Shape and Rate Parameters
Definition
The two parameters of the gamma distribution. The shape parameter controls how peaked or spread the distribution is; the rate parameter (sometimes expressed as its inverse, the scale) controls the units. Together they allow the gamma to fit a wide range of right-skewed data.
- Distribution
- Gamma distribution
- Shape parameter role
- Controls peakedness and spread
- Rate parameter role
- Controls the units (or its inverse, scale)
- Parameter count
- Two
Common questions
Why does the gamma distribution need two parameters instead of one?+
A single parameter could not independently control both the overall shape of the skew and the scale of the values, so the gamma uses shape and rate together to fit a much wider range of right-skewed forensic data than a one-parameter model could.
What kind of forensic data typically gets modelled with a gamma distribution?+
Right-skewed measurements such as time intervals, waiting times between events, or certain concentration measurements are common candidates, since the gamma naturally accommodates values bounded at zero with a long right tail.
Related terms
- Likelihood Ratio (LR)
- The ratio of two conditional probabilities: the probability of the observed evidence given the prosecution's hypothesis (same source), divided by the probability...
- Parameters
- The numerical constants that define the specific shape of a distribution within its family. The normal distribution has two parameters (mean and...
- Probability Distribution
- A function that assigns probabilities to each possible value (or range of values) of a random variable. It fully characterises the uncertainty...
- Rate Parameter (Lambda)
- The single parameter of the Poisson distribution, equal to both the mean and the variance of the distribution. In forensic contexts lambda...
- Right Skew
- A distribution is right-skewed when its tail extends further to the right than to the left. Many forensic measurement quantities (trace concentrations,...