Homework Problem 4, STAT 705, Fall 2015.

Assigned 9/16/2015,  Due Monday 9/28/2015


(a) Write a function  "SimData" with the following 
inputs and outputs:

       INPUTS:
xvec = either NULL (the default) or a fixed numeric vector 
          (of arbitrary length)
simx = vector of (mean,sd,length) parameters for a normally 
          distributed SIMULATED vector   xvec , to be used 
	  in case  xvec  is NULL
errscal = error standard deviation to be used in simulating yvec
coef  = vector with 2 components (intercept,slope) to be used 
	  in simulating yvec

       OUTPUT: a list containing all the (named) components xvec,
simx, errscal, coef from the INPUTs, together with a component yvec
which is a vector of the same length as xvec , simulated to 
follow an Exponential distribution with hazard rate-parameter lambda[i] 
(reciprocal of mean) of yvec[i] equal to
       log(lambda[i]) = coef[1] + coef[2]*xvec[i] + errscal*epsilon[i] 
where epsilon is a vector with pseudo-random independently identically
logistic-distributed entries vector of the same length as xvec, with 
mean 0 and scale-parameter 1.

(b) Test your function in creating some datasets of moderately
large size (say, 300), and show that it is working properly by
calculating some appropriate summary statistics (means, covariances, 
residuals, histograms or whatever: the choice is yours).

The working R lines and outputs for part (b) are restricted to
1/2 page AT MOST. You should submit a few clearly written lines of 
text to explain what you are calculating and why it indicates that the 
simulated-exponential-data function is working. You may also submit 
up to two R-generated pictures if you think that is a more efficient 
way to show the properties of your generated data.