Define cumulant generating function. Obtain a relationship between cumulants and moments.
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- Suppose that the Lorenz Curve for country A is given by yA = x 2.2 and for country B is yB = 0.3x 2 + 0.7x. Use the Gini index to determine which of the two countries has greater inequality in its income distribution.show that e^(4t-3t^2) cannot be a moment generating functionFind kurtosis by using quartile deviation(formula given in picture).
- If X is exponentially distributed with parameter λ and Y is uniformly distributed on the interval [a, b], what is the moment generating function of X + 2Y ?Theorem 6.4 states that the moment-generating function of the gamma distribution is given by Mx(t) = (1-βt)^(-α).In an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from y = 0.98x2.1for one year to y = 0.32x2 + 0.68x for the next year. Find the Gini coefficient of income for both years. (Round your answers to three decimal places.) after before
- Compute acrlength function s(t): (with initial point t=0)solve the ecuation diferential with partial fractions and laplcae transformAssume S = $45, σ = 0.25, r = 0.05, div = 0.0, on a 45 strike call and 55 days until expiration. Given delta = 0.5502 and gamma = 0.0876, what is the delta-gamma approximation for the call price on a $0.90 stock price decline?
