Probability Mass Function vs Probability Measure

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A probability mass function (PMF) is specifically used for discrete distributions, such as the binomial distribution, while a probability density function (PDF) is used for continuous distributions like the Gaussian. The term 'probability measure' describes a function that assigns probabilities to events within a sample space, applicable to both discrete and continuous distributions. Although PMFs and probability measures are related, they are not the same; PMFs are a specific type of probability measure for discrete cases. Understanding these distinctions is crucial for proper application in statistical analysis.
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What is the difference between a probability mass function and a probability measure or are they just the same thing?

Thanks!
 
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Essentially the same. There might be subtle differences due to context.
 
blahblah8724 said:
What is the difference between a probability mass function and a probability measure or are they just the same thing?

Thanks!

The 'probability mass function' (PMF) applies to discrete distributions like the binomial. For continuous distributions like the Gaussian, the term 'probability density function' (PDF) applies. The term 'probability measure' refers to a function which maps from an event space to the interval [0,1] and can apply to either kind of distribution.
 
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