What Is Density Function?
A density function is a statistical function that graphs the probability of certain events. The most common density function is the bell-shaped density function of the normal density. Every probability distribution has two density curves.
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Types of Densisty Functions: Cumulative vs. Probability
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One type of density function is a probability density function (pdf). A pdf has the possible values of the function along the x-axis (the horizontal one) and the probability on the y-axis (the vertical one). For example, the pdf of height for adult males would be bell-shaped. It would peak at about 5 feet 10 inches tall and have tails out to about 4 feet 6 inches and 7 feet 6 inches tall.
A cumulative density function (cdf) has the same x-axis, but the y-axis is the probability of being at that point or lower.
Types of Density Function: Continuous or Discrete
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Both continuous and discrete variables have density functions. In the height example, the variable was continuous. An example of a discrete variable is the roll of a die---it can be 1, 2, 3, 4, 5, or 6, but nothing else. The pdf of the roll of a die would be a flat line at 1/6, because each number is equally likely. The cdf would look like a series of steps, at 1/6 for 1, 1/3 for 2 and so on up to 1 for 6, because every roll will be 6 or less.
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Significance
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The significance of density functions is that they allow you to tell a great deal about a probability distribution from a single graph. You can determine what the most common value is, what the most extreme values are and the rough probability of any value.
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