Hazard and density estimates for Nonparametric Distribution Analysis (Arbitrary Censoring)

Hazard estimates – actuarial estimation method

The hazard function provides a measure of the likelihood of failure as a function of how long a unit has survived (the instantaneous failure rate at a particular time, t).

Although the nonparametric hazard function is not dependent on any specific distribution, you can use it to help determine which distribution might be appropriate for modeling the data if you decide to use parametric estimation methods. Select a distribution that has a hazard function that resembles the nonparametric hazard function.

Example output

Hazards and Densities Hazard Standard Density Standard Time Estimates Error Estimates Error 10000 0.0000000 * 0.0000000 * 25000 0.0000003 0.0000002 0.0000003 0.0000002 35000 0.0000011 0.0000003 0.0000010 0.0000003 45000 0.0000033 0.0000006 0.0000032 0.0000005 55000 0.0000114 0.0000011 0.0000103 0.0000009 65000 0.0000223 0.0000017 0.0000171 0.0000012 75000 0.0000447 0.0000027 0.0000249 0.0000013 85000 0.0000733 0.0000044 0.0000232 0.0000013

Interpretation

For the new muffler data, the likelihood of failure is 10.36 (0.0000114/0.0000011) times greater for the new type of mufflers at 55,000 miles than it is at 35,000 miles.

Density estimates – actuarial estimation method

The density estimates describe the distribution of failure times and provide a measure of the likelihood that a product fails at particular times.

Although the nonparametric density function is not dependent on any specific distribution, you can use it to help determine which distribution might be appropriate for modeling the data if you decide to use a parametric estimation methods. Select a distribution that has a density function that resembles the nonparametric density function.

Example output

Hazards and Densities Hazard Standard Density Standard Time Estimates Error Estimates Error 10000 0.0000000 * 0.0000000 * 25000 0.0000003 0.0000002 0.0000003 0.0000002 35000 0.0000011 0.0000003 0.0000010 0.0000003 45000 0.0000033 0.0000006 0.0000032 0.0000005 55000 0.0000114 0.0000011 0.0000103 0.0000009 65000 0.0000223 0.0000017 0.0000171 0.0000012 75000 0.0000447 0.0000027 0.0000249 0.0000013 85000 0.0000733 0.0000044 0.0000232 0.0000013

Interpretation

For the new muffler data, the likelihood of failure is 10.3 (0.0000103/0.0000010) times greater for the new type of mufflers at 55,000 miles than it is at 35,000 miles.

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