Help with choosing method for duration estimation

In summary, the conversation involves a new person seeking help with estimating the mean value of event duration in a system with multiple types of events occurring in consecutive observation periods. The conversation also mentions the use of formulas and an example to illustrate the problem. One possible solution proposed is to use queueing theory.
  • #1
redford
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Hello everybody,

I am new here and I am not sure whether I put this question in a correct forum. If not I am sorry...anyway I hope you help me...

***** Before all: *****
TESTED: SSD METHOD DOES NOT WORK HERE SUFFICIENTLY RELIABLY.

Here it is:

***** Description: *****
Imagine we have set of N types of events. Each event, when it happens, has certain duration according to let's say lognorm distribution. The events happen after each other during certain period of time, then the period stops and next period starts. There is M periods of observations, during which the events are happening after each other. Each observation is fully or almost filled with event...but there could be some delays.

I know number of events of each type per each observation period and length of each observation period. I want to estimate the mean value of duration of each type of event.

***** Formulas: *****
index of type of event: i=1..N
index of observation: m=1..M
number of events of type i within observation m: X_im (I know)
index for event type i occurence within observation period m: k=1..X_im
mean value of duration of event i: D_i (I want to find)
real duration of event k of type i within observation m:D_imk
sum of durations of events during observation period m: S_m
duration of observation period m: O_m (I know)
event duration ratio: real vs mean value: DR_imk (has probably lognorm distribution, definitely with mean value 1)
observation duration ratio: real vs mean value: OR_m (I don't know what distribution is best, but I know that OR_m<=1 and the values are mostly pretty clost to one...I guess that OR_m<=0.8 should be very rare, for simplification we can assume OR_m=0.95 or something like that)

SUM[D_imk; k=1..X_im, i=1..N]=S_m
D_imk=DR_imk*D_i (DR_imk ~ lognorm (1,sigma=?))
S_m=OR_m*O_m (OR_m <= 1 but close to 1)

***** Example: *****
let's have 5 days of observation: M=2
we have 3 types of events: N=3
First day happened 3 events type 1, 5 events type 2 and no event type 3; second day there are 2 occurences of each event...:
X_11=3, X_21=5, X_31=0,
X_12=2, X_22=2, X_32=2,
X_13=1, X_23=6, X_33=4,
X_14=0, X_24=0, X_34=100,
X_15=2, X_25=3, X_35=10
And here are the durations of the observations each day:
O_1=110, O_2=70, O_3=85, O_4=110, O_5=80
This is what I know and now I want to estimate D_i
(this example was prepared with D_1~20, D_2~10, D_3~1)
(in reality there may be N (number of event types) up to 10, 20 in extreme cases, M (number of observation periods) may be 100 or even more)

So, please help, how to solve it

Thanx lot
Redford
 
Mathematics news on Phys.org

1. What are the different methods for estimating duration in a scientific study?

There are several methods for estimating duration in a scientific study, including self-report measures, behavioral observations, and physiological measurements.

2. How do I determine which method is best for my study?

The best method for estimating duration will depend on the specific goals and design of your study. Consider factors such as the type of data you need, the population being studied, and the resources available.

3. What are the advantages and disadvantages of each method?

Self-report measures are easy to administer but may be subject to bias. Behavioral observations can provide objective data but may be time-consuming. Physiological measurements can provide precise data but may require specialized equipment and expertise.

4. Can I use multiple methods for estimating duration in my study?

Yes, using multiple methods can provide a more comprehensive understanding of duration in your study. However, it is important to carefully consider the potential overlap and limitations of each method.

5. Are there any ethical considerations when choosing a method for duration estimation?

Yes, it is important to consider the potential impact on participants and ensure that the chosen method is ethically sound. This may include obtaining informed consent, protecting participant privacy, and minimizing any potential risks or discomfort.

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