I've done it with Photoshop but used tools of which I'm quite sure PSP also has them.
First make a selection
Then fill it with a black color and undo the selection
Next apply a motion blur wide enough to get a nice gradient
Next apply a Gaussian blur to get the blurry borders as you would like them
With the Smudge tool you can modify the start and end points a bit.
You could apply more layers with similar smaller skidmarks over the big one to simulater that some points have a stronger effect
Here a small skidmark that I will move over the big one:
Here two of the small skidmarks (the same one) are applied over the big skidmark. I did adjust the transparencies to get the best result and variation in the effect.
Another way would be making a gradient with which you might be able to control the gradient much better.
I hope this gives you some ideas to create the effect.