What use cases are there in JavaScript for sparse arrays?

Question

What possible use of the software could take place where a sparse array would be better than a (regular) object?

By sparse array, I mean the one where:

arr = [];                             //Initialize
arr[0] = 'W';
arr[1] = 'T';
arr[3] = 'F';

console.log(arr[0] !== undefined)    //true
console.log(arr[1] !== undefined)    //true
console.log(arr[2] === undefined)    //true
console.log(arr[3] !== undefined)    //true

Or more formally:

An object, O, is said to be sparse if the following algorithm returns true:

1. Let len be the result of calling the [[Get]] internal method of O with argument 
"length".

2. For each integer i in the range 0≤i<ToUint32(len)
    a. Let elem be the result of calling the [[GetOwnProperty]] internal method of O     
    with argument ToString(i).

    b. If elem is undefined, return true.

3. Return false.

ECMA 262 5.1 - 15.4 Array Objects

In addition, the ECMA 262 5.1 standard further defines lengthas:

The length property of this Array is a data property whose value is always numerically greater than the name of each property to delete, whose name is the index of the array.

So, the example above, arr.length === 4despite the fact that only three elements are defined.

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    //Cannot trust arr[i] exists

for(key in arr)
    //Always exists

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