Time-decaying sum sketch

Question

At the Data Mining course at school i've received the following question regarding sketching:

Consider a stream of events with timestamps: t₁ < t₂<...

We are interested in maintaining a sketch of timestamps that would allow us to estimate the time decaying with the current time t with CV of ε

T_α=Σα(t_i)

for any decay function α

I've tried to use the Morris Counter because it has logarithmic size and the probability of sampling the fist timestamps, which has the largest value in the decay function, is larger.

But the CV of the Morris Counter is a constant and I couldn't figure out how to modify it.

edit: my solution so far:

initialize: x = 0, result = 0
for each new timestamp t:   
- sample it with probability of 2^(-x)
- if it is sampled:
   - x++
   - result = result  + α(t)