Statistics How To

Probability Distributions > Helmert’s Distribution What is Helmert’s distribution? Helmert’s distribution is another name for the chi-square distribution. It’s named after F.R. Helmert, who proved the general reproductive property of chi-square distributions [1]. Helmert’s most noted contribution was establishing that if we have a set of independent, normally distributed random variables, the sum of the squared … Read more

Statistics Definitions > Average (Mean) Deviation Contents: What is average deviation? How to find average deviation Workaround to avoid the zero problem Mean deviation for a frequency table Absolute Deviation vs Average Deviation Standard Deviation vs. Average Deviation What is average deviation? Deviation measures the difference between an observed value and the mean value of … Read more

Descriptive Statistics > Symmetric Distribution What is a symmetric distribution? A symmetric distribution is a type of distribution where the left side of the distribution mirrors the right side. A symmetric distribution is never skewed . In contrast, an asymmetric distribution is one with left and right portions that are not mirror images. The normal … Read more

Probability Distributions > Beta-Binomial Distribution What is the beta-binomial distribution?   The beta-binomial distribution is a discrete probability distribution that uses the beta distribution as a prior distribution for the probability of success in a binomial experiment. While the binomial distribution has fixed probabilities, the beta-binomial probabilities can vary from trial to trial, which makes … Read more

Probability and Statistics > Contents: What is Bayesian Statistics? Bayesian vs. Frequentist Important Concepts in Bayesian Statistics Related Articles 1. What is Bayesian Statistics? Bayesian statistics, an alternative to “classical” statistics, involves conditional probabilities, or the probability of one event given that another event has already happened. It is based on Bayes’ theorem and can … Read more

Bayesian Statistics and Probability > Prior distribution What is a prior distribution? A prior distribution, a key part of Bayesian inference, represents your belief about the true value of a parameter, in essence it is your “best guess.” It can be thought of as the process of assigning a prior probability distribution to a parameter, … Read more

Statistics Definitions > Interval Estimate What is an Interval Estimate?   An interval estimate is a range of values for a parameter. For example, you might think that the mean of a data set falls somewhere between 10 and 100 (10 < μ < 100). A related term is a point estimate, which is an … Read more

Probability > Posterior Probability & the Posterior Distribution What is Posterior Probability?   Posterior probability is the conditional probability an event will happen after all evidence or background information has been taken into account. To put that another way: if we know the conditional and unconditional probabilities of one event in advance, we can calculate … Read more

Sampling > Sampling with replacement / Sampling without replacement What is sampling with and without replacement? Sampling without replacement is where items are chosen randomly, and once an observation is chosen it cannot be chosen again. On the other hand, when you sample with replacement, you also choose randomly but an item can be chosen … Read more

Probability Distributions > Generalized Error Distribution / Generalized Normal What is a Generalized Error Distribution? The generalized normal distribution, sometimes called the generalized error distribution or Kapetyn distribution, is a symmetric distribution family commonly used in mathematical modeling. They are particularly useful when errors — the difference between expected and observed values — do not … Read more