Question

This is about a statistical computing problem. Can some

solve this? Coding in R is preferred.

7) Given a probability distribution F and a point x 6 Rd, at depth Mam D measures . ‘ _ d

how close x is to the center of the distribution and deﬁnes a rank order on pomt-S m R with respect to F. Observations which are far from the center of the data are given low ranks, whereas observations close to the center receive higher ranks. The Mahalano‘ois

depth MD; F) of a vector is with respect to a distribution function F with mean vector

piF and dispersion matrix 2;: is deﬁned to be MD(t; F) = [1 + it — #F)’231(t — tell—1- The sample version is computed by plugging in estimated ftp and $1.1. 0 5.. Write a program to generate a sample of size n from a bivariate normal distribution

(F) with mean up = (O, 0), unit variances and Correlation 0.5. If you code in R1 see the function mahalanobis(x, center, cov). Let n = 10. Print the observations, their

mean and covariance, and the depth of each data point. Find and print the bivariate median; i.e. the bivariate vector that maximizes the depth function. e b. Generate n = 1000 bivariate observations from F. Plot all observations and identify the lowest 5 percent of the data in red.

Statistics and Probability