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By Pedroza C.

ISBN-10: 3900051070

ISBN-13: 9783900051075

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Additional resources for A Bayesian forecasting model: predicting U.S. male mortality (2006)(en)(21s)

Example text

11 Let V(X_, Y_) be a test statistic such that the large values of V give evidence that Ho is false. ) € [0,1] is a statistic satisfying P(p{X_, Y) < 7) < 7 for every 6 £ ©0 and every 7 £ [0,1] and such that for any sample point (x, y) p(x, y) = sup P(V(X, Y) > V(x, y)). 66) 9€0 The p-value can be interpreted as the probability to obtain the data that has been observed in our particular experiment if hypothesis Ho is true. HoA practical construction of hypothesis tests is closely associated with interval estimation.

1) Given the samples X_ and Y_, we are interested in point and interval estimation of R = P(X < Y). 1 Transformations of random variables. ) Transforms pdf»«|r) Weibull: f(x\a) = v(a:) = xa 0 =a One-parameter exponential: A 5(£|A) = Ae- «, ^>0. T = X a known, x > 0. X = a~a Pareto: /(x| 0. X=a Power: /(x|cr,A) = Two-parameter exponential: <7(£|M,A) = Ae-A<«-">, 0 < x < A.

1 Given that (X, Y) is observed, the function of 9 defined by L(9\X_,Y_) = f{X_,Y_\8) is called the likelihood function. 2 The maximum likelihood estimator (MLE) 8 = 9(X_, Y_) of the parameter 8 based on the sample (X_, Y_) is the parameter value at which the likelihood function L(8\X_, Y) attains its maximum as a function of 9. ) If 8 is the MLE of 8, then for any function

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A Bayesian forecasting model: predicting U.S. male mortality (2006)(en)(21s) by Pedroza C.

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