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Q: Exponential cumulative probability distribution question ( Answered 5 out of 5 stars,   0 Comments )
Subject: Exponential cumulative probability distribution question
Category: Business and Money > Finance
Asked by: mathdumbie-ga
List Price: $30.00
Posted: 28 Oct 2006 21:27 PDT
Expires: 27 Nov 2006 20:27 PST
Question ID: 777965
An exponential cumulative probability distribution has the following
form: F(x) = 1-exp(-x/m)

What is the probability distribution?
What is the mean and the variance of the distribution?
What is the expected value of exp(x) for such a distribution and what is it called?
The exponential distribution is often assumed as representing a ?time
between events? distribution.  In this case, how would you count the
number of events that occur (for example, the number of claims made by
an insured) over a period of time T?  Just specify the logical
If each event has a loss associated to it with a cumulative
probability distribution G(L), how would you simulate the loss that
the individual has over a period of time T?
Subject: Re: Exponential cumulative probability distribution question
Answered By: hedgie-ga on 29 Oct 2006 06:56 PST
Rated:5 out of 5 stars

   Researcher usually ignore multiple questions in one 'GA question',
particularly for low or mid priced questions like this one .

I am making an exception in the hope that
 you will be able to find all answers in few selected links below.

It should required only a limited effort.

1) p.d.f. is exponential distribution    P=(1/m) * exp (-x/m) 
   it is shown on Figs 2, 3, here:
where you will find basic properties (mean, etc)

2) waiting times for events distributed uniformly have indeed
exponential distribution. Probability that n such event will happen in
a given time
 is given by Poisson distribution.

All this including

3) simulation

is covered by Queue theory. Most textbooks start with example of simples queue
which uses all these concepts you mention and gives examples.

more referrences:

To focus on simulation (as a tool for solving more complex situation) use

SEARCH TERM: discrete event simulation



Request for Answer Clarification by mathdumbie-ga on 29 Oct 2006 08:38 PST
Thank you, this is perfect.  In regards to my last bulleted item, "If
each event has a loss associated to it with a cumulative probability
distribution G(L), how would you simulate the loss that the individual
has over a period of time T" could you please point me in the right
direction as well (or did I just miss it)?

Clarification of Answer by hedgie-ga on 29 Oct 2006 21:59 PST
Well, I did not know which c.d.f.  the G(L)  is. 

a)  Are we still talking about
 uniform-expo-poisson case defined by F(x) and m 

or is (entirely new) topic, namely 

b) For any given c.d.f. G(L) what is the AVERAGE cost rate C  (e.g.
$/day) if cost  of each event is  c1  ?

  I assume here  a stationary (steady state) process, so all I ned is P(n)
   probability that n events happanes in a day (=interval T). Then

 C = (SUM over n) ( P(n) * n*c1 )

 In case a) P(n) is the Poisson distribution  with mean determined from F(x)
 For general G(L) it will not be Poisson, but probability Px(n) than n 
 will happen N trials can be derived same way. See

SEARCH TERM bernoulli  probability distribution, binary 


Poisson is a special case for case of rare events

Rating appreciated

Good Luck with your studies

mathdumbie-ga rated this answer:5 out of 5 stars and gave an additional tip of: $5.00
Excellent resource!

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