Statistics How To

Intro To Statistics > Statistical Assumptions Previous: Binomial Approximation Nearly all statistical tests make specific statistical assumptions about the data being analyzed. If the assumptions are not met, then the test will give questionable results and shouldn’t be used. The assumptions are often related to sample sizes and the nature of the distributions of the … Read more

Probability Distribution: List of Statistical Distributions > The Skellam distribution (also called the Poisson difference distribution) is a discrete probability distribution that shows differences between counts. It is derived from differences between Poisson random variables (i.e., two random variables that originate from a Poisson distribution) [1]. Although the distribution is usually used for independent random … Read more

Probability Distributions > The Gamma Poisson distribution (GaP) is a mixture model with two positive parameters, α and β. This hierarchical distribution is used to model a variety of data including failure rates, RNA-Sequencing data [1] and random distribution of micro-organisms in a food matrix [2]. When a Gamma distribution doesn’t fit data because the … Read more

Probability Distribution: List of Statistical Distributions > Johnson SU distribution What is the Johnson SU distribution? The Johnson SU distribution is an unbounded and continuous probability distribution. It is member of the Johnson system, a family of four probability distributions that also includes the lognormal distribution, the normal distribution, and the Johnson SB distribution. The … Read more

Probability Distributions > Extreme Value Distribution & the Extreme Value Theory Contents: What is an Extreme Value Distribution? Extreme Value Distribution Types I, II, and III The Generalized Extreme Value Distribution What is the Largest Extreme Value Distribution? What is an “Extreme Value?” Extreme Value Theory Comparison to CLT What is an Extreme Value Distribution? … Read more

Probability Distributions > What is the Exponential-Logarithmic Distribution? The exponential-logarithmic (EL) distribution is a log-series mixture distribution of exponential random variables, introduced by Tahmasbi and Rezaei in 2008 [1]. It is created when the rate parameter for the exponential distribution is randomized by the logarithmic distribution. The distribution is used to model decreasing failure or … Read more

Probability distributions > What are Multivariate Gamma Distributions? The Multivariate Gamma Distributions are generalizations of the univariate gamma distributions. Generally speaking, a random vector has a multivariate gamma distribution if it has gamma marginals [1]. There are dozens of different extensions of multivariate gamma distributions; some are defined by density functions, while others are defined … Read more

Probability Distributions > The half-Cauchy distribution is a continuous probability distribution derived from folding the standard Cauchy distribution on the origin (i.e., on the peak). This creates a version of the Cauchy distribution with only positive values. In other words, the half-Cauchy is a Cauchy distribution with a domain restricted to only positive values. In … Read more

Probability Distributions > The half-logistic distribution is a one parameter, continuous probability distribution created by folding the standard logistic distribution (this leads to its alternate name, the folded logistic distribution) [1]; It is equivalent to a logistic distribution with only positive values and a zero mean. This widely used classical distribution is popular for modeling … Read more

Statistics Definitions > What is a Scale Parameter? A scale parameter stretches or squeezes a graph. They are used with location parameters to determine the shape and location of a distribution. Scale Parameter’s Effect on Graphs The graph on the left has a scale parameter of 3; The graph on the right has a scale … Read more