Skewness And Kurtosis Problem: Suppose We Have A Vector Of

Question

Skewness and Kurtosis Problem Suppose we have a vector of Skewness and Kurtosis Problem Suppose we have a vector of Skewness and Kurtosis Problem Suppose we have a vector of numbers x. Give R code to compute the observed moments of x around zero of order one to four (i.e. the average of the powers one to four of the elements of x). Give R code to compute the observed moments of x around the mean of order one to four (i.e. the average of the powers one to four of the elements of x in deviations from the mean). Give R code to compute the skewness and kurtosis of x. Code Preferred format is three R functions that take the vector x as an argument and return a list or vector of results. The functions can call each other if that seems desirable. Try to avoid loops. Do not use built-in function such as mean or var, except possible for checking your results. Definitions Skewness is defined (in terms of moments around the mean) as γ1=μ3(μ2)3/2, while kurtosis is γ2=μ4μ22−3. Test on generated numbers Use built-in R functions such as rnorm(), rcauchy(), rlaplace() and rchisq() to generate random vectors (say of length 1000) to try out your code. Generate a table with skewness and kurtosis results for these four distributions.

Dr. Jack HW Helper · Accepted Answer

To analyze the skewness and kurtosis of a vector of numbers in R, we will define three functions: one for computing the observed moments around zero, another for computing the observed moments around the mean, and a third for calculating skewness and kurtosis. The code will make use of random number generation functions to create data sets for testing purposes. Here’s how we can implement these functionalities: Step 1: Define Functions for Moments First, we will create a function to compute the observed moments around zero for orders one through four: calculate_moments_around_zero n moments for (i in 1:4) { moments[i] } return(moments) } Next, we define a function to compute the observed moments around the mean: calculate_moments_around_mean mean_x n deviations moments for (i in 1:4) { moments[i] } return(moments) } Now we will create a function to calculate skewness and kurtosis: calculate_skewness_kurtosis m3 m2 skewness kurtosis return(list(skewness = skewness, kurtosis = kurtosis)) } Step 2: Generate Random Numbers Next, we generate random vectors and test our code. We use the functions provided to analyze various distributions: set.seed(123) # For reproducibility distributions normal = rnorm(1000), cauchy = rcauchy(1000), laplace = rlaplace(1000), chi_squared = rchisq(1000, df=2) ) results Distribution = character(), Skewness = numeric(), Kurtosis = numeric() ) for (name in names(distributions)) { x moments_zero moments_mean sk_kurt results } print(results) Step 3: Generate Tables To present the results in a Markdown table format, we can format the output as follows: markdown_table cat("| Distribution | Skewness | Kurtosis |
") cat("|---------------|----------|----------|
") for (i in 1:nrow(results)) { cat(sprintf("| %s | %.3f | %.3f |
", results$Distribution[i], results$Skewness[i], results$Kurtosis[i])) } } markdown_table(results) Conclusion The generated table will reflect the skewness and kurtosis of the selected distributions. Skewness indicates the sy

Skewness And Kurtosis Problem: Suppose We Have A Vector Of ✓ Solved

Skewness and Kurtosis Problem Suppose we have a vector of

Paper For Above Instructions

Step 1: Define Functions for Moments

Step 2: Generate Random Numbers

Step 3: Generate Tables

Conclusion

References