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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
Hypergeometric distribution is t he probability distribution related with the sampling without replacement from the population of finite size. If the population comprises of r ele
A manufacturing company has two factories F 1 and F 2 producing a certain commodity that is required at three retail outlets M 1 , M 2 and M 3 . Once produced, the commodity is
Method of moments is the procedure for estimating the parameters in a model by equating sample moments to the population values. A famous early instance of the use of the proced
The model for data containing continuous and categorical variables both.The categorical data are summarized by the contingency table and their marginal distribution, 182by the mult
we are testing : Ho: µ=40 versus Ha: µ>40 (a= 0.01) Suppose that the test statistic is z0=2.75 based on a sample size of n=25. Assume that data are normal with mean mu and standa
The Null Hypothesis - H0: There is no heteroscedasticity i.e. β 1 = 0 The Alternative Hypothesis - H1: There is heteroscedasticity i.e. β 1 0 Reject H0 if Q = ESS/2 >
The probability distribution which is a linear function of the number of component probability distributions. This type of distributions is used to model the populations thought to
Bayes factor : A summary of evidence for the modelM1 against the another modelM0 provided by the set of data D, which can be used in the model selection. Given by the ratio of post
Odds ratio is the ratio of the odds for the binary variable in two groups of the subjects, such as, males and females. If the two possible states of variable are labeled as 'succe
Incidental parameter problem is a problem which sometimes occurs when the number of parameters increases in the tandem with the number of observations. For instance, models for pa
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