[Valmont]

The code follows after this intro.

Look how I also added code to intercept bad input like characters and floating point numbers. So input like j and 2.51 are intercepted. Try it. However, CTRL-Z/D is accepted. /D for *nix systems (bash instead of console).
Also, 2.0 is accepted as well. Since the value is exactly an integer. See if you like it:

 #include <iostream>
#include <string>
#include <limits> //numeric_limits #include <iomanip> //setprecision etc. #include <cmath> //modf() using namespace std;

//Optional function. Depends on IDE. Remove for release version. void wait_for_enter();

int main()
{
   int num_positives(0), num_negatives(0), num_evens(0), num_odds(0);
   double percent_negatives(0), percent_positives(0), percent_evens(0),
      percent_odds(0);

   //Lets make this double, so no cast is needed later in the %-calculations. double total_inputs(0);

   double input; //Trick to check for fractions, wich is also invalid input. int theNumber; ///For conversion from double to int. while(1)
   {
      //need this bogus variable for modf(). modf() requires it. double  intpart;
      cout<<"Please enter an integer (pos or neg). CTRL-Z/D to quit!\n";
      while(!(cin>>input) || modf(input , &intpart) !=0 )
      {
         //CTRL-Z/D entered? If so, then get out of this loop. if(cin.eof())
            break;
         cout<<"You didn't enter a number. Try again please."<<endl;
         cin.clear();
         cin.ignore(numeric_limits<streamsize>::max(), '\n');
      }
      //CTRL-Z/D entered? If so, then get out of this loop as well. if(cin.eof() )
         break;

      total_inputs++;
      //Lets convert, since we need modulo calculation (can't with type double).
      theNumber = static_cast<int> (input);
      if(theNumber%2 == 0)
         num_evens++;
      else
         num_odds++;
         
      if(theNumber<0)
         num_negatives++;
      else
         num_positives++;
   }
   
   /*CTRL-Z/D is entered, so we end up here. */
   
   cout<<"\t\tTHE RESULTS OF THE ENTRIES"<<endl;
   cout<<"\t\tTotal valid integers: "<<total_inputs<<endl;
   cout<<"\t\tTotal positive numbers: "<<num_positives<<endl;
   cout<<"\t\tTotal negative numbers: "<<num_negatives<<endl;
   cout<<"\t\tTotal even numbers: "<<num_evens<<endl;
   cout<<"\t\tTotal odd numbers: "<<num_odds<<endl;
   
   //Skip if no valid input: avoid dividing by zero and unneeded calculations. if(total_inputs > 0)
   {
      //Lets show 10 digit-precision.
      cout<<fixed<<setprecision(10);

      cout<<"\t\tPercent positive numbers: "<<
         num_positives/total_inputs*100<<"%"<<endl;
      cout<<"\t\tPercent negative numbers: "<<
         num_negatives/total_inputs*100<<"%"<<endl;
      cout<<"\t\tPercent even numbers: "<<
         num_evens/total_inputs*100<<"%"<<endl;
      cout<<"\t\tPercent odd numbers: "<<
         num_odds/total_inputs*100<<"%"<<endl;
   }
   else
      cout<<endl<<"\t*** STATISTICS OMITTED: no (valid) integers entered ***"<<endl;

   //Optional. Depends on IDE. Remove for release version.
   wait_for_enter();
   return 0;
}

//Optional. Depends on IDE. Remove for release version. void wait_for_enter()
{
  cout << "press <enter> to continue...\n";
  // Reset failstate, just in case.
  cin.clear();
  string line;
  getline( cin, line);
}