Difference Between Discrete and Continuous Distributions
Table of Contents
Discrete vs Continuous Distributions
The distribution of a variable is a description of the frequency of occurrence of each possible outcome. A function can be defined from the set of possible outcomes to the set of real numbers in such a way that ƒ(x) = P(X = x) (the probability of X being equal to x) for each possible outcome x. This particular function ƒ is called the probability mass/density function of the variable X. Now the probability mass function of X, in this particular example, can be written as ƒ(0) = 0.25, ƒ(1) = 0.5, and ƒ(2) = 0.25.
Also, a function called cumulative distribution function (F) can be defined from the set of real numbers to the set of real numbers as F(x) = P(X ≤ x) (the probability of X being less than or equal to x) for each possible outcome x. Now the probability density function of X, in this particular example, can be written as F(a) = 0, if a<0; F(a) = 0.25, if 0≤a<1; F(a) = 0.75, if 1≤a<2 and F(a) = 1, if a≥2.
What is a discrete distribution?
If the variable associated with the distribution is discrete, then such a distribution is called discrete. Such a distribution is specified by a probability mass function (ƒ). The example given above is an example of such a distribution since the variable X can have only a finite number of values. Common examples of discrete distributions are binomial distribution, Poisson distribution, Hyper-geometric distribution and multinomial distribution. As seen from the example, cumulative distribution function (F) is a step function and ∑ ƒ(x) = 1.
What is a continuous distribution?
If the variable associated with the distribution is continuous, then such a distribution is said to be continuous. Such a distribution is defined using a cumulative distribution function (F). Then it is observed that the density function ƒ(x) = dF(x)/dx and that ∫ƒ(x) dx = 1. Normal distribution, student t distribution, chi squared distribution, F distribution are common examples for continuous distributions.
What is the difference between discrete distribution and continuous distribution? •In discrete distributions, the variable associated with it is discrete, whereas in continuous distributions, the variable is continuous. •Continuous distributions are introduced using density functions, but discrete distributions are introduced using mass functions. •The frequency plot of a discrete distribution is not continuous, but it is continuous when the distribution is continuous. •The probability that a continuous variable will assume a particular value is zero, but it is not the case in discrete variables. |
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