Compare Distributions

The Compare Distributions report lets you fit and compare different failure time distributions. Two lists appear:

Select a distribution for the response. Different distributions appear based on characteristics of the data. For details about which distributions are available, see Available Parametric Distributions.

Scale

Select a scale for the probability axis. The probability scale corresponds to the distribution listed to the left of the Scale button. Using this scale, the fitted model is represented by a line. Suppose that you fit a given distribution and then scale the axis using that distribution. If the points generally fall along a line, this indicates that the distribution provides a reasonable fit.

The default plot shows the nonparametric estimates (Kaplan-Meier-Turnbull) for the uncensored data values and their confidence intervals. The confidence intervals are indicated by horizontal blue lines.

Tip: To customize the plot of the nonparametric estimates, select File > Preferences > Platforms > Life Distribution and select one or more of the following preferences: Show Shaded Pointwise Intervals, Show Shaded Simultaneous Intervals, or Show Staircase Style Function.

By default, there is a panel at the top of the plot that displays times of right-censored observations.

Tip: To hide the panel that contains markers for right-censored observations, select File > Preferences > Platforms > Life Distribution and uncheck Show Markers for Right Censored Observations.

For each distribution that you select, the Compare Distributions report is updated to show the following:

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the estimated cumulative distribution curve, which appears on the probability plot

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a shaded region that indicates confidence intervals for the cumulative distribution

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a Distribution Profiler that shows the cumulative probability of failure for a given period of time

Figure 3.9 shows an example of the Compare Distributions report. The Logistic (yellow) and Exponential (magenta) distributions are shown. The plot is scaled using the Exponential distribution.

Figure 3.9 Compare Distributions Report and Distribution Profiler

Available Parametric Distributions

This section addresses the distributions available in the Compare Distributions report.

Note: Distributions for the Competing Cause report are covered in Available Distributions for Competing Cause Compare Distributions Reports.

The available distributions are listed and described in detail in Parametric Distributions. There are four major groupings of parametric distributions:

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Basic Failure-Time Distributions

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Threshold Distributions

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Defective Subpopulation Distributions

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Zero-Inflated Distributions

Tip: To restrict which distributions are available by default, select File > Preferences > Platforms > Life Distribution and uncheck the distributions that you do not want to appear. The distributions listed include the Threshold, Defective Subpopulation, Zero-Inflated, LogGenGamma, and GenGamma distributions. By default, all of the distributions are checked and available.

The rules that determine which distributions appear in the Compare Distributions panel depend on the particular implementation. As a general guide, distributions are available if they are not disabled in Preferences and if they are appropriate in the given situation.

Basic Failure-Time Distributions

The basic failure-time distributions are available whenever all failure times are positive. They include the following:

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