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Q: Exponential cumulative probability distribution question ( Answered ,   0 Comments )
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 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 procedure. 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?```
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 Subject: Re: Exponential cumulative probability distribution question Answered By: hedgie-ga on 29 Oct 2006 06:56 PST Rated:
 ```Hello 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: http://cnx.org/content/m13128/latest/ 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. http://en.wikipedia.org/wiki/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. http://people.bu.edu/pekoz/feed.pdf more referrences: http://www.answers.com/topic/poisson-process http://www.ise.canberra.edu.au/un6538/Lectures/2006/Poisson.pdf http://en.wikipedia.org/wiki/Queuing_theory http://www2.uwindsor.ca/~hlynka/qonline.html To focus on simulation (as a tool for solving more complex situation) use SEARCH TERM: discrete event simulation e.g. http://www.mathworks.com/access/helpdesk/help/toolbox/simevents/ug/index.html?/access/helpdesk/help/toolbox/simevents/ug/bp8wu4e.html Hedgie``` 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 e.g. http://www.statsoft.com/textbook/stdisfit.html Poisson is a special case for case of rare events Rating appreciated Good Luck with your studies Hedgie```
 mathdumbie-ga rated this answer: and gave an additional tip of: \$5.00 `Excellent resource!`

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