Individual Distribution Identification

Data Fitted with 14 Distributions and 2 Transformations - Table of Percentiles

  

The percentile for P percent is the value below which you expect P percent of the population values to fall. Sometimes it can be difficult to determine the best distribution based on the probability plot and goodness-of-fit measures. Use the table of percentiles for several selected distributions to see how your conclusions change depending on the distribution chosen.

·    If several distributions provide a reasonable fit to the data, and they also provide similar conclusions, then it probably does not matter which distribution you choose.

·    On the other hand, if your conclusions differ depending on the distribution you chose, you can report the most conservative conclusion or collect more information.

Example Output

Table of Percentiles

 

                                               Standard

Distribution             Percent  Percentiles     Error   95.0% CI

Normal                         5      46.2344   0.60235  45.1  47.4

Box-Cox Transformation         5       0.0000   0.00000   0.0   0.0

Lognormal                      5      46.4243   0.54293  45.4  47.5

3-Parameter Lognormal          5      47.2553   0.29629  46.7  47.8

Exponential                    5       2.6048   0.36837   2.0   3.4

2-Parameter Exponential        5      46.9272   0.02947  46.9  47.0

Weibull                        5      44.1343   0.93755  42.3  46.0

3-Parameter Weibull            5      47.2723   0.17351  46.9  47.6

Smallest Extreme Value         5      43.4339   1.11157  41.3  45.6

Largest Extreme Value          5      47.1229   0.35058  46.4  47.8

Gamma                          5      46.4076   0.55357  45.3  47.5

3-Parameter Gamma              5      47.2157   0.24845  46.7  47.7

Logistic                       5      45.8759   0.65347  44.6  47.2

Loglogistic                    5      46.0949   0.59123  45.0  47.3

3-Parameter Loglogistic        5      47.2549   0.34441  46.6  47.9

Johnson Transformation         5      -1.5714   0.21197  -2.0  -1.2

Interpretation

For 3-parameter Weibull and largest extreme value, two of the better fitting distributions, you can expect 5% of the calcium data to fall below 47.2723 and 47.1229. Depending on the context, this additional data may help you select the better distribution. For instance, if one value provided a larger margin of safety in your decision making you might select that distribution.

The values for the Box-Cox (0.0000) and Johnson (-1.5714) transformations are based on the transformed values rather than the raw data making the percentiles difficult to interpret.