Template:Example: Lognormal General Example Interval Data

Lognormal Distribution General Example Interval Data

Determine the lognormal parameter estimates for the data given in Table below.

Solution

This is a sequence of interval times-to-failure where the intervals vary substantially in length. Using Weibull++, the computed parameters for maximum likelihood are calculated to be:


 * $$\begin{align}

& {{{\hat{\mu }}}^{\prime }}= & 3.64 \\ & {{{\hat{\sigma }}}_}= & 0.18 \end{align}$$

For rank regression on $$X\ \ :$$


 * $$\begin{align}

& {{{\hat{\mu }}}^{\prime }}= & 3.64 \\ & {{{\hat{\sigma }}}_}= & 0.17 \end{align}$$

For rank regression on $$Y\ \ :$$


 * $$\begin{align}

& {{{\hat{\mu }}}^{\prime }}= & 3.64 \\ & {{{\hat{\sigma }}}_}= & 0.21 \end{align}$$