Template:Example: Lognormal Distribution Bayesian Bound (Parameters)

Lognormal Distribution Bayesian Bound Example (Parameters)

Determine the two-sided 90% Bayesian confidence bounds on the lognormal parameter estimates for the data given next:

[math]\displaystyle{ \begin{matrix} \text{Data Point Index} & \text{State End Time} \\ \text{1} & \text{2} \\ \text{2} & \text{5} \\ \text{3} & \text{11} \\ \text{4} & \text{23} \\ \text{5} & \text{29} \\ \text{6} & \text{37} \\ \text{7} & \text{43} \\ \text{8} & \text{59} \\ \end{matrix} }[/math]

Solution

The data is entered into a Times-to-failure data sheet. The lognormal distribution is selected under Distributions. The Bayesian confidence bounds method only applies for the MLE analysis method, therefore, Maximum Likelihood (MLE) is selected under Analysis Method and Use Bayesian is selected under the Confidence Bounds Method in the Analysis tab.

The two-sided 90% Bayesian confidence bounds on the lognormal parameter are obtained using the QCP and clicking on the Calculate Bounds button in the Parameter Bounds tab as follows:

[math]\displaystyle{ }[/math]