Distribution Analyses |

*Parametric density estimation* assumes that the data are from a known family of distributions, such as the normal, lognormal, exponential, and Weibull. After choosing **Curves:Parametric Density** from the menu, you specify the family of distributions in the **Parametric Density Estimation** dialog, as shown in Figure 38.23.

**Figure 38.23:** Parametric Density Dialog

The default uses a normal distribution with the sample mean and standard deviation as estimates for and .You can also specify your own and parameters for the normal distribution by choosing **Method:Specification** in the dialog.

For the lognormal, exponential, and Weibull distributions, you can specify your own threshold parameter in the **Parameter:MLE, Theta** entry field and have the remaining parameters estimated by the maximum-likelihood estimates (MLE) by choosing **Method:Sample Estimates/MLE**. Otherwise, you can specify all the parameters in the **Specification** fields and choose **Method:Specification** in the dialog.

If you select a **Weight** variable, only normal density can be created. For **Method:Sample Estimates/MLE**, and *s*_{w} are used to display the density with vardef=**WDF/WGT**; 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 density with vardef=**WDF/WGT**; the values of **Mean/Theta** and **Sigma**/are used with vardef=**DF/N**.

Figure 38.24 displays a normal density estimate with (the sample mean) and (the sample standard deviation). It also displays a lognormal density estimate with and with and estimated by the MLE.

**Figure 38.24:** Parametric Density Estimation

The **Mode** is the point with the largest estimated density. Use sliders in the table to change the density estimate. When MLE is used for the lognormal, exponential, and Weibull distributions, changing the value of in the **Mean/Theta** slider also causes the remaining parameters to be estimated by the MLE for the new .

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