Probability Distributions in Excel

Use of a statistical function in Excel
The RAND function being used in Excel to generate a random number between 0 and 1. C.K.Taylor

Software is indispensable to the study and practice of statistics. The use of statistical software can be faster, more reliable, and give better estimates than the use of tables. One place where this is apparent is in the calculation of probabilities from a probability distribution. Rather than use a table for these types of calculations, we can quickly obtain accurate results by using functions in Excel.

The following lists the types of distributions that are programmed into Excel, along with some details of when they are useful.

List of Probability Distributions in Excel

  • Beta – a continuous random variable with beta distribution is defined on the closed interval [0, 1]. This type of distribution is useful for modeling random phenomena with outcomes that occur within a finite interval.
  • Binomial – this distribution is for a discrete random variable. We repeat independently a trial with constant probability of success a specified number of times, and count the number of successes.
  • Chi Square – this distribution arises as a special case of the gamma distribution. It is very useful in constructing confidence intervals about a population variance, and for the goodness of fit test.
  • Exponential - a random variable with an exponential distribution is continuous and models the wait time of a Poisson process until a single change occurs.
  • F-Distribution - this distribution is used for one factor analysis of variance (ANOVA).
  • Gamma - a random variable with an exponential distribution is continuous and models the wait time of a Poisson process until a single change occurs.
  • Hypergeometric - this distribution is for a discrete random variable that counts the number of successes when sampling is done without replacement from a finite population.
  • Log-Normal – a random variable has a log-normal distribution if the natural logarithm of the random variable is normally distribution. This distribution is sometimes referred to as the Galton distribution.
  • Normal – this is perhaps the most commonly used distribution in an introductory statistics class. It is the distribution associated to the curve popularly known as the bell curve. Due to the Central Limit Theorem, this distribution is important for many theoretical and practical reasons.
  • Poisson – this discrete distribution gives the probability of a specified number of discrete changes to occur in a continuum, provided that these changes are independent from one another.
  • Student’s T –Distribution – t-distributions have many similar features to the standard normal distribution. This type of distribution allows for greater variability than the standard normal distribution, which accounts for the extra weight in the two tails.
  • Weibull Distribution - this distribution is used to predict the time until failure when the failure rate is proportional to a power of time. Thus it models situations in which components age and wear down.

Of course there are an infinite number of probability distributions.

If the one that we want is not in the list, then we do have some options. As long as we know the probability mass function or the probability density function, then we can program it into Excel.