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Parametric Estimate - <Distribution Name> (one report appears for each distribution that you select in the Compare Distributions report)
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The Model Comparisons report provides the AICc, -2*LogLikelihood, and BIC statistics for each fitted distribution. Smaller values of each of these statistics indicate a better fit. For more details about these statistics, see Likelihood, AICc, and BIC in the Fitting Linear Models book.
Initially, the rows are sorted by AICc. To change the statistic used to sort the report, select Comparison Criterion from the Life Distribution red triangle menu. See Life Distribution Report Options for details about this option.
Simultaneous 95% confidence intervals. You can change the confidence level by selecting Change Confidence Level from the report options. See Nair (1984) and Meeker and Escobar (1998).
See Nonparametric Fit for more information about nonparametric estimates.
Displays a window for each factor enabling you to enter a specific value for the factor’s current setting, to lock that setting, and to control aspects of the grid. For details, see Reset Factor Grid in the Profilers book.
Provides a menu that consists of several options. For details, see Factor Settings in the Profilers book.
Opens a report where you can specify the value of parameters. Enter your fixed parameter values, select the appropriate check box, and then click Update. JMP re-estimates the other parameters, covariances, and profilers based on the new parameters, and shows them in the Fix Parameter report. A distribution profiler of the unconstrained model is shown below the distribution profiler for the fixed parameter model. For an example in a competing cause situation, see Specify a Fixed Parameter Model as a Distribution for a Cause.
For the Weibull distribution, the Fix Parameter option lets you select the Weibayes method. For an example, see Weibayes Estimates. The Weibayes option is not available for interval-censored data.
Performs Bayesian estimation of parameters for certain distributions based on three methods of specifying prior distributions (Location and Scale Priors, Quantile and Parameter Priors, and Failure Probability Priors). See Bayesian Estimation - <Distribution Name>. This option is available only for the following distributions: Lognormal, Weibull, Loglogistic, Fréchet, Normal, SEV, Logistic, LEV.
Provides calculators that enable you to predict failure probabilities, survival probabilities, and quantiles for specific time and failure probability values. Each calculated quantity includes confidence intervals, which can be two-sided or one-sided (in either direction). Two reports appear: Estimate Probability and Estimate Quantile. See Custom Estimation.
Provides a calculator that enables you to estimate the mean remaining life of a unit. In the Mean Remaining Life Calculator, enter a Time and press Enter to see the estimate. Click the plus sign to enter additional times. This calculator is available for the following distributions: Lognormal, Weibull, Loglogistic, Fréchet, Normal, SEV, Logistic, LEV, and Exponential.
For certain distributions, the platform fits Bayesian models. This is done using a Markov Chain Monte Carlo (MCMC) algorithm. More specifically, Bayesian estimation uses an independence chain sampler variation of the Metropolis-Hastings algorithm. See Robert and Casella (2004).
From the Parametric Estimate - <Distribution Name> report outline, select Bayesian Estimates. This opens an outline called Bayesian Estimation - <Distribution Name>. The initial report is a control panel where you can specify the parameters for the priors and control aspects of the simulation.
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Enables you to specify hyperparameters for prior distributions on generic parameters (location and scale parameters). Select the Prior Distribution red triangle menu to select a distribution for each parameter. You can enter new values for the hyperparameters of the priors. The initial values that are provided are estimates consistent with the MLEs. For details, see Prior Distributions for Bayesian Estimation.
Enables you to specify prior information about a quantile and the scale parameter (or Weibull β if the parametric fit is Weibull). The quantile is defined by the value next to Probability. The default Probability value is 0.10, but you can specify a value that corresponds to the quantile of interest. Specify information about the prior information in terms of Lower and Upper 99% limits on the range of each prior distribution. See Meeker and Escobar (1998). The initial values that are provided are estimates consistent with the MLEs. For details, see Prior Distributions for Bayesian Estimation.
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The values shown in the Distribution Profiler, at a given time t, are calculated as follows:
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The plot and confidence limits shown in the Quantile Profiler are obtained in a similar fashion. For a given Probability value p, the quantiles corresponding to p are calculated from the distributions associated with the posterior parameter values.
In a zero-failure situation, no units fail. All observations are right censored. If you have zero-failure data, it is possible to conduct either Bayesian estimation or Weibayes inference. See Weibayes Report.
Note: By default, zero-failure data is analyzed using the Weibayes method. If you want to conduct a broader Bayesian analysis on zero-failure data, select File > Preferences > Platforms > Life Distribution and uncheck Weibayes Only for Zero Failure Data.
The Custom Estimation option produces two reports: Estimate Probability and Estimate Quantile. The Estimate Probability report contains a calculator that enables you to predict failure and survival probabilities for specific time values. The Estimate Quantile report contains a calculator that enables you to predict quantiles for specific failure probability values. Both Wald-based and likelihood-based confidence intervals appear for each estimated quantity. The confidence level for these intervals is determined by the Change Confidence Level option in the Life Distribution red triangle menu.
In the Estimate Probability calculator, enter a value for Time. Press Enter to see the estimates of failure probabilities, survival probabilities, and corresponding confidence intervals. To calculate multiple probability estimates, click the plus sign, enter another Time value in the box, and press Enter. Click the minus sign to remove the last entry.
In the Estimate Quantile report, enter a value for Failure Probability. Press Enter to see the quantile estimates and corresponding confidence intervals. To calculate multiple quantile estimates, click the plus sign, enter another Failure Probability value in the box, and press Enter. Click the minus sign to remove the last entry.