PDF vs CDF vs PMF – Comparison & Differences

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Alisha John

PDF and CDF and CDF are theories or concepts that are highly useful in different subjects. The full name of the PDF is the probability density function that we employ in a continuous random variable. On the other hand, PMF is the short key of the probability mass function.

Main Difference

PMF uses discrete random variables. On the other hand, CDF, the full name, is a cumulative distribution function that occurs in measurable subsets. Moreover, many people do not know PDF, CDF, and PMF theories. In detail, let us discuss the main differences between PDF, CDF, and PMF.

What is PDF?

PDF is a theory, and its full name is the probability Density function. The PDF uses a continuous random variable approach. Moreover, it specifies the probability in a specific limit of values. In the PDF, a variable equals the matter we take.

Furthermore, for the representation of the possibility with areas, users use PDF. It tells the importance of probability to fill the weight. It is the most reliable theory, and it relates to other concepts. In addition, PDF is the derivative of CDF.

What is CDF?

CDF is the abbreviation of Cumulative Distribution Function. Mathematicians use it to calculate the sum of probabilities from 0,1,2,3……….. X values. Its graphical form is quite different from the graphic form of the probability density function(PDF). CDF helps solve most of the binomial functions. Calculators also assist in directly calculating the CDF value.

What is PMF?

PMF is the abbreviation of Probability Mass Function. It is the most efficient method to calculate the probability of a binomial equation. This probability is useful to check whether either variable is equal or not. PMF measures the possible values of random variables in multinomial equalities. Its mathematical form is:


Key Differences – PDF, CDF, and PMF

  1. PDF is a binomial, CDF is cumulative, and PMF is a probability mass function.
  2. PDF measures continuous variables, CDF random variables, and CMF measure probability functions.
  3. PDF reflects probability density, while CDF and PMF refer to just probability.
  4. PDF is a monomial, PMF is a binomial, and CDF is a multinomial function.
  5. The Histogram of PDF is quite different from that of CDF and PMF.
  6. PDF performs integration functions, while CDF and PMF give the solutions of proportion, counting, and sum.

Comparison table between PDF, CDF, and PMF

PDF CDF PMF                
It is a probability density function It is a cumulative distribution function It is a probability mass function
Measures continuous variables Measures random variables Find probability functions
Solve monomial Solve binomial Solve Multinomial
Discontinuous histogram Continuous histogram Discrete Histogram


In a nutshell, we can say that PDF, CDF, and PMF differ in various aspects. They serve different functions in the world of mathematics.