Exponential cumulative probability distribution question
Category: Business and Money > Finance
Asked by: mathdumbie-ga
List Price: $30.00
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?
Re: Exponential cumulative probability distribution question
Answered By: hedgie-ga on 29 Oct 2006 06:56 PST
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
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