*The Business Professor*, updated September 10, 2019, last accessed October 20, 2020, https://thebusinessprofessor.com/lesson/uniform-distribution-definition/.

### Uniform Distribution Definition

Uniform distribution is also called rectangular distribution, it is a term commonly used in statistics and probability theory to depict the equal probability of all outcomes in a family. Uniform Distribution refers to the equal distribution of outcomes or uniform probabilities assigned to outcomes in a likely occurrence. In a sample space, when all outcomes have the same probability, uniform distribution has come to play. A good example of uniform distribution is a coin that when it is tossed, it can either get a head or tail, both head and tail are outcomes with equal probability.

### A Little More on What is a Uniform Distribution

In a uniform distribution, all outcomes in a probability distribution are the same. Uniform distribution is categorized into two, they are;

Discrete uniform distribution and Continuous uniform distribution.

For example, a die has six figures: 1, 2, 3, 4, 5, and 6. A die is an example of a discrete uniform distribution because when rolling a die, you will probably roll any of the figures as combination and not figures that do not appear on the die such as 7.8, 8.9 and so on. A continuous uniform distribution can be exemplified using an object that generates numbers randomly in which every number has the probability of appearing continuously.

Here are the major things to not about uniform distribution;

- In a uniform distribution, all outcomes have equal likely outcomes.
- For instance, a head and tail are the two outcomes that a coin can give when it is tossed. These outcomes have equal probability.
- Discrete and continuous uniform distributions are the two classifications of uniform distribution.

### Visualizing Uniform Distributions

There are many types of probability distributions, uniform distribution is one of them. In uniform distribution, all outcomes are equally likely. When a set of variables have an equal possibility of happening, this is an instance of uniform distribution. When plotted on a graph, a uniform distribution takes the form of a rectangle which is why it is also referred to as a rectangular distribution.

### References for “**Uniform Distribution****”**

https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)

https://www.investopedia.com › Business › Business Leaders › Math & Statistics

https://www.statisticshowto.datasciencecentral.com/uniform-distribution/

### Academic research for “**Uniform Distribution****”**

** **Random generation of combinatorial structures from a **uniform distribution**, **Jerrum, M. R., Valiant, L. G., & Vazirani, V. V. (1986). Random generation of combinatorial structures from a uniform distribution. ***Theoretical Computer Science***, ***43***, 169-188.**

### Characterizations of uniform and exponential **distributions**, **Too, Y. H., & Lin, G. D. (1989). Characterizations of uniform and exponential distributions. ***Statistics & Probability Letters***, ***7***(5), 357-359.**

*Statistics & Probability Letters*

*7*

### A characterization of **rectangular distributions**, **Terrell, G. R. (1983). A characterization of rectangular distributions. ***The Annals of Probability***, ***11***(3), 823-826.**** **

*The Annals of Probability*

*11*

### The **uniform distribution**: A rigorous justification for its use in robustness analysis, **Barmish, B. R., & Lagoa, C. M. (1997). The uniform distribution: A rigorous justification for its use in robustness analysis. ***Mathematics of Control, Signals and Systems***, ***10***(3), 203-222.**** **

*Mathematics of Control, Signals and Systems*

*10*

### An efficient membership-query algorithm for learning DNF with respect to the **uniform distribution**, **Jackson, J. C. (1997). An efficient membership-query algorithm for learning DNF with respect to the uniform distribution. ***Journal of Computer and System Sciences***, ***55***(3), 414-440.**

*Journal of Computer and System Sciences*

*55*

**Uniform distribution **of Heegner points, **Vatsal, V. (2002). Uniform distribution of Heegner points. ***Inventiones mathematicae***, ***148***(1), 1-46.**

*Inventiones mathematicae*

*148*

**Uniform distribution **of sequences of integers, **Niven, I. (1961). Uniform distribution of sequences of integers. ***Transactions of the American Mathematical Society***, ***98***(1), 52-61.**

*Transactions of the American Mathematical Society*

*98*

### An O (nlog log n) learning algorithm for DNF under the **uniform distribution**, **Mansour, Y. (1995). An O (nlog log n) learning algorithm for DNF under the uniform distribution. ***Journal of Computer and System Sciences***, ***50***(3), 543-550.**

*Journal of Computer and System Sciences*

*50*