This is a simple one: an even probability for all data values (Fig. 6.21). Not very
common for real data.
應用
一、概率密度函數和分布函數
分布函數是概率密度函數從負無窮到正無窮上的積分；
在坐標軸上，概率密度函數的函數值y表示落在x點上的概率為y；
分布函數的函數值y則表示x落在區間(-∞，+∞）上的概率。
二、均勻分布的概率密度函數
假設x服從[a,b]上的均勻分布，則x的概率密度函數如下
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Understanding Uniform Distribution
There are two types of uniform distributions: discrete and continuous. The possible results of rolling a die provide an example of a discrete uniform distribution: it is possible to roll a 1, 2, 3, 4, 5 or 6, but it is not possible to roll a 2.3, 4.7 or 5.5. Therefore, the roll of a die generates a discrete distribution with p = 1/6 for each outcome.
Some uniform distributions are continuous rather than discrete. An idealized random number generator would be considered a continuous uniform distribution. With this type of distribution, every variable has an equal opportunity of appearing, yet there are a continuous (or possibly infinite) number of points that can exist.
There are several other important continuous distributions, such as the normal distribution, chi-square, and Student's t-distribution. A uniform distribution with only two possible outcomes is a special case of the binomial distribution.
There are also several data generating or data analyzing functions associated with distributions to help understand the variables and their variance within a data set. These functions include probability density function, cumulative density and moment generating functions.
KEY TAKEAWAYS
- Uniform distributions are probability distributions with equally likely outcomes.
- There are two types of uniform distributions: discrete and continuous. In the former type of distribution, each outcome is discrete. In a continuous distribution, outcomes are continuous and infinite.
Visualizing Uniform Distributions
A distribution is a simple way to visualize a set of data, either as a graph or in a list of stating which random variables have lower or higher chances of happening. There are many different types of probability distributions, and the uniform distribution is perhaps the simplest of them all.
Under a uniform distribution, the set of variables all have the exact same possibility of happening. This distribution, when displayed as a bar or line graph, has the same height for each potential outcome. In this way, it can look like a rectangle and therefore is sometimes described as the rectangle distribution. If you think about the possibility of drawing a particular suit from a deck of playing cards, there is a random yet equal chance of pulling a hearts as there is for pulling a spade - that is, 1/4.
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