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# Bayesian Reliability Analysis

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How do I derive the posterior density of a Weibull Distribution?

##### Solution Summary

The solution answers the question(s) below. Posterior density of Weibull distribution

##### Solution Preview

The question is very general. Therefore, I've got to start from Bayesian estimation and an example follows. Please refer to the attachment.

Bayesian estimation
Now let's focus on the problem of estimation of a 1 dimensional parameter. Mean Squared Error corresponds to using

The risk function of a procedure (estimator) is

Now consider using a prior with density . The Bayes risk of is

How should we choose to minimize ? The solution lies in recognizing that is really a joint density

For this joint density the conditional density of X given is just the model . From now on I write the model as to emphasize this fact. We can now compute a ...

##### Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

##### Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

##### Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.