By Lee Bain, Max Englehardt
Textbook for a tools direction or reference for an experimenter who's more often than not attracted to information analyses instead of within the mathematical improvement of the approaches. offers the main invaluable statistical ideas, not just for the conventional distribution, yet for different vital distributions
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Additional info for Statistical Analysis of Reliability and Life-Testing Models: Theory and Methods, Second Edition,
Example text
3. After subtracting 1, changing signs, taking logarithms, differentiation of both sides and some simplification, the desired result follows. It can be shown that only functions with certain properties can be the MRL of a life-testing model. The following theorem characterizes functions which can serve as MRL functions for continuous distributions. 5 tinuous life-testing model if and only if the following conditions are satisfied: 1. µ(x) 2. µ(0) > 0 ~ 0 for all x ? 0 3. µ(x) is a continuous function 4.
L~(t), is independent of~· 1he principle of sufficiency is that in drawing inferences about the unknown parameter Q, attention may be restricted to the statistic S rather than to all n sample observations. If S = (S , ... , Sk) is a vector, it is often referred to as a set of 1 jointly sufficient statistics. 1he whole sample or the set of or- der statistics are joint sufficient statistics, but the primary purpose is to reduce the sample to a small set of statistics which are jointly sufficient.
Eff. " (S 1 , 8 ) = 2 Var (8" 2 ) " Var(8 1 ) Relative to this criterion, (e e e1 is e2 better than if Rel. Eff. , ) > 1. Although bias and variance are important pro2 1 perties, they can not be used alone as absolute measures of the goodness of an estimator. mator ec For example, consider the constant esti- = c. This is clearly not a desirable estimator and does " not even depend on the sample, yet Var(8c) = 0. This example also shows why it is impossible to find an estimator which has minimum mean squared error uniformly over all 8, since for 8 = c, MSE(8) E(e - c) 2 = (c - c) 2 = O, and by letting c change, an estimator c with zero MSE can be found for any specified value of 8.