Cumulative Distribution Function
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Cumulative Distribution Function |
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The cumulative distribution function, F(x),
is usually estimated from the median rank, but other estimates such as the mean rank and
the Kaplan-Meier product limit estimator are also used. The
median rank estimate for F(x) is
where O i is the modified order of failure of the ith data point.A modified order of failure is only needed if censored data is involved; if not the original order of failure, i, is equivalent to the modified order of failure. The logic for a modified order of failure is as follows. Consider three items; the first was tested for 3 hours and the test was stopped without failure, the second item was tested and failed after 4 hours, and the third item was tested and failed after 4.5 hours. For this data set the failure order is unclear. The first item could have been either the first failure, the second failure or the third failure; thus it is not certain that the first item to fail, the second item, is the first ordered failure. The modified order of failure is computed from the expression where I iIi is the increment for the ith failure, and is computed from the expressionwhere: n is the total number of points in the data set, both
censored and uncensored, Example Solution
Example
Solution
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