Statistics How To

< Hypothesis Testing < Pycke Test What is the Pycke Test? The Pycke test is a non-parametric statistical method used in circular statistics to assess the uniformity of angular data around a circle. In other words, it checks whether circular data—such as angles, directions, or times—is spread out evenly around a circle or if it … Read more

< Hypothesis Testing < Kuiper Test What is the Kuiper Test? Goodness-of-fit tests help us determine how well a theoretical distribution fits observed data. Among these tests, the Kuiper test holds is particularly useful when dealing with cyclical or periodic data. The Kuiper test, developed by Dutch mathematician Nicolaas Kuiper in 1960, is an adaptation … Read more

< List of Probability Distributions < Bivariate Poisson Distribution What is the Bivariate Poisson Distribution? The bivariate Poisson distribution (BPD), a special case of the bivariate Hermite distribution, is a way to count two types of events that may happen together or affect each other. It builds on the regular Poisson distribution, which counts one … Read more

Probability Distributions > Compound Probability Distribution What is a Compound Probability Distribution? A compound probability distribution has random variables drawn from a “compound” parametric distribution, where one or more of the distributions parameters (i.e. the mean) are taken from other probability distributions [1]. Compounding distributions make it easier to analyze and visualize data as a … Read more

Statistics Definitions > Variability What is Variability in Statistics? Variability, also called spread or dispersion, tells us how much a dataset is spread out. It can explain how much datasets differ, giving us a numerical way to compare datasets. The four main ways to describe variability in a data set are: range Interquartile range Variance … Read more

Statistics Definitions > Rician Distribution What is a Rice/Rician Distribution? A Rice or Rician distribution (also known as a Nakagami-n distribution) is one way to model the paths scattered signals take to a receiver. Specifically, this distribution models line-of-sight scatter — transmissions between two stations in view of each other that have an unobstructed path … Read more

Probability Distributions > Edgeworth series distribution What is the Edgeworth series distribution? The Edgeworth series distribution, introduced by Francis Ysidro Edgeworth in 1897, is a continuous probability distribution that approximates a non-normal probability distribution in terms of its cumulants and Hermite polynomials. It relates the probability density function (pdf) of a non-normal distribution to a … Read more

Probability Distributions > Wallenius’ Distribution What is Wallenius’ distribution? The Wallenius’ Distribution, more formally called the Wallenius’ noncentral hypergeometric distribution, is a distribution with biased sampling. It is usually described as an urn model without replacement and with bias. The distribution is named after Kenneth Ted Wallenius, who first described it in 1963 [1]. General … Read more

Probability Distributions > Rademacher distribution What is a Rademacher Distribution? The Rademacher distribution is a recoding of the Bernoulli distribution with two possible values {-1, 1}. It’s second moment (the variance) equals 1; all other moments equal 0 [1]. It is named after German-American mathematician Hans Rademacher and denoted Rad½. Like the Bernoulli, a random … Read more

Hypothesis Testing > Rejection Region   What is a Rejection Region? Watch the video for an overview of the rejection region, or read on below. Can’t see the video? Click here to watch it on YouTube. A rejection region, also called a critical region, is an area where the null hypothesis is rejected. If the … Read more