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Clayton copula model: Denote by τ1, . . . , τm the default times of m companies. Assume that the τi are exponentially distributed with parameters λi, i = 1, 2, (P (τi ≤ t) = 1 - exp(-λit)) and that they follow a copula model with Clayton copula with parameter θ.
a) Write down the joint survival function and the corresponding mixture represen- tation explicitly.
b) Assume that you have a random number generator that is able to generate in- dependent Gamma distributed and uniformly distributed random variables. Write down an algorithm to generate a sample of τ1, τm via the mixture distribution.
c) Assume that λ1 = ... = λm. Write down
limθ→∞ P (τ1 ≤ T, τm ≤ T ) and limθ→0P(τ1 ≤ T, τm ≤ T ).
If the two hypotheses have equal prior probability, for what values of x is the posterior probability of H0 greater than that of H1 and what is the form of the likelihood ratio test of H0 versus H1?
A special SCSU Minnesota license plate starts with two letters selected from 18 possible letters of the alphabet followed by three digits 0-9. How many different SCSU Minnesota license plates are possible?
find the affine coordinates of x (0)/ with respect to {p0, p1,p2}.
refer to and use the following abbreviations for the problems belowbt box of teasamph shipping and handlingp desired
most railroad cars are owned by individual railroad companies. when a car leaves its home trackage it becomes part of a
Write Boolean expression & draw the gate logic diagram & typical PLC logic ladder diagram for a control system wherein a fan is to run only when all of the following conditions are met:
Problem 1: A certain function f is given by the graph.
represents an estimate of the average cost of gas for year x starting in 1997 ("Consumer price index," 2006). The year 1997 would be represented by x = 1, for example, because it is the first year in the study. Similarly, 2005 would be year 9, or ..
new engraver cost 25000one-year loan cost 12 interestrevenue per day from engraving 975profit margin on engraving
How do we explain the y=mx+b equation using graphical method to solve?
in a local district 800 republicans, 500 democrats and 200 independent voters. if a voter is chosen at random what is the prabability that the voter selected is not republican?
Find the steady state oscillation of the mass spring system modeled by the given ODE. y'' + 8y' + 15y = 717.5cos(4t). Solve the given non-homogeneous ODE by variation of parameters or undetermined coefficients. Give a general solution
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