1. J

    General Equilibrium Pareto set allocations (2 producers/2 goods)

    Hey there, it is the first time I seek help on a math board as I have to study for this exam by books only due to a very inconvenient situation. I only have exercises (without solutions) and the referenced book to the class. The task is the following:Consider an economy with production formed...
  2. A

    Verifying that Uniform and Pareto distributions are probability densities

    Show that the following functions are probability densities, i.e. f(x)\geq 0 and \int_{-\infty}^{\infty}f(x) dx =1 Uniform distribution: f(x)=\left\{\begin{array}{cc}\frac{1}{b-a} & \mbox{ for } a\leq x \leq b\\0 & \mbox{ otherwise }\end{array}\right. Pareto distribution: For k>0...
  3. F

    Pareto Optimal Allocation

    An economy consist of 2 people. Person 1 has endowment of (3,12) Person 2 has endowment of (6,6) They have the same Utility function: U(x,y)=XY At every Pareto Optimal Allocation, (is a multiple choice and answer is : "Person 1 consumes 9 good x for every 18 good y that he/she consumes") I...
  4. D

    log likelihood in Pareto distribution

    I'm having some trouble finding the log-likelihood in these questions: Question 1 Pareto distribution is: f(yt) = θ / (yt ^ (1+θ)) What is the log-likelihood, log L (θ) Question 2 Geometric distribution: f (yt) = θ (1 − θ)^yt, yt = 0, 1, 2, · · · where θ > 0, is an unknown parameter. Let {y1...
  5. K

    Pareto Distribution

    Would appreciate if anyone can help solve this.
  6. K

    Pareto Distribution

    Hi, would be thankful if anyone can solve this.
  7. O


    I want to generate a range of numbers that follow a Pareto distribution. I want these numbers to assume a mean value of say 1000. With the pareto distribution I need to specify my shape and location parameters (or alpha and beta depending on the terminology you would like to use). In...
  8. S

    Mixture of Gamma, Poison, and Pareto Distribution

    I got this far: \frac{\Gamma(\alpha + k)}{\Gamma(h) \Gamma(\alpha) \Gamma(k)} \int^{\infty}_0 \int^{\infty}_0 \frac{e^{-(h^{-1} + \lambda) \theta}\theta^{h+x-1} \lambda^{k+x-1} h^{-2k}}{(1+h^{-1} \lambda)^{\alpha + k}}d \lambda d \theta now I'm stuck. Not sure how to integrate with...
  9. C

    pareto distrubution

    the block of car insurance business you are considering, there's 50% chance that a claim will be made during upcoming yr. once a claim is submitted, the claim size has the pareto distribution with parameters 3 and 1000 (theta) . only one claim will happen during the yr. determine the variance...
  10. V

    Pareto PDF

    Can someone show me how this integrates to 1? \int_{-\infty}^{\infty} \frac{\gamma \theta^{\gamma}}{x^{\gamma +1}} Also, can you show me how to derive the variance and quartiles? Thank you.
  11. W

    Pareto type PDFs

    The distributions of incomes in the two cities follow two Pareto type pdfs f(x) = 2/x^3 1 < x < infinity and g(y) = 3/y^4 1 <y < infinity Here one unit represents 20,000 dollars. One person with income is selected at random from city and let X and Y be their respective incomes. Compute P(X <...
  12. C

    Pareto distribution

    Need help on the Pareto distribution, please. Thanks! I can get the mean loss amount \frac {\alpha\beta}{\alpha-1} but I don't understand how to get (ii) and (iii)