Naor's distribution
- Introduced by Moni Naor in 1992 to model skewed random variables.
- Characterized by a long tail, allowing a higher probability of extreme values than a Gaussian.
- Often used for variables that are bounded in range (for example, completion times or annual income).
Definition
Section titled “Definition”Naor’s distribution is a mathematical concept that describes the distribution of certain types of random variables. It was introduced by Moni Naor in 1992 as a way to model the distribution of random variables that have a skewed distribution.
Explanation
Section titled “Explanation”Naor’s distribution is used when the observed variable departs from the symmetric, short-tailed behavior of a Gaussian (bell curve). A key characteristic is a long tail, which implies a higher probability of extreme values compared with a Gaussian distribution. It is also frequently applied to variables that have a bounded range, so the model can account for both skewness and bounds on possible values.
Examples
Section titled “Examples”Task completion time
Section titled “Task completion time”If a person is given a task to complete in 10 minutes and they complete the task in exactly 10 minutes, that would be considered a “normal” completion time and represented by a Gaussian (bell curve) distribution. If the person takes significantly longer than 10 minutes, that is a “skewed” completion time; a Naor distribution would be used to model this skewed distribution and provide a more accurate representation of completion times.
Annual income
Section titled “Annual income”For most people, income falls within a certain range and may appear Gaussian. However, a small number of people may have income significantly higher or lower than average (for reasons such as winning the lottery, having a high-paying job, or financial hardship). A Naor distribution can model this skewed income distribution and accommodate the presence of extreme values.
Use cases
Section titled “Use cases”- Modeling skewed random variables where extreme values are more likely than under a Gaussian.
- Modeling variables that have a bounded range (for example, completion times or annual income).
Notes or pitfalls
Section titled “Notes or pitfalls”- Compared with a Gaussian distribution, Naor’s distribution has a long tail and therefore assigns a higher probability to extreme observations.
- It is particularly relevant when the variable is bounded and exhibits skewness.
Related terms
Section titled “Related terms”- Gaussian distribution (bell curve)