Re: Gamma Distribution application for modeling arrivals

On Aug 4, 9:16 pm, Jack Tomsky <jtom...@xxxxxxxxxxxxx> wrote:
Hello Everyone,

I am modeling the patient arrival rates during a mass
casualty event
and as we all know, they are time dependent and not
constant. I am
trying to use gamma distribution to model the arrival
process. I am
aware that gamma distribution is characterized by two
parameters
namely the shape and the scale parameter. Now during
a disaster
situation, the patients arriving to the hospital
usually arrive in two
waves, the first wave arrives within 5-30 minutes
from the time the
event occurs and the

Hello Everyone,

I am modeling the patient arrival rates during a mass
casualty event
and as we all know, they are time dependent and not
constant. I am
trying to use gamma distribution to model the arrival
process. I am
aware that gamma distribution is characterized by two
parameters
namely the shape and the scale parameter. Now during
a disaster
situation, the patients arriving to the hospital
usually arrive in two
waves, the first wave arrives within 5-30 minutes
from the time the
event occurs and the second wave after 30 mins may
be. Following are
my questions:

1. Relationship between the gamma parameters keeping
in mind the
arrival rate. How will the two parameters impact the
arrival rate and
pattern? I need to know what is the significance of
each of these
parameters in defining the arrival rate and pattern.

If the gamma density distribution is defined by

F(t; k,theta) = t^(k-1)*exp(-t/theta)/[Gamma(k)*theta^k]

then k is a shape parameter and theta is a scale parameter.

2. How can I find the gamma parameters that would
give the above said
delay times?

The mean is k*theta and the variance is k*theta^2.

One way of estimating these parameters from the data is by the method of moments. Let tbar be the sample mean and let s^2 be the sample variance. By equating the sample moments to the population moments, we obtain

khat = (tbar^2)/(s^2)
thetahat = (s^2)/tbar

as the method-of-moment estimators. If you want to refine these estimates, you can use them as starting values in a numerical algorithm for the maximum likelihood estimates.

Jack



3. I want to model the arrival as gamma distribution
over a time
horizon with the time horizon divided into several
small time
intervals and within each of the small time intervals
the arrival rate
follows an exponential distribution. How do I model
this in the
simulation model designed by me. I need what way
should I specify the
same in the create block to which represents arrivals
in my model.

Thanks a lot.
Amita.

Hey thanks for the email. Unfortunately, I do not have any data and I
am trying to find the effect of the shape and the scale parameter used
in arrival distribution on the system simulated by me. I am trying to
simulate a bombing scenario and trying to see which of the arrival
rates are sensitive to the system and which are not. I want to model
the arrival rate as follows:

Say the duration for which the victims are arriving is 4 hrs (Time
horizon for the event). I want to divide this time horizon into many
small subintervals say of 5 minutes each. The arrival within these
subintervals follow an exponential distribution with arrival rate
lamda, But the overall distribution of the arrival shall follow gamma
distribution. How do I estimate different shape and scale parameters
in this case and how do I use this logic to represent an expression?
For example, when we want to mention that the arrival follows
exponential distribution with a mean of 3 then we represent it as expo
(3) right?? How do I represent in the case I mentioned above.

I also confused with the scale parameter and the arrival rate...is it
that in my case arrival rate value is equal to the scale parameter
value??

Thanks.
Amita
.

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