Probability Distribution
Definition
A function that assigns probabilities to each possible value (or range of values) of a random variable. It fully characterises the uncertainty about that variable before data are observed.
- Types
- Discrete, continuous
- Common examples
- Binomial, normal, Poisson
- Key property
- Sums or integrates to 1
- Describes
- Uncertainty before data are observed
Common questions
Why does the choice of probability distribution matter in forensic statistics?+
Assuming the wrong distribution for a random variable, such as treating a count as normal when it is actually Poisson, distorts confidence intervals and significance tests, which can overstate or understate the strength of evidence presented in court.
What is the difference between a probability distribution and a likelihood function?+
A probability distribution describes how likely different outcomes are for fixed parameters, while a likelihood function fixes the observed data and asks how plausible different parameter values are, the reverse framing used when estimating quantities like allele frequencies from a sample.
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...
- 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...