Background of probability distributions

Probabilities can be calculated for different distributions. You can calculate the probability density for continuous distributions (probability mass function for discrete distributions), cumulative functions, or inverse cumulative functions.

Probability distribution function

The probability distribution function shows areas of higher and lower probabilities for values of the random variable. For a normal distribution, for example, the highest value is in the middle of the distribution, whereas lower values are at the end of the distribution.

For continuous distributions, such as the normal distribution, the probability density function is calculated.

For discrete distributions, for example, Bernoulli, binomial, geometric, negative binomial, or Poisson, the probability mass function is calculated.

Cumulative distribution function

The cumulative distribution function calculates the cumulative probability according to the value that you specify for the variable.

Thus, you can determine the probability that an arbitrary observation of individuals is less than or equal to a specific value. For example, a cumulative distribution function can show the proportion of bushes in a timberland that have height measurements of 40 inches or less.

Inverse cumulative distribution function

The inverse cumulative distribution function calculates the value of the variable that is associated with a specific cumulative probability.

For example, as an electronic engineer, you want to determine the time by which specific parts of the electronic device fail. By using the inverse cumulative distribution function, you can determine the 90th percentile of the failure time distribution.