Parameters
Definition
The numerical constants that define the specific shape of a distribution within its family. The normal distribution has two parameters (mean and variance); the Poisson has one (rate); the binomial has two (number of trials and success probability); the gamma has two (shape and rate).
- Role
- Fix the specific shape within a distribution family
- Normal distribution
- Mean and variance, 2 parameters
- Poisson distribution
- Rate, 1 parameter
- Binomial distribution
- Trials and success probability, 2 parameters
Common questions
Why does it matter that a distribution's parameters, not just its family, are specified in a forensic report?+
Two normal distributions with the same family but different means and variances describe very different populations, so citing 'normally distributed' without the parameter values leaves the statistical claim unverifiable and open to challenge on cross-examination.
How are parameters typically estimated from forensic sample data rather than assumed?+
Analysts calculate sample statistics, such as the sample mean and sample variance, from observed measurements and use them as estimates of the underlying population parameters, a step that should be distinguished clearly from a parameter value taken from prior literature.
Related terms
- Likelihood Ratio (LR)
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- 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,...
- Shape and Rate Parameters
- The two parameters of the gamma distribution. The shape parameter controls how peaked or spread the distribution is; the rate parameter (sometimes...