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A unified approach to all problems of prediction, estimation, and hypothesis testing. It is based on concept of the decision function, which tells the performer of experiment how to conduct the statistical aspects of an experiment and which action to take for each possible outcome. Choosing the decision function needs a loss function to be defined which assigns numerical values to making bad or good decisions. Explicitly a general loss function is denoted by L d; expressing how bad it would be to make decision d if the parameter value were. A quadratic loss function, it could be defined as and a bilinear loss function as
Geometric distribution: The probability distribution of the number of trials (N) before the first success in the sequence of Bernoulli trials. Specifically the distribution is can
Collector's problem : A problem which derives from the schemes in which packets of a particular brand of coffe, cereal etc., are sold with coupons, cards, or other tokens. There ar
Indirect standardization is the procedure of adjusting the crude mortality or morbidity rate for one or more variables by making use of a known reference population. It may, for in
Remedian: The robust estimator of location which is computed by an iterative process. By assuming that the sample size n can be written as bk where b and k are the integers, the s
#q A paper mill products two grade of paper viz., X & Y. Because of raw material restriction, it cannot produce more than 400 tons of grade X paper & 300 tons of grade Y paper in a
The special cases of the probability distributions in which the random variable's distribution is concentrated at one point only. For instance, a discrete uniform distribution when
The linear component ηi, de?ned just in the traditional way: η i = x' 1 A monotone differentiable link function g that describes how E(Yi) = µi is related to the linear compon
Genetic algorithms: The optimization events motivated by the biological analogies. The prime idea is to try to mimic the 'survival of the fittest' rule of the genetic mutation in
Quality-adjusted survival analysis is a method for evaluating the effects of treatment on survival which allows the consideration of quality of life as well as the quantity of lif
A directed graph is simple if each ordered pair of vertices is the head and tail of at most one edge; one loop may be present at each vertex. For each n ≥ 1, prove or disprove the
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