iPhone 6 touch sensitivity problem near edges of screen

I'm wondering if others are experiencing the problem I'm having with the sensitivity of the touch screen near the edges of the screen.

Often times I have the press harder or multiple times on buttons near the edges of the screen. When typing on the keyboard, it will often miss my first attempts at pressing the letters "A", "Z", "123", "L", etc. When using the calculator, I often have to press the "+" or "1" two or more times before it recognizes the press. All of these letters are near the edges of the screen. I tried typing on my wife's iPhone 6 Plus and do not have the same problem.

Do I have a faulty touchscreen, or is this a common problem?