The purpose of this assignment is to learn about the basics of simulation and sorting.
Write a function double rand_unif() that
generates a U(0, 1) pseudo-random number using the
random() function.
Write a function void dswap(double *x, double
*y) that swaps the values stored in the locations
x and y. Here, x and
y are to be interpreted as pointers to scalars,
not arrays. For example, the code snippet
double x = 0, y = 1; dswap(&x, &y);should result in
x having value 1 and y
having value 0. Write a function void dsort(double *x, int n, int
*ncomp, int *nswap) that takes an array x as
input and changes it "in-place" to its sorted version.
The function should also compute the number of comparisons made and
the number of swaps done, and record these in the locations pointed
to by ncomp and nswap. This is a common
trick used in C programming to "return" more than one
value.
Implement whatever sorting algorithm you can think of yourself, rather than trying to find an efficient one. We will discuss various sorting algorithms in class later.
Write a function double *rbeta(int m, int n, int
dsize) that uses rand_unif() and
dsort() to simulate an array (of length
dsize) of Beta(m, n) random
variates.
Using the lgamma function in math.h
and relevant parts from assignment 2, write a function void
beta_mle(double *x, int *m, int *n, int k) that computes the
MLE of (m, n) for integer m and n where 1 \leq m, n \leq k, and stores the resulting
estimates in *m and *n.
Write a function void sim_beta_mle(int m, int n, int
dsize, int k) that simulates dsize Beta(m, n) random variates, computes the MLE
for integer 1 \leq m, n \leq k, and prints
the MLEs of m and n (in a single line).
Write a main function that uses command-line
arguments to obtain integers m, n, dsize, and nrep (in that order)
from the user, computes k = 2 * max(m, n), and then
calls sim_beta_mle(m, n, dsize, k) nrep
times (thus producing a printout of the MLEs, one replication per
line).
Submit your program by email by midnight of Monday February 13.