Parametric CDF

Distribution Analyses

Parametric CDF

You can fit the normal, lognormal, exponential, and Weibull distributions to your data. You specify the family of distributions either in the cumulative distribution options dialog or from the Parametric CDF Estimation dialog after choosing Curves:Parametric CDF from the menu.

Figure 38.29: Parametric CDF Dialog

For the normal distribution, you can specify your own $\mu$ and $\sigma$ parameters from the Fit Parametric menu. Otherwise, you can use the sample mean and standard deviation as estimates for $\mu$ and $\sigma$ by selecting Fit Parametric:Normal in the cumulative distribution options dialog or by choosing Distribution:Normal and Method:Sample Estimates/MLE in the Parametric CDF Estimation dialog.

For the lognormal, exponential, and Weibull distributions, you can specify your own threshold parameter $\theta$ and have the remaining parameters estimated by the maximum- likelihood method, or you can specify all the distribution parameters in the Parametric CDF Estimation dialog. Otherwise, you can have the threshold parameter set to 0 and the remaining parameters estimated by the maximum-likelihood method. To do this, select Lognormal, Exponential, or Weibull in the Cumulative Distribution Output dialog or choose Method:Sample Estimates/MLE and Parameter:MLE, Theta:0 in the Parametric CDF Estimation dialog.

If you select a Weight variable, only normal CDF can be created. For Method:Sample Estimates/MLE, ${{\overline y_{w}}}$ and s_w are used to display the cumulative distribution function with vardef=WDF/WGT; ${{\overline y_{w}}}$ and s_a are used with vardef=DF/N. For Method:Specification, the values in the entry fields Mean/Theta and Sigma are used to display the cumulative distribution function with vardef=WDF/WGT; the values of Mean/Theta and Sigma/ ${\sqrt{{\overline w}}}$ are used with vardef=DF/N.

Figure 38.30 displays a normal distribution function with $\mu$ = 58.4333 (the sample mean) and $\sigma$ = 8.2807 (the sample standard deviation); it also displays a lognormal distribution function with $\theta$ = 30 and $\sigma$ and $\zeta$ estimated by the MLE.

Figure 38.30: Parametric CDF

Use sliders to change the CDF estimate. When MLE is used for the lognormal, exponential, and Weibull distributions, changing the value of $\theta$ in the slider also causes the remaining parameters to be estimated by the MLE for the new $\theta$ .

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