Question

Program a code for the random variable (Exponential distribution), where the user informs the data and parameters necessary to generate the Probability Density function (PDF) and the Cumulative Distribution Function (CDF).

Answer 1

The formula for exponential distribution is given below

Here   is the probability density function.

The program to generate exponential distribution is given below

#include <stdio.h>            // Needed for printf()
#include <stdlib.h>           // Needed for exit() and ato*()
#include <math.h>             // Needed for log()

//----- Function prototypes -------------------------------------------------
double expon(double x);       // Returns an exponential random variable
double rand_val(int seed);   

//===== Main program ========================================================
void main(void)
{
  char   in_string[256];      // Input string
  FILE   *fp;                 // File pointer to output file
  double lambda;              // Mean rate
  double exp_rv;              // Exponential random variable
  int    num_values;          // Number of values
  int    i;                   // Loop counter

  // Output banner
  printf("----------------------------------------- genexp.c ----- \n");
  printf("-  Program to generate exponential random variables    - \n");
  printf("-------------------------------------------------------- \n");

  // Prompt for output filename and then create/open the file
  printf("Output file name ===================================> ");
  scanf("%s", in_string);
  fp = fopen(in_string, "w");
  if (fp == NULL)
  {
    printf("ERROR in creating output file (%s) \n", in_string);
    exit(1);
  }

  // Prompt for random number seed and then use it
  printf("Random number seed (greater than 0) ================> ");
  scanf("%s", in_string);
  rand_val((int) atoi(in_string));

  // Prompt for rate (lambda)
  printf("Rate parameter (lambda) ============================> ");
  scanf("%s", in_string);
  lambda = atof(in_string);

  // Prompt for number of values to generate
  printf("Number of values to generate =======================> ");
  scanf("%s", in_string);
  num_values = atoi(in_string);

  // Output message and generate interarrival times
  printf("-------------------------------------------------------- \n");
  printf("-  Generating samples to file                          - \n");
  printf("-------------------------------------------------------- \n");

  // Generate and output exponential random variables
  for (i=0; i<num_values; i++)
  {
    exp_rv = expon(1.0 / lambda);
    fprintf(fp, "%f \n", exp_rv);
  }

  // Output message and close the output file
  printf("-------------------------------------------------------- \n");
  printf("-  Done! \n");
  printf("-------------------------------------------------------- \n");
  fclose(fp);
}

//===========================================================================
//=  Function to generate exponentially distributed random variables        =
//=    - Input:  Mean value of distribution                                 =
//=    - Output: Returns with exponentially distributed random variable     =
//===========================================================================
double expon(double x)
{
  double z;                     // Uniform random number (0 < z < 1)
  double exp_value;             // Computed exponential value to be returned

  // Pull a uniform random number (0 < z < 1)
  do
  {
    z = rand_val(0);
  }
  while ((z == 0) || (z == 1));

  // Compute exponential random variable using inversion method
  exp_value = -x * log(z);

  return(exp_value);
}

double rand_val(int seed)
{
  const long  a =      16807;  // Multiplier
  const long  m = 2147483647;  // Modulus
  const long  q =     127773;  // m div a
  const long  r =       2836;  // m mod a
  static long x;               // Random int value
  long        x_div_q;         // x divided by q
  long        x_mod_q;         // x modulo q
  long        x_new;           // New x value

  // Set the seed if argument is non-zero and then return zero
  if (seed > 0)
  {
    x = seed;
    return(0.0);
  }

  // RNG using integer arithmetic
  x_div_q = x / q;
  x_mod_q = x % q;
  x_new = (a * x_mod_q) - (r * x_div_q);
  if (x_new > 0)
    x = x_new;
  else
    x = x_new + m;

  // Return a random value between 0.0 and 1.0
  return((double) x / m);
}

Here you will enter the lambda parameter and get upto 5 values in the output file provided by you.