Contents
- Index
Bounds, Distribution
Certain distributions like the normal distribution and logistic distribution are unbounded. Values generated from these distributions range from -infinity to infinity.
Distributions like the lognormal distribution and gamma distribution have lower bounds. They range from this lower bound to infinity.
Distributions like the negative of the lognormal distribution and negative of the gamma distribution have upper bounds. They range from -infinity to this upper bound.
Finally distributions like the beta distribution have both upper and lower bounds. They range from the lower bound to the upper bound.
Bounded distributions can only transform values within the range of the distribution. If a spec limit or data point were outside the range of the distribution, it could not be transformed. The maximum likelihood method of fitting a distribution to a set of data assures the data is within the range of the distribution. The method of moments method of fitting a distribution to a set of data does not generally assure the data is within the range of the distribution. However, the method of moments approach has been modified, when possible, to reduce the number of moments matched to ensure the data is within the range of the distribution.
Neither approach ensures the spec limits are within the range of the distribution. Both approaches have been modified so that the user can specify a range of values that must be in the range of the selected distribution. This range can be specified using the Select Distribution to Fit Data dialog box. When the Find Best Distribution button is clicked in the Data window, the required range is automatically specified as at least 1 standard deviation beyond any spec limits. This assures the spec limits are within the range of the distribution and can be transformed.