this project on Canvas. The file name is norweginafire.txt.  Complete this project using R Markdown and provide your R m

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arkdown files (2 files). If you miss to supply both files your project will not be graded. The pdf/or html file must show: R code, output, and figures properly. Otherwise, your project will not be graded and your score will be 1/20 to recognize your attempt to submit.



Each question below is worth 2pts. All derivations by hand must be provided for grading. Late submissions will not be graded (those sent by email). Group work is allowed, but each student must provide individual submission of his/her own work. If two submissions are found to be identical they will each receive zero score.

Filter the data for one particular year that is assigned to your group.  The project is the defined as follows

Table C1-1981

Table C3-1982

Table C5-1983

Table D1-1984

Table D3-1985

Table C2-1986

Table C4-1987

Table D2-1988

Table D4-1989



Find the parameter estimates using the MM method assuming that the data came from a normal distribution.
Plot the density on top of your histogram. Discuss your findings using 3 full sentences.
Repeat 1) assuming that the data generating process is gamma distribution.
Plot the density of gamma on top of this histogram. Discuss your findings in 3 full sentences.
Plot gamma and normal density on top on the histogram using different colors. Discuss your findings. Min 2 full sentences.
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Find the parameter estimates using the MLE method assuming that the data came from a normal distribution.
Repeat 6) assuming that the data came from log-normal distribution.
Repeat 6) assuming that the data came from gamma distribution.
Plot densities of log-normal, gamma, and normal and discuss your findings. Min 3 full sentences are required for full credit.
Reflect on this project. Min 5 sentences are required.
NOTE
Due to truncation of loss data, you need to divide the pdf() for each observation by 1- F(t), where t represents the truncation point. This needs to be accounted for when deriving the log-likelihood function. You need to take screen shoots of all your derivations required for codding of this project in R.